From making 2D line plots to making 3D surface plots: How to preserve my current workflow?
You are now following this question
- You will see updates in your followed content feed.
- You may receive emails, depending on your communication preferences.
An Error Occurred
Unable to complete the action because of changes made to the page. Reload the page to see its updated state.
Show older comments
0 votes
Hi there!
Below, I think the explanation, originally a comment by me, is more clear, so I am posting it here as the question.
Just to describe my workflow a bit more clearly: I loop through beta and, for each beta, I calculate values of F, a scalar-valued function, for all alpha = linspace(0, 2pi, 1001). I am only looping through beta, not alpha, which I really like. (I notice that nested loops can cause the code to take much longer to run.) I might choose 10 or 11 evenly spaced values of beta to loop through, using linspace( ).
Then, I made nice line plots, going from subplots to tiled layouts, which seems to be advantageous; e.g. global title, global colorbar, etc. are made easy using tiledLayout rather than with subplot. In my 2D line plots, each tile would have the 11 curves, with alpha being the independent variable, and I use colors from a colormap to show the variation in beta. This figure of 6 tiles, I think, is really pretty -- and communicative.
Now, instead of 2D line plots, I want to present this exact same information using 3D surface plots, just to compare and see which figure is more communicative. However, since my functions that I am plotting are scalar-valued functions, I am getting the error that my functions need to be matrices. By the way, I have plenty of vectors expressed as linear combinations of basis vectors, but the final functions to be plotted are all scalar-valued, gotten from using dot products.
So, as of now, I can basically write a poor man's version of a code that gives the surface plots (very pretty), but this is not good and systematic:
- I would like to continue looping through beta;
- To keep things organized and de-cluttered, I would like to continue calling my functions which are stored in separate files;
- For doing careful mathematics, I would like to continue expressing vectors as linear combinations of basis vectors; and
- I would like to keep all the functions to be plotted scalar-valued.
It seems if in the beginning of my surface-plotting code I define a meshgrid [Alpha,Beta] = meshgrid(alpha,beta), and use the variables Alpha and Beta as inputs, then I start running into issues with arrays having incompatible sizes. I have one current guess at a solution, as of now: Maybe define my functions locally in the same file as my surface-plotting code, rather than call them from another separate file? I would rather not do this, because my intuition is that my errors should be easy enough to fix.
I look forward to hearing from you.
Thanks for your time!
Accepted Answer
Star Strider
on 2 Jan 2025
Theree is not enough information proviided to determine what the problem is. If ‘i’ and ‘j’ are scalars, or matrices conformable under matrix multiplication with ‘Alpha’ and ‘Beta’ (that have the same sizes), your code should work.
The problem is not in the quoted code.
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
●
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.0240
j = rand
j = 0.1758
vx = cos(Alpha) * i
vx = 100×20
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
0.0240 0.0237 0.0227 0.0211 0.0189 0.0163 0.0131 0.0096 0.0059 0.0020 -0.0020 -0.0059 -0.0096 -0.0131 -0.0163 -0.0189 -0.0211 -0.0227 -0.0237 -0.0240
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = sin(Beta) * j
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177 0.0177
0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353 0.0353
0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524 0.0524
0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691 0.0691
0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850 0.0850
0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001 0.1001
0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142 0.1142
0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271 0.1271
0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387 0.1387
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
.
29 Comments
Hi Star Strider!
Let's say the basis vectors are rotating basis vectors:
ip = cos(theta)*i + sin(theta)*j
jp = -sin(theta)*i + cos(theta)*j, and
kp = k = [0,0,1].
I am using the basis vectors ip and jp.
So, at angle theta = 0, ip = (1,0,0) and jp = (0,1,0).
First, ‘i’ and ‘j’ do not appear to add anything, so just delete them. I cannot figure out how you define the third dimension of ‘ip’, ‘jp’ and ‘kp’.
If you want to define them such that:
So, at angle theta = 0, ip = (1,0,0) and jp = (0,1,0).
you will need to do something like this —
ip = @(theta) [ cos(theta) sin(theta) something_else]
jp = @(theta) [-sin(theta) cos(theta) something_else]
kp = @(theta) [something something someething_else]
If ‘theta’ is a column vector, that should work.
Beyond that, I am completely lost.
.
Hi Star Strider!
Yes the third coordinate of ip and jp is zero; my problem is quasi-2D.
The issue is, say I have this
velocity = vx * ip + vy * jp,
where vx = cos(beta)*sin(alpha),
and vy is something similar.
The surface plot will be against beta and alpha, so I write
beta = linspace(0,pi,20)
alpha = (0,pi/2,100).
But now, vx * ip gives the error that arrays are incompatible.
This is getting murkier rather than clearer —
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.2010
j = rand
j = 0.9653
vx = cos(Beta) .* sin(Alpha)
vx = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = -sin(Beta) .* cos(Alpha)
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954 0.0995 0.1008
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898 0.1979 0.2006
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822 0.2943 0.2984
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718 0.3878 0.3931
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576 0.4773 0.4839
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388 0.5619 0.5696
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144 0.6407 0.6496
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838 0.7131 0.7230
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462 0.7782 0.7889
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
ip = @(theta) [ cos(theta(:)) sin(theta(:)) 0]
ip = function_handle with value:
@(theta)[cos(theta(:)),sin(theta(:)),0]
jp = @(theta) [-sin(theta(:)) cos(theta(:)) 0]
jp = function_handle with value:
@(theta)[-sin(theta(:)),cos(theta(:)),0]
kp = @(theta) [0 0 1]
kp = function_handle with value:
@(theta)[0,0,1]
velocity = vx * ip(theta) + vy * jp(theta)
Unrecognized function or variable 'theta'.
% where vx = cos(beta)*sin(alpha),
%
% and vy is something similar.
%
% The surface plot will be against beta and alpha, so I write
beta = linspace(0,pi,20)
alpha = [0,pi/2,100]
vx_times_ip = vx .* ip(theta)
.
Sorry for the late response: I think I’ll loop through Beta?
Set theta = 0, since my model is invariant to changes in theta.
Perhaps —
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
theta = zeros(size(beta));
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.2369
j = rand
j = 0.3853
vx = cos(Beta) .* sin(Alpha)
vx = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = -sin(Beta) .* cos(Alpha)
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954 0.0995 0.1008
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898 0.1979 0.2006
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822 0.2943 0.2984
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718 0.3878 0.3931
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576 0.4773 0.4839
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388 0.5619 0.5696
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144 0.6407 0.6496
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838 0.7131 0.7230
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462 0.7782 0.7889
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
ip = @(theta) [ cos(theta(:)) sin(theta(:)) zeros(size(theta(:)))]
ip = function_handle with value:
@(theta)[cos(theta(:)),sin(theta(:)),zeros(size(theta(:)))]
jp = @(theta) [-sin(theta(:)) cos(theta(:)) zeros(size(theta(:)))]
jp = function_handle with value:
@(theta)[-sin(theta(:)),cos(theta(:)),zeros(size(theta(:)))]
kp = @(theta) [zeros(size(theta(:))) zeros(size(theta(:))) ones(size(theta(:)))]
kp = function_handle with value:
@(theta)[zeros(size(theta(:))),zeros(size(theta(:))),ones(size(theta(:)))]
ipm = ip(theta)
ipm = 100×3
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
jpm = jp(theta)
jpm = 100×3
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
for k = 1:3
velocity(:,:,k) = vx .* ipm(:,k) + vy .* jpm(:,k) % Cell Array Or 3D Matrix Necessary Here
end
velocity = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
velocity =
velocity(:,:,1) =
Columns 1 through 18
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995
0 0.0875 0.1727 0.2531 0.3266 0.3912 0.4452 0.4870 0.5155 0.5300 0.5300 0.5155 0.4870 0.4452 0.3912 0.3266 0.2531 0.1727
0 0.0730 0.1441 0.2112 0.2725 0.3264 0.3714 0.4063 0.4301 0.4422 0.4422 0.4301 0.4063 0.3714 0.3264 0.2725 0.2112 0.1441
0 0.0578 0.1140 0.1671 0.2156 0.2583 0.2939 0.3215 0.3403 0.3498 0.3498 0.3403 0.3215 0.2939 0.2583 0.2156 0.1671 0.1140
0 0.0419 0.0827 0.1213 0.1565 0.1875 0.2133 0.2334 0.2470 0.2540 0.2540 0.2470 0.2334 0.2133 0.1875 0.1565 0.1213 0.0827
0 0.0257 0.0507 0.0743 0.0958 0.1148 0.1306 0.1429 0.1512 0.1555 0.1555 0.1512 0.1429 0.1306 0.1148 0.0958 0.0743 0.0507
0 0.0092 0.0181 0.0265 0.0342 0.0409 0.0466 0.0509 0.0539 0.0554 0.0554 0.0539 0.0509 0.0466 0.0409 0.0342 0.0265 0.0181
0 -0.0075 -0.0147 -0.0216 -0.0279 -0.0334 -0.0380 -0.0415 -0.0440 -0.0452 -0.0452 -0.0440 -0.0415 -0.0380 -0.0334 -0.0279 -0.0216 -0.0147
0 -0.0240 -0.0474 -0.0694 -0.0896 -0.1073 -0.1221 -0.1336 -0.1414 -0.1454 -0.1454 -0.1414 -0.1336 -0.1221 -0.1073 -0.0896 -0.0694 -0.0474
0 -0.0403 -0.0795 -0.1165 -0.1504 -0.1802 -0.2050 -0.2242 -0.2374 -0.2440 -0.2440 -0.2374 -0.2242 -0.2050 -0.1802 -0.1504 -0.1165 -0.0795
0 -0.0562 -0.1108 -0.1625 -0.2097 -0.2512 -0.2858 -0.3126 -0.3309 -0.3402 -0.3402 -0.3309 -0.3126 -0.2858 -0.2512 -0.2097 -0.1625 -0.1108
0 -0.0715 -0.1411 -0.2068 -0.2668 -0.3196 -0.3637 -0.3978 -0.4211 -0.4329 -0.4329 -0.4211 -0.3978 -0.3637 -0.3196 -0.2668 -0.2068 -0.1411
0 -0.0861 -0.1698 -0.2489 -0.3213 -0.3848 -0.4379 -0.4790 -0.5070 -0.5213 -0.5213 -0.5070 -0.4790 -0.4379 -0.3848 -0.3213 -0.2489 -0.1698
0 -0.0998 -0.1969 -0.2886 -0.3724 -0.4461 -0.5076 -0.5553 -0.5878 -0.6043 -0.6043 -0.5878 -0.5553 -0.5076 -0.4461 -0.3724 -0.2886 -0.1969
0 -0.1125 -0.2219 -0.3253 -0.4198 -0.5028 -0.5721 -0.6259 -0.6625 -0.6811 -0.6811 -0.6625 -0.6259 -0.5721 -0.5028 -0.4198 -0.3253 -0.2219
0 -0.1240 -0.2447 -0.3587 -0.4628 -0.5544 -0.6308 -0.6901 -0.7305 -0.7510 -0.7510 -0.7305 -0.6901 -0.6308 -0.5544 -0.4628 -0.3587 -0.2447
0 -0.1343 -0.2650 -0.3884 -0.5012 -0.6004 -0.6831 -0.7473 -0.7910 -0.8132 -0.8132 -0.7910 -0.7473 -0.6831 -0.6004 -0.5012 -0.3884 -0.2650
0 -0.1432 -0.2825 -0.4141 -0.5344 -0.6402 -0.7284 -0.7968 -0.8435 -0.8672 -0.8672 -0.8435 -0.7968 -0.7284 -0.6402 -0.5344 -0.4141 -0.2825
0 -0.1507 -0.2972 -0.4357 -0.5622 -0.6735 -0.7663 -0.8383 -0.8874 -0.9123 -0.9123 -0.8874 -0.8383 -0.7663 -0.6735 -0.5622 -0.4357 -0.2972
0 -0.1566 -0.3089 -0.4528 -0.5843 -0.6999 -0.7964 -0.8712 -0.9222 -0.9481 -0.9481 -0.9222 -0.8712 -0.7964 -0.6999 -0.5843 -0.4528 -0.3089
0 -0.1609 -0.3174 -0.4653 -0.6004 -0.7192 -0.8184 -0.8952 -0.9476 -0.9742 -0.9742 -0.9476 -0.8952 -0.8184 -0.7192 -0.6004 -0.4653 -0.3174
0 -0.1636 -0.3227 -0.4730 -0.6104 -0.7312 -0.8320 -0.9101 -0.9634 -0.9904 -0.9904 -0.9634 -0.9101 -0.8320 -0.7312 -0.6104 -0.4730 -0.3227
0 -0.1646 -0.3247 -0.4759 -0.6142 -0.7357 -0.8371 -0.9157 -0.9693 -0.9965 -0.9965 -0.9693 -0.9157 -0.8371 -0.7357 -0.6142 -0.4759 -0.3247
0 -0.1639 -0.3234 -0.4740 -0.6117 -0.7327 -0.8337 -0.9120 -0.9654 -0.9925 -0.9925 -0.9654 -0.9120 -0.8337 -0.7327 -0.6117 -0.4740 -0.3234
0 -0.1616 -0.3187 -0.4672 -0.6030 -0.7222 -0.8218 -0.8990 -0.9516 -0.9783 -0.9783 -0.9516 -0.8990 -0.8218 -0.7222 -0.6030 -0.4672 -0.3187
0 -0.1576 -0.3109 -0.4557 -0.5881 -0.7044 -0.8015 -0.8768 -0.9282 -0.9542 -0.9542 -0.9282 -0.8768 -0.8015 -0.7044 -0.5881 -0.4557 -0.3109
0 -0.1520 -0.2999 -0.4395 -0.5672 -0.6794 -0.7731 -0.8457 -0.8952 -0.9203 -0.9203 -0.8952 -0.8457 -0.7731 -0.6794 -0.5672 -0.4395 -0.2999
0 -0.1449 -0.2858 -0.4189 -0.5406 -0.6475 -0.7368 -0.8060 -0.8531 -0.8771 -0.8771 -0.8531 -0.8060 -0.7368 -0.6475 -0.5406 -0.4189 -0.2858
0 -0.1362 -0.2688 -0.3939 -0.5084 -0.6090 -0.6929 -0.7580 -0.8024 -0.8249 -0.8249 -0.8024 -0.7580 -0.6929 -0.6090 -0.5084 -0.3939 -0.2688
0 -0.1262 -0.2490 -0.3650 -0.4710 -0.5642 -0.6420 -0.7023 -0.7434 -0.7643 -0.7643 -0.7434 -0.7023 -0.6420 -0.5642 -0.4710 -0.3650 -0.2490
0 -0.1149 -0.2267 -0.3323 -0.4289 -0.5137 -0.5846 -0.6395 -0.6769 -0.6959 -0.6959 -0.6769 -0.6395 -0.5846 -0.5137 -0.4289 -0.3323 -0.2267
0 -0.1025 -0.2021 -0.2963 -0.3824 -0.4580 -0.5212 -0.5701 -0.6035 -0.6204 -0.6204 -0.6035 -0.5701 -0.5212 -0.4580 -0.3824 -0.2963 -0.2021
0 -0.0890 -0.1755 -0.2572 -0.3320 -0.3976 -0.4524 -0.4949 -0.5239 -0.5386 -0.5386 -0.5239 -0.4949 -0.4524 -0.3976 -0.3320 -0.2572 -0.1755
0 -0.0745 -0.1470 -0.2155 -0.2781 -0.3332 -0.3791 -0.4147 -0.4390 -0.4513 -0.4513 -0.4390 -0.4147 -0.3791 -0.3332 -0.2781 -0.2155 -0.1470
0 -0.0594 -0.1171 -0.1716 -0.2215 -0.2653 -0.3019 -0.3303 -0.3496 -0.3594 -0.3594 -0.3496 -0.3303 -0.3019 -0.2653 -0.2215 -0.1716 -0.1171
0 -0.0436 -0.0860 -0.1260 -0.1626 -0.1948 -0.2216 -0.2425 -0.2566 -0.2638 -0.2638 -0.2566 -0.2425 -0.2216 -0.1948 -0.1626 -0.1260 -0.0860
0 -0.0273 -0.0540 -0.0791 -0.1021 -0.1222 -0.1391 -0.1522 -0.1611 -0.1656 -0.1656 -0.1611 -0.1522 -0.1391 -0.1222 -0.1021 -0.0791 -0.0540
0 -0.0108 -0.0214 -0.0314 -0.0405 -0.0485 -0.0551 -0.0603 -0.0639 -0.0657 -0.0657 -0.0639 -0.0603 -0.0551 -0.0485 -0.0405 -0.0314 -0.0214
0 0.0058 0.0114 0.0167 0.0215 0.0258 0.0294 0.0321 0.0340 0.0350 0.0350 0.0340 0.0321 0.0294 0.0258 0.0215 0.0167 0.0114
0 0.0223 0.0441 0.0646 0.0833 0.0998 0.1136 0.1242 0.1315 0.1352 0.1352 0.1315 0.1242 0.1136 0.0998 0.0833 0.0646 0.0441
0 0.0387 0.0763 0.1118 0.1443 0.1728 0.1966 0.2151 0.2277 0.2341 0.2341 0.2277 0.2151 0.1966 0.1728 0.1443 0.1118 0.0763
0 0.0546 0.1077 0.1579 0.2037 0.2440 0.2777 0.3038 0.3216 0.3306 0.3306 0.3216 0.3038 0.2777 0.2440 0.2037 0.1579 0.1077
0 0.0700 0.1380 0.2023 0.2611 0.3128 0.3559 0.3893 0.4121 0.4237 0.4237 0.4121 0.3893 0.3559 0.3128 0.2611 0.2023 0.1380
0 0.0846 0.1670 0.2448 0.3159 0.3783 0.4305 0.4709 0.4985 0.5125 0.5125 0.4985 0.4709 0.4305 0.3783 0.3159 0.2448 0.1670
0 0.0984 0.1942 0.2847 0.3674 0.4400 0.5007 0.5477 0.5798 0.5961 0.5961 0.5798 0.5477 0.5007 0.4400 0.3674 0.2847 0.1942
0 0.1112 0.2195 0.3217 0.4151 0.4973 0.5658 0.6190 0.6552 0.6736 0.6736 0.6552 0.6190 0.5658 0.4973 0.4151 0.3217 0.2195
0 0.1229 0.2425 0.3554 0.4587 0.5494 0.6252 0.6839 0.7239 0.7442 0.7442 0.7239 0.6839 0.6252 0.5494 0.4587 0.3554 0.2425
0 0.1333 0.2630 0.3855 0.4975 0.5959 0.6781 0.7418 0.7852 0.8072 0.8072 0.7852 0.7418 0.6781 0.5959 0.4975 0.3855 0.2630
0 0.1424 0.2809 0.4117 0.5313 0.6364 0.7242 0.7922 0.8385 0.8621 0.8621 0.8385 0.7922 0.7242 0.6364 0.5313 0.4117 0.2809
0 0.1500 0.2959 0.4337 0.5597 0.6704 0.7628 0.8345 0.8833 0.9081 0.9081 0.8833 0.8345 0.7628 0.6704 0.5597 0.4337 0.2959
0 0.1561 0.3078 0.4512 0.5823 0.6975 0.7937 0.8682 0.9191 0.9449 0.9449 0.9191 0.8682 0.7937 0.6975 0.5823 0.4512 0.3078
0 0.1605 0.3167 0.4642 0.5991 0.7176 0.8165 0.8932 0.9455 0.9720 0.9720 0.9455 0.8932 0.8165 0.7176 0.5991 0.4642 0.3167
0 0.1634 0.3223 0.4724 0.6097 0.7303 0.8310 0.9090 0.9622 0.9892 0.9892 0.9622 0.9090 0.8310 0.7303 0.6097 0.4724 0.3223
0 0.1646 0.3246 0.4758 0.6141 0.7356 0.8370 0.9156 0.9692 0.9964 0.9964 0.9692 0.9156 0.8370 0.7356 0.6141 0.4758 0.3246
0 0.1641 0.3236 0.4744 0.6122 0.7333 0.8345 0.9128 0.9663 0.9934 0.9934 0.9663 0.9128 0.8345 0.7333 0.6122 0.4744 0.3236
0 0.1619 0.3194 0.4681 0.6041 0.7236 0.8234 0.9007 0.9535 0.9802 0.9802 0.9535 0.9007 0.8234 0.7236 0.6041 0.4681 0.3194
0 0.1581 0.3118 0.4571 0.5899 0.7066 0.8040 0.8795 0.9310 0.9571 0.9571 0.9310 0.8795 0.8040 0.7066 0.5899 0.4571 0.3118
0 0.1526 0.3011 0.4414 0.5696 0.6823 0.7764 0.8493 0.8990 0.9242 0.9242 0.8990 0.8493 0.7764 0.6823 0.5696 0.4414 0.3011
0 0.1457 0.2873 0.4212 0.5435 0.6511 0.7408 0.8104 0.8578 0.8819 0.8819 0.8578 0.8104 0.7408 0.6511 0.5435 0.4212 0.2873
0 0.1372 0.2706 0.3967 0.5119 0.6132 0.6977 0.7632 0.8079 0.8306 0.8306 0.8079 0.7632 0.6977 0.6132 0.5119 0.3967 0.2706
0 0.1273 0.2511 0.3681 0.4751 0.5691 0.6475 0.7083 0.7498 0.7708 0.7708 0.7498 0.7083 0.6475 0.5691 0.4751 0.3681 0.2511
0 0.1161 0.2291 0.3358 0.4334 0.5191 0.5907 0.6462 0.6840 0.7032 0.7032 0.6840 0.6462 0.5907 0.5191 0.4334 0.3358 0.2291
0 0.1038 0.2047 0.3001 0.3873 0.4639 0.5279 0.5774 0.6113 0.6284 0.6284 0.6113 0.5774 0.5279 0.4639 0.3873 0.3001 0.2047
0 0.0904 0.1783 0.2613 0.3372 0.4040 0.4597 0.5028 0.5323 0.5472 0.5472 0.5323 0.5028 0.4597 0.4040 0.3372 0.2613 0.1783
0 0.0760 0.1500 0.2199 0.2838 0.3399 0.3868 0.4231 0.4479 0.4604 0.4604 0.4479 0.4231 0.3868 0.3399 0.2838 0.2199 0.1500
0 0.0609 0.1202 0.1762 0.2274 0.2724 0.3099 0.3390 0.3589 0.3689 0.3689 0.3589 0.3390 0.3099 0.2724 0.2274 0.1762 0.1202
0 0.0452 0.0892 0.1307 0.1687 0.2021 0.2299 0.2515 0.2662 0.2737 0.2737 0.2662 0.2515 0.2299 0.2021 0.1687 0.1307 0.0892
0 0.0290 0.0572 0.0839 0.1083 0.1297 0.1476 0.1614 0.1709 0.1757 0.1757 0.1709 0.1614 0.1476 0.1297 0.1083 0.0839 0.0572
0 0.0125 0.0247 0.0362 0.0468 0.0560 0.0637 0.0697 0.0738 0.0759 0.0759 0.0738 0.0697 0.0637 0.0560 0.0468 0.0362 0.0247
0 -0.0041 -0.0081 -0.0118 -0.0152 -0.0182 -0.0208 -0.0227 -0.0240 -0.0247 -0.0247 -0.0240 -0.0227 -0.0208 -0.0182 -0.0152 -0.0118 -0.0081
0 -0.0207 -0.0407 -0.0597 -0.0771 -0.0923 -0.1051 -0.1149 -0.1216 -0.1251 -0.1251 -0.1216 -0.1149 -0.1051 -0.0923 -0.0771 -0.0597 -0.0407
0 -0.0370 -0.0730 -0.1070 -0.1381 -0.1655 -0.1883 -0.2059 -0.2180 -0.2241 -0.2241 -0.2180 -0.2059 -0.1883 -0.1655 -0.1381 -0.1070 -0.0730
0 -0.0530 -0.1046 -0.1533 -0.1978 -0.2369 -0.2696 -0.2949 -0.3121 -0.3209 -0.3209 -0.3121 -0.2949 -0.2696 -0.2369 -0.1978 -0.1533 -0.1046
0 -0.0684 -0.1350 -0.1979 -0.2554 -0.3059 -0.3481 -0.3808 -0.4031 -0.4144 -0.4144 -0.4031 -0.3808 -0.3481 -0.3059 -0.2554 -0.1979 -0.1350
0 -0.0832 -0.1641 -0.2405 -0.3104 -0.3718 -0.4231 -0.4628 -0.4899 -0.5037 -0.5037 -0.4899 -0.4628 -0.4231 -0.3718 -0.3104 -0.2405 -0.1641
0 -0.0971 -0.1915 -0.2807 -0.3623 -0.4340 -0.4938 -0.5402 -0.5718 -0.5878 -0.5878 -0.5718 -0.5402 -0.4938 -0.4340 -0.3623 -0.2807 -0.1915
0 -0.1100 -0.2170 -0.3181 -0.4105 -0.4917 -0.5595 -0.6120 -0.6478 -0.6660 -0.6660 -0.6478 -0.6120 -0.5595 -0.4917 -0.4105 -0.3181 -0.2170
0 -0.1218 -0.2402 -0.3521 -0.4544 -0.5443 -0.6194 -0.6776 -0.7172 -0.7373 -0.7373 -0.7172 -0.6776 -0.6194 -0.5443 -0.4544 -0.3521 -0.2402
0 -0.1323 -0.2610 -0.3826 -0.4938 -0.5915 -0.6730 -0.7362 -0.7793 -0.8012 -0.8012 -0.7793 -0.7362 -0.6730 -0.5915 -0.4938 -0.3826 -0.2610
0 -0.1415 -0.2792 -0.4092 -0.5281 -0.6326 -0.7198 -0.7874 -0.8335 -0.8569 -0.8569 -0.8335 -0.7874 -0.7198 -0.6326 -0.5281 -0.4092 -0.2792
0 -0.1493 -0.2945 -0.4316 -0.5570 -0.6672 -0.7592 -0.8305 -0.8792 -0.9038 -0.9038 -0.8792 -0.8305 -0.7592 -0.6672 -0.5570 -0.4316 -0.2945
0 -0.1555 -0.3068 -0.4497 -0.5803 -0.6951 -0.7909 -0.8652 -0.9159 -0.9416 -0.9416 -0.9159 -0.8652 -0.7909 -0.6951 -0.5803 -0.4497 -0.3068
0 -0.1602 -0.3159 -0.4631 -0.5976 -0.7159 -0.8146 -0.8911 -0.9432 -0.9697 -0.9697 -0.9432 -0.8911 -0.8146 -0.7159 -0.5976 -0.4631 -0.3159
0 -0.1632 -0.3219 -0.4718 -0.6089 -0.7293 -0.8299 -0.9078 -0.9610 -0.9879 -0.9879 -0.9610 -0.9078 -0.8299 -0.7293 -0.6089 -0.4718 -0.3219
0 -0.1645 -0.3245 -0.4757 -0.6139 -0.7354 -0.8368 -0.9153 -0.9689 -0.9961 -0.9961 -0.9689 -0.9153 -0.8368 -0.7354 -0.6139 -0.4757 -0.3245
0 -0.1642 -0.3239 -0.4748 -0.6127 -0.7339 -0.8351 -0.9135 -0.9670 -0.9941 -0.9941 -0.9670 -0.9135 -0.8351 -0.7339 -0.6127 -0.4748 -0.3239
0 -0.1622 -0.3200 -0.4690 -0.6052 -0.7250 -0.8249 -0.9024 -0.9552 -0.9820 -0.9820 -0.9552 -0.9024 -0.8249 -0.7250 -0.6052 -0.4690 -0.3200
0 -0.1585 -0.3127 -0.4584 -0.5916 -0.7086 -0.8063 -0.8821 -0.9337 -0.9599 -0.9599 -0.9337 -0.8821 -0.8063 -0.7086 -0.5916 -0.4584 -0.3127
0 -0.1533 -0.3023 -0.4432 -0.5719 -0.6851 -0.7795 -0.8527 -0.9027 -0.9280 -0.9280 -0.9027 -0.8527 -0.7795 -0.6851 -0.5719 -0.4432 -0.3023
0 -0.1464 -0.2889 -0.4234 -0.5464 -0.6545 -0.7448 -0.8147 -0.8624 -0.8866 -0.8866 -0.8624 -0.8147 -0.7448 -0.6545 -0.5464 -0.4234 -0.2889
0 -0.1381 -0.2724 -0.3994 -0.5154 -0.6173 -0.7024 -0.7684 -0.8134 -0.8362 -0.8362 -0.8134 -0.7684 -0.7024 -0.6173 -0.5154 -0.3994 -0.2724
Columns 19 through 20
0.1646 0.0000
0.1638 0.0000
0.1612 0.0000
0.1571 0.0000
0.1513 0.0000
0.1440 0.0000
0.1353 0.0000
0.1251 0.0000
0.1137 0.0000
0.1011 0.0000
0.0875 0.0000
0.0730 0.0000
0.0578 0.0000
0.0419 0.0000
0.0257 0.0000
0.0092 0.0000
-0.0075 -0.0000
-0.0240 -0.0000
-0.0403 -0.0000
-0.0562 -0.0000
-0.0715 -0.0000
-0.0861 -0.0000
-0.0998 -0.0000
-0.1125 -0.0000
-0.1240 -0.0000
-0.1343 -0.0000
-0.1432 -0.0000
-0.1507 -0.0000
-0.1566 -0.0000
-0.1609 -0.0000
-0.1636 -0.0000
-0.1646 -0.0000
-0.1639 -0.0000
-0.1616 -0.0000
-0.1576 -0.0000
-0.1520 -0.0000
-0.1449 -0.0000
-0.1362 -0.0000
-0.1262 -0.0000
-0.1149 -0.0000
-0.1025 -0.0000
-0.0890 -0.0000
-0.0745 -0.0000
-0.0594 -0.0000
-0.0436 -0.0000
-0.0273 -0.0000
-0.0108 -0.0000
0.0058 0.0000
0.0223 0.0000
0.0387 0.0000
0.0546 0.0000
0.0700 0.0000
0.0846 0.0000
0.0984 0.0000
0.1112 0.0000
0.1229 0.0000
0.1333 0.0000
0.1424 0.0000
0.1500 0.0000
0.1561 0.0000
0.1605 0.0000
0.1634 0.0000
0.1646 0.0000
0.1641 0.0000
0.1619 0.0000
0.1581 0.0000
0.1526 0.0000
0.1457 0.0000
0.1372 0.0000
0.1273 0.0000
0.1161 0.0000
0.1038 0.0000
0.0904 0.0000
0.0760 0.0000
0.0609 0.0000
0.0452 0.0000
0.0290 0.0000
0.0125 0.0000
-0.0041 -0.0000
-0.0207 -0.0000
-0.0370 -0.0000
-0.0530 -0.0000
-0.0684 -0.0000
-0.0832 -0.0000
-0.0971 -0.0000
-0.1100 -0.0000
-0.1218 -0.0000
-0.1323 -0.0000
-0.1415 -0.0000
-0.1493 -0.0000
-0.1555 -0.0000
-0.1602 -0.0000
-0.1632 -0.0000
-0.1645 -0.0000
-0.1642 -0.0000
-0.1622 -0.0000
-0.1585 -0.0000
-0.1533 -0.0000
-0.1464 -0.0000
-0.1381 -0.0000
velocity(:,:,2) =
Columns 1 through 18
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462
-0.8469 -0.8353 -0.8010 -0.7448 -0.6683 -0.5736 -0.4632 -0.3402 -0.2079 -0.0699 0.0699 0.2079 0.3402 0.4632 0.5736 0.6683 0.7448 0.8010
-0.8962 -0.8840 -0.8476 -0.7882 -0.7072 -0.6070 -0.4902 -0.3600 -0.2200 -0.0740 0.0740 0.2200 0.3600 0.4902 0.6070 0.7072 0.7882 0.8476
-0.9364 -0.9236 -0.8856 -0.8235 -0.7389 -0.6342 -0.5121 -0.3761 -0.2299 -0.0773 0.0773 0.2299 0.3761 0.5121 0.6342 0.7389 0.8235 0.8856
-0.9670 -0.9538 -0.9146 -0.8504 -0.7631 -0.6549 -0.5289 -0.3884 -0.2374 -0.0799 0.0799 0.2374 0.3884 0.5289 0.6549 0.7631 0.8504 0.9146
-0.9878 -0.9743 -0.9342 -0.8687 -0.7795 -0.6690 -0.5403 -0.3968 -0.2425 -0.0816 0.0816 0.2425 0.3968 0.5403 0.6690 0.7795 0.8687 0.9342
-0.9985 -0.9848 -0.9444 -0.8781 -0.7879 -0.6762 -0.5461 -0.4011 -0.2451 -0.0825 0.0825 0.2451 0.4011 0.5461 0.6762 0.7879 0.8781 0.9444
-0.9990 -0.9853 -0.9448 -0.8786 -0.7883 -0.6766 -0.5464 -0.4013 -0.2452 -0.0825 0.0825 0.2452 0.4013 0.5464 0.6766 0.7883 0.8786 0.9448
-0.9893 -0.9758 -0.9357 -0.8701 -0.7807 -0.6700 -0.5411 -0.3974 -0.2429 -0.0817 0.0817 0.2429 0.3974 0.5411 0.6700 0.7807 0.8701 0.9357
-0.9696 -0.9563 -0.9170 -0.8527 -0.7651 -0.6567 -0.5303 -0.3895 -0.2380 -0.0801 0.0801 0.2380 0.3895 0.5303 0.6567 0.7651 0.8527 0.9170
-0.9399 -0.9271 -0.8890 -0.8266 -0.7417 -0.6366 -0.5141 -0.3776 -0.2307 -0.0776 0.0776 0.2307 0.3776 0.5141 0.6366 0.7417 0.8266 0.8890
-0.9007 -0.8884 -0.8519 -0.7921 -0.7108 -0.6100 -0.4926 -0.3618 -0.2211 -0.0744 0.0744 0.2211 0.3618 0.4926 0.6100 0.7108 0.7921 0.8519
-0.8523 -0.8407 -0.8061 -0.7496 -0.6726 -0.5773 -0.4662 -0.3424 -0.2092 -0.0704 0.0704 0.2092 0.3424 0.4662 0.5773 0.6726 0.7496 0.8061
-0.7952 -0.7844 -0.7521 -0.6994 -0.6275 -0.5386 -0.4349 -0.3194 -0.1952 -0.0657 0.0657 0.1952 0.3194 0.4349 0.5386 0.6275 0.6994 0.7521
-0.7300 -0.7201 -0.6905 -0.6420 -0.5761 -0.4944 -0.3993 -0.2932 -0.1792 -0.0603 0.0603 0.1792 0.2932 0.3993 0.4944 0.5761 0.6420 0.6905
-0.6574 -0.6484 -0.6218 -0.5782 -0.5188 -0.4452 -0.3596 -0.2641 -0.1614 -0.0543 0.0543 0.1614 0.2641 0.3596 0.4452 0.5188 0.5782 0.6218
-0.5781 -0.5702 -0.5467 -0.5084 -0.4562 -0.3915 -0.3162 -0.2322 -0.1419 -0.0477 0.0477 0.1419 0.2322 0.3162 0.3915 0.4562 0.5084 0.5467
-0.4928 -0.4861 -0.4661 -0.4334 -0.3889 -0.3338 -0.2695 -0.1980 -0.1210 -0.0407 0.0407 0.1210 0.1980 0.2695 0.3338 0.3889 0.4334 0.4661
-0.4026 -0.3971 -0.3808 -0.3540 -0.3177 -0.2727 -0.2202 -0.1617 -0.0988 -0.0332 0.0332 0.0988 0.1617 0.2202 0.2727 0.3177 0.3540 0.3808
-0.3082 -0.3040 -0.2915 -0.2711 -0.2432 -0.2087 -0.1686 -0.1238 -0.0757 -0.0255 0.0255 0.0757 0.1238 0.1686 0.2087 0.2432 0.2711 0.2915
-0.2107 -0.2078 -0.1993 -0.1853 -0.1663 -0.1427 -0.1152 -0.0846 -0.0517 -0.0174 0.0174 0.0517 0.0846 0.1152 0.1427 0.1663 0.1853 0.1993
-0.1111 -0.1095 -0.1050 -0.0977 -0.0876 -0.0752 -0.0607 -0.0446 -0.0273 -0.0092 0.0092 0.0273 0.0446 0.0607 0.0752 0.0876 0.0977 0.1050
-0.0103 -0.0101 -0.0097 -0.0090 -0.0081 -0.0070 -0.0056 -0.0041 -0.0025 -0.0008 0.0008 0.0025 0.0041 0.0056 0.0070 0.0081 0.0090 0.0097
0.0906 0.0894 0.0857 0.0797 0.0715 0.0614 0.0496 0.0364 0.0222 0.0075 -0.0075 -0.0222 -0.0364 -0.0496 -0.0614 -0.0715 -0.0797 -0.0857
0.1906 0.1880 0.1802 0.1676 0.1504 0.1291 0.1042 0.0766 0.0468 0.0157 -0.0157 -0.0468 -0.0766 -0.1042 -0.1291 -0.1504 -0.1676 -0.1802
0.2886 0.2847 0.2730 0.2538 0.2277 0.1955 0.1578 0.1159 0.0708 0.0238 -0.0238 -0.0708 -0.1159 -0.1578 -0.1955 -0.2277 -0.2538 -0.2730
0.3837 0.3784 0.3629 0.3374 0.3028 0.2598 0.2098 0.1541 0.0942 0.0317 -0.0317 -0.0942 -0.1541 -0.2098 -0.2598 -0.3028 -0.3374 -0.3629
0.4748 0.4684 0.4491 0.4176 0.3747 0.3216 0.2597 0.1907 0.1166 0.0392 -0.0392 -0.1166 -0.1907 -0.2597 -0.3216 -0.3747 -0.4176 -0.4491
0.5612 0.5535 0.5308 0.4935 0.4428 0.3801 0.3069 0.2254 0.1378 0.0463 -0.0463 -0.1378 -0.2254 -0.3069 -0.3801 -0.4428 -0.4935 -0.5308
0.6418 0.6330 0.6070 0.5644 0.5064 0.4347 0.3510 0.2578 0.1575 0.0530 -0.0530 -0.1575 -0.2578 -0.3510 -0.4347 -0.5064 -0.5644 -0.6070
0.7158 0.7061 0.6770 0.6295 0.5649 0.4848 0.3915 0.2875 0.1757 0.0591 -0.0591 -0.1757 -0.2875 -0.3915 -0.4848 -0.5649 -0.6295 -0.6770
0.7826 0.7719 0.7402 0.6883 0.6176 0.5300 0.4280 0.3144 0.1921 0.0646 -0.0646 -0.1921 -0.3144 -0.4280 -0.5300 -0.6176 -0.6883 -0.7402
0.8414 0.8299 0.7958 0.7400 0.6640 0.5698 0.4602 0.3380 0.2065 0.0695 -0.0695 -0.2065 -0.3380 -0.4602 -0.5698 -0.6640 -0.7400 -0.7958
0.8916 0.8794 0.8433 0.7841 0.7036 0.6039 0.4877 0.3581 0.2189 0.0736 -0.0736 -0.2189 -0.3581 -0.4877 -0.6039 -0.7036 -0.7841 -0.8433
0.9327 0.9200 0.8822 0.8203 0.7360 0.6317 0.5101 0.3747 0.2290 0.0770 -0.0770 -0.2290 -0.3747 -0.5101 -0.6317 -0.7360 -0.8203 -0.8822
0.9643 0.9512 0.9121 0.8481 0.7610 0.6531 0.5274 0.3874 0.2367 0.0796 -0.0796 -0.2367 -0.3874 -0.5274 -0.6531 -0.7610 -0.8481 -0.9121
0.9861 0.9726 0.9327 0.8672 0.7782 0.6679 0.5393 0.3961 0.2421 0.0814 -0.0814 -0.2421 -0.3961 -0.5393 -0.6679 -0.7782 -0.8672 -0.9327
0.9978 0.9842 0.9438 0.8776 0.7874 0.6758 0.5458 0.4008 0.2450 0.0824 -0.0824 -0.2450 -0.4008 -0.5458 -0.6758 -0.7874 -0.8776 -0.9438
0.9994 0.9858 0.9452 0.8789 0.7887 0.6769 0.5466 0.4014 0.2453 0.0825 -0.0825 -0.2453 -0.4014 -0.5466 -0.6769 -0.7887 -0.8789 -0.9452
0.9908 0.9772 0.9371 0.8713 0.7818 0.6710 0.5419 0.3980 0.2432 0.0818 -0.0818 -0.2432 -0.3980 -0.5419 -0.6710 -0.7818 -0.8713 -0.9371
0.9720 0.9588 0.9194 0.8549 0.7671 0.6583 0.5316 0.3905 0.2386 0.0803 -0.0803 -0.2386 -0.3905 -0.5316 -0.6583 -0.7671 -0.8549 -0.9194
0.9434 0.9305 0.8923 0.8297 0.7445 0.6389 0.5160 0.3790 0.2316 0.0779 -0.0779 -0.2316 -0.3790 -0.5160 -0.6389 -0.7445 -0.8297 -0.8923
0.9051 0.8928 0.8561 0.7960 0.7143 0.6130 0.4951 0.3636 0.2222 0.0747 -0.0747 -0.2222 -0.3636 -0.4951 -0.6130 -0.7143 -0.7960 -0.8561
0.8576 0.8459 0.8112 0.7543 0.6768 0.5809 0.4691 0.3445 0.2105 0.0708 -0.0708 -0.2105 -0.3445 -0.4691 -0.5809 -0.6768 -0.7543 -0.8112
0.8014 0.7905 0.7580 0.7048 0.6324 0.5428 0.4383 0.3219 0.1967 0.0662 -0.0662 -0.1967 -0.3219 -0.4383 -0.5428 -0.6324 -0.7048 -0.7580
0.7370 0.7270 0.6971 0.6482 0.5816 0.4992 0.4031 0.2961 0.1809 0.0609 -0.0609 -0.1809 -0.2961 -0.4031 -0.4992 -0.5816 -0.6482 -0.6971
0.6651 0.6560 0.6291 0.5849 0.5249 0.4505 0.3638 0.2672 0.1633 0.0549 -0.0549 -0.1633 -0.2672 -0.3638 -0.4505 -0.5249 -0.5849 -0.6291
0.5864 0.5784 0.5546 0.5157 0.4628 0.3972 0.3207 0.2356 0.1440 0.0484 -0.0484 -0.1440 -0.2356 -0.3207 -0.3972 -0.4628 -0.5157 -0.5546
0.5017 0.4949 0.4746 0.4413 0.3959 0.3398 0.2744 0.2015 0.1232 0.0414 -0.0414 -0.1232 -0.2015 -0.2744 -0.3398 -0.3959 -0.4413 -0.4746
0.4120 0.4063 0.3896 0.3623 0.3251 0.2790 0.2253 0.1655 0.1011 0.0340 -0.0340 -0.1011 -0.1655 -0.2253 -0.2790 -0.3251 -0.3623 -0.3896
0.3180 0.3136 0.3007 0.2796 0.2509 0.2154 0.1739 0.1277 0.0781 0.0263 -0.0263 -0.0781 -0.1277 -0.1739 -0.2154 -0.2509 -0.2796 -0.3007
0.2207 0.2177 0.2088 0.1941 0.1742 0.1495 0.1207 0.0887 0.0542 0.0182 -0.0182 -0.0542 -0.0887 -0.1207 -0.1495 -0.1742 -0.1941 -0.2088
0.1213 0.1196 0.1147 0.1067 0.0957 0.0821 0.0663 0.0487 0.0298 0.0100 -0.0100 -0.0298 -0.0487 -0.0663 -0.0821 -0.0957 -0.1067 -0.1147
0.0206 0.0203 0.0194 0.0181 0.0162 0.0139 0.0112 0.0083 0.0050 0.0017 -0.0017 -0.0050 -0.0083 -0.0112 -0.0139 -0.0162 -0.0181 -0.0194
-0.0804 -0.0793 -0.0760 -0.0707 -0.0634 -0.0544 -0.0440 -0.0323 -0.0197 -0.0066 0.0066 0.0197 0.0323 0.0440 0.0544 0.0634 0.0707 0.0760
-0.1805 -0.1780 -0.1707 -0.1587 -0.1424 -0.1222 -0.0987 -0.0725 -0.0443 -0.0149 0.0149 0.0443 0.0725 0.0987 0.1222 0.1424 0.1587 0.1707
-0.2787 -0.2749 -0.2636 -0.2451 -0.2200 -0.1888 -0.1525 -0.1120 -0.0684 -0.0230 0.0230 0.0684 0.1120 0.1525 0.1888 0.2200 0.2451 0.2636
-0.3742 -0.3690 -0.3539 -0.3291 -0.2953 -0.2534 -0.2046 -0.1503 -0.0918 -0.0309 0.0309 0.0918 0.1503 0.2046 0.2534 0.2953 0.3291 0.3539
-0.4658 -0.4594 -0.4405 -0.4096 -0.3675 -0.3154 -0.2547 -0.1871 -0.1143 -0.0385 0.0385 0.1143 0.1871 0.2547 0.3154 0.3675 0.4096 0.4405
-0.5526 -0.5451 -0.5227 -0.4860 -0.4361 -0.3743 -0.3023 -0.2220 -0.1357 -0.0456 0.0456 0.1357 0.2220 0.3023 0.3743 0.4361 0.4860 0.5227
-0.6338 -0.6252 -0.5995 -0.5574 -0.5002 -0.4293 -0.3467 -0.2546 -0.1556 -0.0523 0.0523 0.1556 0.2546 0.3467 0.4293 0.5002 0.5574 0.5995
-0.7086 -0.6989 -0.6702 -0.6232 -0.5592 -0.4799 -0.3876 -0.2846 -0.1740 -0.0585 0.0585 0.1740 0.2846 0.3876 0.4799 0.5592 0.6232 0.6702
-0.7761 -0.7656 -0.7341 -0.6826 -0.6125 -0.5257 -0.4245 -0.3118 -0.1905 -0.0641 0.0641 0.1905 0.3118 0.4245 0.5257 0.6125 0.6826 0.7341
-0.8358 -0.8244 -0.7905 -0.7350 -0.6595 -0.5661 -0.4571 -0.3357 -0.2052 -0.0690 0.0690 0.2052 0.3357 0.4571 0.5661 0.6595 0.7350 0.7905
-0.8869 -0.8748 -0.8388 -0.7800 -0.6999 -0.6007 -0.4851 -0.3563 -0.2177 -0.0732 0.0732 0.2177 0.3563 0.4851 0.6007 0.6999 0.7800 0.8388
-0.9289 -0.9163 -0.8786 -0.8170 -0.7331 -0.6292 -0.5081 -0.3732 -0.2280 -0.0767 0.0767 0.2280 0.3732 0.5081 0.6292 0.7331 0.8170 0.8786
-0.9615 -0.9484 -0.9094 -0.8457 -0.7588 -0.6512 -0.5259 -0.3862 -0.2360 -0.0794 0.0794 0.2360 0.3862 0.5259 0.6512 0.7588 0.8457 0.9094
-0.9843 -0.9709 -0.9310 -0.8657 -0.7768 -0.6667 -0.5384 -0.3954 -0.2416 -0.0813 0.0813 0.2416 0.3954 0.5384 0.6667 0.7768 0.8657 0.9310
-0.9971 -0.9835 -0.9431 -0.8769 -0.7869 -0.6753 -0.5454 -0.4005 -0.2448 -0.0823 0.0823 0.2448 0.4005 0.5454 0.6753 0.7869 0.8769 0.9431
-0.9997 -0.9861 -0.9455 -0.8792 -0.7889 -0.6771 -0.5468 -0.4016 -0.2454 -0.0826 0.0826 0.2454 0.4016 0.5468 0.6771 0.7889 0.8792 0.9455
-0.9921 -0.9786 -0.9383 -0.8725 -0.7829 -0.6719 -0.5426 -0.3985 -0.2435 -0.0819 0.0819 0.2435 0.3985 0.5426 0.6719 0.7829 0.8725 0.9383
-0.9744 -0.9611 -0.9216 -0.8569 -0.7689 -0.6599 -0.5329 -0.3914 -0.2392 -0.0805 0.0805 0.2392 0.3914 0.5329 0.6599 0.7689 0.8569 0.9216
-0.9467 -0.9338 -0.8954 -0.8326 -0.7471 -0.6412 -0.5178 -0.3803 -0.2324 -0.0782 0.0782 0.2324 0.3803 0.5178 0.6412 0.7471 0.8326 0.8954
-0.9094 -0.8970 -0.8602 -0.7998 -0.7177 -0.6160 -0.4974 -0.3653 -0.2233 -0.0751 0.0751 0.2233 0.3653 0.4974 0.6160 0.7177 0.7998 0.8602
-0.8629 -0.8511 -0.8161 -0.7589 -0.6809 -0.5844 -0.4720 -0.3466 -0.2118 -0.0713 0.0713 0.2118 0.3466 0.4720 0.5844 0.6809 0.7589 0.8161
-0.8075 -0.7965 -0.7638 -0.7102 -0.6372 -0.5469 -0.4417 -0.3244 -0.1982 -0.0667 0.0667 0.1982 0.3244 0.4417 0.5469 0.6372 0.7102 0.7638
-0.7439 -0.7338 -0.7036 -0.6543 -0.5871 -0.5038 -0.4069 -0.2988 -0.1826 -0.0614 0.0614 0.1826 0.2988 0.4069 0.5038 0.5871 0.6543 0.7036
-0.6727 -0.6636 -0.6363 -0.5917 -0.5309 -0.4556 -0.3680 -0.2702 -0.1651 -0.0556 0.0556 0.1651 0.2702 0.3680 0.4556 0.5309 0.5917 0.6363
-0.5947 -0.5866 -0.5625 -0.5230 -0.4693 -0.4028 -0.3253 -0.2389 -0.1460 -0.0491 0.0491 0.1460 0.2389 0.3253 0.4028 0.4693 0.5230 0.5625
-0.5106 -0.5036 -0.4829 -0.4491 -0.4029 -0.3458 -0.2793 -0.2051 -0.1253 -0.0422 0.0422 0.1253 0.2051 0.2793 0.3458 0.4029 0.4491 0.4829
-0.4213 -0.4156 -0.3985 -0.3705 -0.3325 -0.2853 -0.2304 -0.1692 -0.1034 -0.0348 0.0348 0.1034 0.1692 0.2304 0.2853 0.3325 0.3705 0.3985
-0.3277 -0.3232 -0.3099 -0.2882 -0.2586 -0.2219 -0.1792 -0.1316 -0.0804 -0.0271 0.0271 0.0804 0.1316 0.1792 0.2219 0.2586 0.2882 0.3099
-0.2308 -0.2276 -0.2183 -0.2029 -0.1821 -0.1563 -0.1262 -0.0927 -0.0566 -0.0191 0.0191 0.0566 0.0927 0.1262 0.1563 0.1821 0.2029 0.2183
-0.1315 -0.1297 -0.1243 -0.1156 -0.1037 -0.0890 -0.0719 -0.0528 -0.0323 -0.0109 0.0109 0.0323 0.0528 0.0719 0.0890 0.1037 0.1156 0.1243
-0.0308 -0.0304 -0.0292 -0.0271 -0.0243 -0.0209 -0.0169 -0.0124 -0.0076 -0.0025 0.0025 0.0076 0.0124 0.0169 0.0209 0.0243 0.0271 0.0292
0.0701 0.0692 0.0663 0.0617 0.0553 0.0475 0.0383 0.0282 0.0172 0.0058 -0.0058 -0.0172 -0.0282 -0.0383 -0.0475 -0.0553 -0.0617 -0.0663
0.1703 0.1680 0.1611 0.1498 0.1344 0.1154 0.0932 0.0684 0.0418 0.0141 -0.0141 -0.0418 -0.0684 -0.0932 -0.1154 -0.1344 -0.1498 -0.1611
0.2688 0.2652 0.2543 0.2364 0.2122 0.1821 0.1470 0.1080 0.0660 0.0222 -0.0222 -0.0660 -0.1080 -0.1470 -0.1821 -0.2122 -0.2364 -0.2543
0.3646 0.3596 0.3448 0.3207 0.2877 0.2469 0.1994 0.1465 0.0895 0.0301 -0.0301 -0.0895 -0.1465 -0.1994 -0.2469 -0.2877 -0.3207 -0.3448
0.4566 0.4504 0.4319 0.4016 0.3604 0.3093 0.2498 0.1834 0.1121 0.0377 -0.0377 -0.1121 -0.1834 -0.2498 -0.3093 -0.3604 -0.4016 -0.4319
0.5440 0.5366 0.5145 0.4785 0.4293 0.3685 0.2976 0.2185 0.1335 0.0449 -0.0449 -0.1335 -0.2185 -0.2976 -0.3685 -0.4293 -0.4785 -0.5145
Columns 19 through 20
0 0
0.0995 0.1008
0.1979 0.2006
0.2943 0.2984
0.3878 0.3931
0.4773 0.4839
0.5619 0.5696
0.6407 0.6496
0.7131 0.7230
0.7782 0.7889
0.8353 0.8469
0.8840 0.8962
0.9236 0.9364
0.9538 0.9670
0.9743 0.9878
0.9848 0.9985
0.9853 0.9990
0.9758 0.9893
0.9563 0.9696
0.9271 0.9399
0.8884 0.9007
0.8407 0.8523
0.7844 0.7952
0.7201 0.7300
0.6484 0.6574
0.5702 0.5781
0.4861 0.4928
0.3971 0.4026
0.3040 0.3082
0.2078 0.2107
0.1095 0.1111
0.0101 0.0103
-0.0894 -0.0906
-0.1880 -0.1906
-0.2847 -0.2886
-0.3784 -0.3837
-0.4684 -0.4748
-0.5535 -0.5612
-0.6330 -0.6418
-0.7061 -0.7158
-0.7719 -0.7826
-0.8299 -0.8414
-0.8794 -0.8916
-0.9200 -0.9327
-0.9512 -0.9643
-0.9726 -0.9861
-0.9842 -0.9978
-0.9858 -0.9994
-0.9772 -0.9908
-0.9588 -0.9720
-0.9305 -0.9434
-0.8928 -0.9051
-0.8459 -0.8576
-0.7905 -0.8014
-0.7270 -0.7370
-0.6560 -0.6651
-0.5784 -0.5864
-0.4949 -0.5017
-0.4063 -0.4120
-0.3136 -0.3180
-0.2177 -0.2207
-0.1196 -0.1213
-0.0203 -0.0206
0.0793 0.0804
0.1780 0.1805
0.2749 0.2787
0.3690 0.3742
0.4594 0.4658
0.5451 0.5526
0.6252 0.6338
0.6989 0.7086
0.7656 0.7761
0.8244 0.8358
0.8748 0.8869
0.9163 0.9289
0.9484 0.9615
0.9709 0.9843
0.9835 0.9971
0.9861 0.9997
0.9786 0.9921
0.9611 0.9744
0.9338 0.9467
0.8970 0.9094
0.8511 0.8629
0.7965 0.8075
0.7338 0.7439
0.6636 0.6727
0.5866 0.5947
0.5036 0.5106
0.4156 0.4213
0.3232 0.3277
0.2276 0.2308
0.1297 0.1315
0.0304 0.0308
-0.0692 -0.0701
-0.1680 -0.1703
-0.2652 -0.2688
-0.3596 -0.3646
-0.4504 -0.4566
-0.5366 -0.5440
velocity =
velocity(:,:,1) =
Columns 1 through 18
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995
0 0.0875 0.1727 0.2531 0.3266 0.3912 0.4452 0.4870 0.5155 0.5300 0.5300 0.5155 0.4870 0.4452 0.3912 0.3266 0.2531 0.1727
0 0.0730 0.1441 0.2112 0.2725 0.3264 0.3714 0.4063 0.4301 0.4422 0.4422 0.4301 0.4063 0.3714 0.3264 0.2725 0.2112 0.1441
0 0.0578 0.1140 0.1671 0.2156 0.2583 0.2939 0.3215 0.3403 0.3498 0.3498 0.3403 0.3215 0.2939 0.2583 0.2156 0.1671 0.1140
0 0.0419 0.0827 0.1213 0.1565 0.1875 0.2133 0.2334 0.2470 0.2540 0.2540 0.2470 0.2334 0.2133 0.1875 0.1565 0.1213 0.0827
0 0.0257 0.0507 0.0743 0.0958 0.1148 0.1306 0.1429 0.1512 0.1555 0.1555 0.1512 0.1429 0.1306 0.1148 0.0958 0.0743 0.0507
0 0.0092 0.0181 0.0265 0.0342 0.0409 0.0466 0.0509 0.0539 0.0554 0.0554 0.0539 0.0509 0.0466 0.0409 0.0342 0.0265 0.0181
0 -0.0075 -0.0147 -0.0216 -0.0279 -0.0334 -0.0380 -0.0415 -0.0440 -0.0452 -0.0452 -0.0440 -0.0415 -0.0380 -0.0334 -0.0279 -0.0216 -0.0147
0 -0.0240 -0.0474 -0.0694 -0.0896 -0.1073 -0.1221 -0.1336 -0.1414 -0.1454 -0.1454 -0.1414 -0.1336 -0.1221 -0.1073 -0.0896 -0.0694 -0.0474
0 -0.0403 -0.0795 -0.1165 -0.1504 -0.1802 -0.2050 -0.2242 -0.2374 -0.2440 -0.2440 -0.2374 -0.2242 -0.2050 -0.1802 -0.1504 -0.1165 -0.0795
0 -0.0562 -0.1108 -0.1625 -0.2097 -0.2512 -0.2858 -0.3126 -0.3309 -0.3402 -0.3402 -0.3309 -0.3126 -0.2858 -0.2512 -0.2097 -0.1625 -0.1108
0 -0.0715 -0.1411 -0.2068 -0.2668 -0.3196 -0.3637 -0.3978 -0.4211 -0.4329 -0.4329 -0.4211 -0.3978 -0.3637 -0.3196 -0.2668 -0.2068 -0.1411
0 -0.0861 -0.1698 -0.2489 -0.3213 -0.3848 -0.4379 -0.4790 -0.5070 -0.5213 -0.5213 -0.5070 -0.4790 -0.4379 -0.3848 -0.3213 -0.2489 -0.1698
0 -0.0998 -0.1969 -0.2886 -0.3724 -0.4461 -0.5076 -0.5553 -0.5878 -0.6043 -0.6043 -0.5878 -0.5553 -0.5076 -0.4461 -0.3724 -0.2886 -0.1969
0 -0.1125 -0.2219 -0.3253 -0.4198 -0.5028 -0.5721 -0.6259 -0.6625 -0.6811 -0.6811 -0.6625 -0.6259 -0.5721 -0.5028 -0.4198 -0.3253 -0.2219
0 -0.1240 -0.2447 -0.3587 -0.4628 -0.5544 -0.6308 -0.6901 -0.7305 -0.7510 -0.7510 -0.7305 -0.6901 -0.6308 -0.5544 -0.4628 -0.3587 -0.2447
0 -0.1343 -0.2650 -0.3884 -0.5012 -0.6004 -0.6831 -0.7473 -0.7910 -0.8132 -0.8132 -0.7910 -0.7473 -0.6831 -0.6004 -0.5012 -0.3884 -0.2650
0 -0.1432 -0.2825 -0.4141 -0.5344 -0.6402 -0.7284 -0.7968 -0.8435 -0.8672 -0.8672 -0.8435 -0.7968 -0.7284 -0.6402 -0.5344 -0.4141 -0.2825
0 -0.1507 -0.2972 -0.4357 -0.5622 -0.6735 -0.7663 -0.8383 -0.8874 -0.9123 -0.9123 -0.8874 -0.8383 -0.7663 -0.6735 -0.5622 -0.4357 -0.2972
0 -0.1566 -0.3089 -0.4528 -0.5843 -0.6999 -0.7964 -0.8712 -0.9222 -0.9481 -0.9481 -0.9222 -0.8712 -0.7964 -0.6999 -0.5843 -0.4528 -0.3089
0 -0.1609 -0.3174 -0.4653 -0.6004 -0.7192 -0.8184 -0.8952 -0.9476 -0.9742 -0.9742 -0.9476 -0.8952 -0.8184 -0.7192 -0.6004 -0.4653 -0.3174
0 -0.1636 -0.3227 -0.4730 -0.6104 -0.7312 -0.8320 -0.9101 -0.9634 -0.9904 -0.9904 -0.9634 -0.9101 -0.8320 -0.7312 -0.6104 -0.4730 -0.3227
0 -0.1646 -0.3247 -0.4759 -0.6142 -0.7357 -0.8371 -0.9157 -0.9693 -0.9965 -0.9965 -0.9693 -0.9157 -0.8371 -0.7357 -0.6142 -0.4759 -0.3247
0 -0.1639 -0.3234 -0.4740 -0.6117 -0.7327 -0.8337 -0.9120 -0.9654 -0.9925 -0.9925 -0.9654 -0.9120 -0.8337 -0.7327 -0.6117 -0.4740 -0.3234
0 -0.1616 -0.3187 -0.4672 -0.6030 -0.7222 -0.8218 -0.8990 -0.9516 -0.9783 -0.9783 -0.9516 -0.8990 -0.8218 -0.7222 -0.6030 -0.4672 -0.3187
0 -0.1576 -0.3109 -0.4557 -0.5881 -0.7044 -0.8015 -0.8768 -0.9282 -0.9542 -0.9542 -0.9282 -0.8768 -0.8015 -0.7044 -0.5881 -0.4557 -0.3109
0 -0.1520 -0.2999 -0.4395 -0.5672 -0.6794 -0.7731 -0.8457 -0.8952 -0.9203 -0.9203 -0.8952 -0.8457 -0.7731 -0.6794 -0.5672 -0.4395 -0.2999
0 -0.1449 -0.2858 -0.4189 -0.5406 -0.6475 -0.7368 -0.8060 -0.8531 -0.8771 -0.8771 -0.8531 -0.8060 -0.7368 -0.6475 -0.5406 -0.4189 -0.2858
0 -0.1362 -0.2688 -0.3939 -0.5084 -0.6090 -0.6929 -0.7580 -0.8024 -0.8249 -0.8249 -0.8024 -0.7580 -0.6929 -0.6090 -0.5084 -0.3939 -0.2688
0 -0.1262 -0.2490 -0.3650 -0.4710 -0.5642 -0.6420 -0.7023 -0.7434 -0.7643 -0.7643 -0.7434 -0.7023 -0.6420 -0.5642 -0.4710 -0.3650 -0.2490
0 -0.1149 -0.2267 -0.3323 -0.4289 -0.5137 -0.5846 -0.6395 -0.6769 -0.6959 -0.6959 -0.6769 -0.6395 -0.5846 -0.5137 -0.4289 -0.3323 -0.2267
0 -0.1025 -0.2021 -0.2963 -0.3824 -0.4580 -0.5212 -0.5701 -0.6035 -0.6204 -0.6204 -0.6035 -0.5701 -0.5212 -0.4580 -0.3824 -0.2963 -0.2021
0 -0.0890 -0.1755 -0.2572 -0.3320 -0.3976 -0.4524 -0.4949 -0.5239 -0.5386 -0.5386 -0.5239 -0.4949 -0.4524 -0.3976 -0.3320 -0.2572 -0.1755
0 -0.0745 -0.1470 -0.2155 -0.2781 -0.3332 -0.3791 -0.4147 -0.4390 -0.4513 -0.4513 -0.4390 -0.4147 -0.3791 -0.3332 -0.2781 -0.2155 -0.1470
0 -0.0594 -0.1171 -0.1716 -0.2215 -0.2653 -0.3019 -0.3303 -0.3496 -0.3594 -0.3594 -0.3496 -0.3303 -0.3019 -0.2653 -0.2215 -0.1716 -0.1171
0 -0.0436 -0.0860 -0.1260 -0.1626 -0.1948 -0.2216 -0.2425 -0.2566 -0.2638 -0.2638 -0.2566 -0.2425 -0.2216 -0.1948 -0.1626 -0.1260 -0.0860
0 -0.0273 -0.0540 -0.0791 -0.1021 -0.1222 -0.1391 -0.1522 -0.1611 -0.1656 -0.1656 -0.1611 -0.1522 -0.1391 -0.1222 -0.1021 -0.0791 -0.0540
0 -0.0108 -0.0214 -0.0314 -0.0405 -0.0485 -0.0551 -0.0603 -0.0639 -0.0657 -0.0657 -0.0639 -0.0603 -0.0551 -0.0485 -0.0405 -0.0314 -0.0214
0 0.0058 0.0114 0.0167 0.0215 0.0258 0.0294 0.0321 0.0340 0.0350 0.0350 0.0340 0.0321 0.0294 0.0258 0.0215 0.0167 0.0114
0 0.0223 0.0441 0.0646 0.0833 0.0998 0.1136 0.1242 0.1315 0.1352 0.1352 0.1315 0.1242 0.1136 0.0998 0.0833 0.0646 0.0441
0 0.0387 0.0763 0.1118 0.1443 0.1728 0.1966 0.2151 0.2277 0.2341 0.2341 0.2277 0.2151 0.1966 0.1728 0.1443 0.1118 0.0763
0 0.0546 0.1077 0.1579 0.2037 0.2440 0.2777 0.3038 0.3216 0.3306 0.3306 0.3216 0.3038 0.2777 0.2440 0.2037 0.1579 0.1077
0 0.0700 0.1380 0.2023 0.2611 0.3128 0.3559 0.3893 0.4121 0.4237 0.4237 0.4121 0.3893 0.3559 0.3128 0.2611 0.2023 0.1380
0 0.0846 0.1670 0.2448 0.3159 0.3783 0.4305 0.4709 0.4985 0.5125 0.5125 0.4985 0.4709 0.4305 0.3783 0.3159 0.2448 0.1670
0 0.0984 0.1942 0.2847 0.3674 0.4400 0.5007 0.5477 0.5798 0.5961 0.5961 0.5798 0.5477 0.5007 0.4400 0.3674 0.2847 0.1942
0 0.1112 0.2195 0.3217 0.4151 0.4973 0.5658 0.6190 0.6552 0.6736 0.6736 0.6552 0.6190 0.5658 0.4973 0.4151 0.3217 0.2195
0 0.1229 0.2425 0.3554 0.4587 0.5494 0.6252 0.6839 0.7239 0.7442 0.7442 0.7239 0.6839 0.6252 0.5494 0.4587 0.3554 0.2425
0 0.1333 0.2630 0.3855 0.4975 0.5959 0.6781 0.7418 0.7852 0.8072 0.8072 0.7852 0.7418 0.6781 0.5959 0.4975 0.3855 0.2630
0 0.1424 0.2809 0.4117 0.5313 0.6364 0.7242 0.7922 0.8385 0.8621 0.8621 0.8385 0.7922 0.7242 0.6364 0.5313 0.4117 0.2809
0 0.1500 0.2959 0.4337 0.5597 0.6704 0.7628 0.8345 0.8833 0.9081 0.9081 0.8833 0.8345 0.7628 0.6704 0.5597 0.4337 0.2959
0 0.1561 0.3078 0.4512 0.5823 0.6975 0.7937 0.8682 0.9191 0.9449 0.9449 0.9191 0.8682 0.7937 0.6975 0.5823 0.4512 0.3078
0 0.1605 0.3167 0.4642 0.5991 0.7176 0.8165 0.8932 0.9455 0.9720 0.9720 0.9455 0.8932 0.8165 0.7176 0.5991 0.4642 0.3167
0 0.1634 0.3223 0.4724 0.6097 0.7303 0.8310 0.9090 0.9622 0.9892 0.9892 0.9622 0.9090 0.8310 0.7303 0.6097 0.4724 0.3223
0 0.1646 0.3246 0.4758 0.6141 0.7356 0.8370 0.9156 0.9692 0.9964 0.9964 0.9692 0.9156 0.8370 0.7356 0.6141 0.4758 0.3246
0 0.1641 0.3236 0.4744 0.6122 0.7333 0.8345 0.9128 0.9663 0.9934 0.9934 0.9663 0.9128 0.8345 0.7333 0.6122 0.4744 0.3236
0 0.1619 0.3194 0.4681 0.6041 0.7236 0.8234 0.9007 0.9535 0.9802 0.9802 0.9535 0.9007 0.8234 0.7236 0.6041 0.4681 0.3194
0 0.1581 0.3118 0.4571 0.5899 0.7066 0.8040 0.8795 0.9310 0.9571 0.9571 0.9310 0.8795 0.8040 0.7066 0.5899 0.4571 0.3118
0 0.1526 0.3011 0.4414 0.5696 0.6823 0.7764 0.8493 0.8990 0.9242 0.9242 0.8990 0.8493 0.7764 0.6823 0.5696 0.4414 0.3011
0 0.1457 0.2873 0.4212 0.5435 0.6511 0.7408 0.8104 0.8578 0.8819 0.8819 0.8578 0.8104 0.7408 0.6511 0.5435 0.4212 0.2873
0 0.1372 0.2706 0.3967 0.5119 0.6132 0.6977 0.7632 0.8079 0.8306 0.8306 0.8079 0.7632 0.6977 0.6132 0.5119 0.3967 0.2706
0 0.1273 0.2511 0.3681 0.4751 0.5691 0.6475 0.7083 0.7498 0.7708 0.7708 0.7498 0.7083 0.6475 0.5691 0.4751 0.3681 0.2511
0 0.1161 0.2291 0.3358 0.4334 0.5191 0.5907 0.6462 0.6840 0.7032 0.7032 0.6840 0.6462 0.5907 0.5191 0.4334 0.3358 0.2291
0 0.1038 0.2047 0.3001 0.3873 0.4639 0.5279 0.5774 0.6113 0.6284 0.6284 0.6113 0.5774 0.5279 0.4639 0.3873 0.3001 0.2047
0 0.0904 0.1783 0.2613 0.3372 0.4040 0.4597 0.5028 0.5323 0.5472 0.5472 0.5323 0.5028 0.4597 0.4040 0.3372 0.2613 0.1783
0 0.0760 0.1500 0.2199 0.2838 0.3399 0.3868 0.4231 0.4479 0.4604 0.4604 0.4479 0.4231 0.3868 0.3399 0.2838 0.2199 0.1500
0 0.0609 0.1202 0.1762 0.2274 0.2724 0.3099 0.3390 0.3589 0.3689 0.3689 0.3589 0.3390 0.3099 0.2724 0.2274 0.1762 0.1202
0 0.0452 0.0892 0.1307 0.1687 0.2021 0.2299 0.2515 0.2662 0.2737 0.2737 0.2662 0.2515 0.2299 0.2021 0.1687 0.1307 0.0892
0 0.0290 0.0572 0.0839 0.1083 0.1297 0.1476 0.1614 0.1709 0.1757 0.1757 0.1709 0.1614 0.1476 0.1297 0.1083 0.0839 0.0572
0 0.0125 0.0247 0.0362 0.0468 0.0560 0.0637 0.0697 0.0738 0.0759 0.0759 0.0738 0.0697 0.0637 0.0560 0.0468 0.0362 0.0247
0 -0.0041 -0.0081 -0.0118 -0.0152 -0.0182 -0.0208 -0.0227 -0.0240 -0.0247 -0.0247 -0.0240 -0.0227 -0.0208 -0.0182 -0.0152 -0.0118 -0.0081
0 -0.0207 -0.0407 -0.0597 -0.0771 -0.0923 -0.1051 -0.1149 -0.1216 -0.1251 -0.1251 -0.1216 -0.1149 -0.1051 -0.0923 -0.0771 -0.0597 -0.0407
0 -0.0370 -0.0730 -0.1070 -0.1381 -0.1655 -0.1883 -0.2059 -0.2180 -0.2241 -0.2241 -0.2180 -0.2059 -0.1883 -0.1655 -0.1381 -0.1070 -0.0730
0 -0.0530 -0.1046 -0.1533 -0.1978 -0.2369 -0.2696 -0.2949 -0.3121 -0.3209 -0.3209 -0.3121 -0.2949 -0.2696 -0.2369 -0.1978 -0.1533 -0.1046
0 -0.0684 -0.1350 -0.1979 -0.2554 -0.3059 -0.3481 -0.3808 -0.4031 -0.4144 -0.4144 -0.4031 -0.3808 -0.3481 -0.3059 -0.2554 -0.1979 -0.1350
0 -0.0832 -0.1641 -0.2405 -0.3104 -0.3718 -0.4231 -0.4628 -0.4899 -0.5037 -0.5037 -0.4899 -0.4628 -0.4231 -0.3718 -0.3104 -0.2405 -0.1641
0 -0.0971 -0.1915 -0.2807 -0.3623 -0.4340 -0.4938 -0.5402 -0.5718 -0.5878 -0.5878 -0.5718 -0.5402 -0.4938 -0.4340 -0.3623 -0.2807 -0.1915
0 -0.1100 -0.2170 -0.3181 -0.4105 -0.4917 -0.5595 -0.6120 -0.6478 -0.6660 -0.6660 -0.6478 -0.6120 -0.5595 -0.4917 -0.4105 -0.3181 -0.2170
0 -0.1218 -0.2402 -0.3521 -0.4544 -0.5443 -0.6194 -0.6776 -0.7172 -0.7373 -0.7373 -0.7172 -0.6776 -0.6194 -0.5443 -0.4544 -0.3521 -0.2402
0 -0.1323 -0.2610 -0.3826 -0.4938 -0.5915 -0.6730 -0.7362 -0.7793 -0.8012 -0.8012 -0.7793 -0.7362 -0.6730 -0.5915 -0.4938 -0.3826 -0.2610
0 -0.1415 -0.2792 -0.4092 -0.5281 -0.6326 -0.7198 -0.7874 -0.8335 -0.8569 -0.8569 -0.8335 -0.7874 -0.7198 -0.6326 -0.5281 -0.4092 -0.2792
0 -0.1493 -0.2945 -0.4316 -0.5570 -0.6672 -0.7592 -0.8305 -0.8792 -0.9038 -0.9038 -0.8792 -0.8305 -0.7592 -0.6672 -0.5570 -0.4316 -0.2945
0 -0.1555 -0.3068 -0.4497 -0.5803 -0.6951 -0.7909 -0.8652 -0.9159 -0.9416 -0.9416 -0.9159 -0.8652 -0.7909 -0.6951 -0.5803 -0.4497 -0.3068
0 -0.1602 -0.3159 -0.4631 -0.5976 -0.7159 -0.8146 -0.8911 -0.9432 -0.9697 -0.9697 -0.9432 -0.8911 -0.8146 -0.7159 -0.5976 -0.4631 -0.3159
0 -0.1632 -0.3219 -0.4718 -0.6089 -0.7293 -0.8299 -0.9078 -0.9610 -0.9879 -0.9879 -0.9610 -0.9078 -0.8299 -0.7293 -0.6089 -0.4718 -0.3219
0 -0.1645 -0.3245 -0.4757 -0.6139 -0.7354 -0.8368 -0.9153 -0.9689 -0.9961 -0.9961 -0.9689 -0.9153 -0.8368 -0.7354 -0.6139 -0.4757 -0.3245
0 -0.1642 -0.3239 -0.4748 -0.6127 -0.7339 -0.8351 -0.9135 -0.9670 -0.9941 -0.9941 -0.9670 -0.9135 -0.8351 -0.7339 -0.6127 -0.4748 -0.3239
0 -0.1622 -0.3200 -0.4690 -0.6052 -0.7250 -0.8249 -0.9024 -0.9552 -0.9820 -0.9820 -0.9552 -0.9024 -0.8249 -0.7250 -0.6052 -0.4690 -0.3200
0 -0.1585 -0.3127 -0.4584 -0.5916 -0.7086 -0.8063 -0.8821 -0.9337 -0.9599 -0.9599 -0.9337 -0.8821 -0.8063 -0.7086 -0.5916 -0.4584 -0.3127
0 -0.1533 -0.3023 -0.4432 -0.5719 -0.6851 -0.7795 -0.8527 -0.9027 -0.9280 -0.9280 -0.9027 -0.8527 -0.7795 -0.6851 -0.5719 -0.4432 -0.3023
0 -0.1464 -0.2889 -0.4234 -0.5464 -0.6545 -0.7448 -0.8147 -0.8624 -0.8866 -0.8866 -0.8624 -0.8147 -0.7448 -0.6545 -0.5464 -0.4234 -0.2889
0 -0.1381 -0.2724 -0.3994 -0.5154 -0.6173 -0.7024 -0.7684 -0.8134 -0.8362 -0.8362 -0.8134 -0.7684 -0.7024 -0.6173 -0.5154 -0.3994 -0.2724
Columns 19 through 20
0.1646 0.0000
0.1638 0.0000
0.1612 0.0000
0.1571 0.0000
0.1513 0.0000
0.1440 0.0000
0.1353 0.0000
0.1251 0.0000
0.1137 0.0000
0.1011 0.0000
0.0875 0.0000
0.0730 0.0000
0.0578 0.0000
0.0419 0.0000
0.0257 0.0000
0.0092 0.0000
-0.0075 -0.0000
-0.0240 -0.0000
-0.0403 -0.0000
-0.0562 -0.0000
-0.0715 -0.0000
-0.0861 -0.0000
-0.0998 -0.0000
-0.1125 -0.0000
-0.1240 -0.0000
-0.1343 -0.0000
-0.1432 -0.0000
-0.1507 -0.0000
-0.1566 -0.0000
-0.1609 -0.0000
-0.1636 -0.0000
-0.1646 -0.0000
-0.1639 -0.0000
-0.1616 -0.0000
-0.1576 -0.0000
-0.1520 -0.0000
-0.1449 -0.0000
-0.1362 -0.0000
-0.1262 -0.0000
-0.1149 -0.0000
-0.1025 -0.0000
-0.0890 -0.0000
-0.0745 -0.0000
-0.0594 -0.0000
-0.0436 -0.0000
-0.0273 -0.0000
-0.0108 -0.0000
0.0058 0.0000
0.0223 0.0000
0.0387 0.0000
0.0546 0.0000
0.0700 0.0000
0.0846 0.0000
0.0984 0.0000
0.1112 0.0000
0.1229 0.0000
0.1333 0.0000
0.1424 0.0000
0.1500 0.0000
0.1561 0.0000
0.1605 0.0000
0.1634 0.0000
0.1646 0.0000
0.1641 0.0000
0.1619 0.0000
0.1581 0.0000
0.1526 0.0000
0.1457 0.0000
0.1372 0.0000
0.1273 0.0000
0.1161 0.0000
0.1038 0.0000
0.0904 0.0000
0.0760 0.0000
0.0609 0.0000
0.0452 0.0000
0.0290 0.0000
0.0125 0.0000
-0.0041 -0.0000
-0.0207 -0.0000
-0.0370 -0.0000
-0.0530 -0.0000
-0.0684 -0.0000
-0.0832 -0.0000
-0.0971 -0.0000
-0.1100 -0.0000
-0.1218 -0.0000
-0.1323 -0.0000
-0.1415 -0.0000
-0.1493 -0.0000
-0.1555 -0.0000
-0.1602 -0.0000
-0.1632 -0.0000
-0.1645 -0.0000
-0.1642 -0.0000
-0.1622 -0.0000
-0.1585 -0.0000
-0.1533 -0.0000
-0.1464 -0.0000
-0.1381 -0.0000
velocity(:,:,2) =
Columns 1 through 18
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462
-0.8469 -0.8353 -0.8010 -0.7448 -0.6683 -0.5736 -0.4632 -0.3402 -0.2079 -0.0699 0.0699 0.2079 0.3402 0.4632 0.5736 0.6683 0.7448 0.8010
-0.8962 -0.8840 -0.8476 -0.7882 -0.7072 -0.6070 -0.4902 -0.3600 -0.2200 -0.0740 0.0740 0.2200 0.3600 0.4902 0.6070 0.7072 0.7882 0.8476
-0.9364 -0.9236 -0.8856 -0.8235 -0.7389 -0.6342 -0.5121 -0.3761 -0.2299 -0.0773 0.0773 0.2299 0.3761 0.5121 0.6342 0.7389 0.8235 0.8856
-0.9670 -0.9538 -0.9146 -0.8504 -0.7631 -0.6549 -0.5289 -0.3884 -0.2374 -0.0799 0.0799 0.2374 0.3884 0.5289 0.6549 0.7631 0.8504 0.9146
-0.9878 -0.9743 -0.9342 -0.8687 -0.7795 -0.6690 -0.5403 -0.3968 -0.2425 -0.0816 0.0816 0.2425 0.3968 0.5403 0.6690 0.7795 0.8687 0.9342
-0.9985 -0.9848 -0.9444 -0.8781 -0.7879 -0.6762 -0.5461 -0.4011 -0.2451 -0.0825 0.0825 0.2451 0.4011 0.5461 0.6762 0.7879 0.8781 0.9444
-0.9990 -0.9853 -0.9448 -0.8786 -0.7883 -0.6766 -0.5464 -0.4013 -0.2452 -0.0825 0.0825 0.2452 0.4013 0.5464 0.6766 0.7883 0.8786 0.9448
-0.9893 -0.9758 -0.9357 -0.8701 -0.7807 -0.6700 -0.5411 -0.3974 -0.2429 -0.0817 0.0817 0.2429 0.3974 0.5411 0.6700 0.7807 0.8701 0.9357
-0.9696 -0.9563 -0.9170 -0.8527 -0.7651 -0.6567 -0.5303 -0.3895 -0.2380 -0.0801 0.0801 0.2380 0.3895 0.5303 0.6567 0.7651 0.8527 0.9170
-0.9399 -0.9271 -0.8890 -0.8266 -0.7417 -0.6366 -0.5141 -0.3776 -0.2307 -0.0776 0.0776 0.2307 0.3776 0.5141 0.6366 0.7417 0.8266 0.8890
-0.9007 -0.8884 -0.8519 -0.7921 -0.7108 -0.6100 -0.4926 -0.3618 -0.2211 -0.0744 0.0744 0.2211 0.3618 0.4926 0.6100 0.7108 0.7921 0.8519
-0.8523 -0.8407 -0.8061 -0.7496 -0.6726 -0.5773 -0.4662 -0.3424 -0.2092 -0.0704 0.0704 0.2092 0.3424 0.4662 0.5773 0.6726 0.7496 0.8061
-0.7952 -0.7844 -0.7521 -0.6994 -0.6275 -0.5386 -0.4349 -0.3194 -0.1952 -0.0657 0.0657 0.1952 0.3194 0.4349 0.5386 0.6275 0.6994 0.7521
-0.7300 -0.7201 -0.6905 -0.6420 -0.5761 -0.4944 -0.3993 -0.2932 -0.1792 -0.0603 0.0603 0.1792 0.2932 0.3993 0.4944 0.5761 0.6420 0.6905
-0.6574 -0.6484 -0.6218 -0.5782 -0.5188 -0.4452 -0.3596 -0.2641 -0.1614 -0.0543 0.0543 0.1614 0.2641 0.3596 0.4452 0.5188 0.5782 0.6218
-0.5781 -0.5702 -0.5467 -0.5084 -0.4562 -0.3915 -0.3162 -0.2322 -0.1419 -0.0477 0.0477 0.1419 0.2322 0.3162 0.3915 0.4562 0.5084 0.5467
-0.4928 -0.4861 -0.4661 -0.4334 -0.3889 -0.3338 -0.2695 -0.1980 -0.1210 -0.0407 0.0407 0.1210 0.1980 0.2695 0.3338 0.3889 0.4334 0.4661
-0.4026 -0.3971 -0.3808 -0.3540 -0.3177 -0.2727 -0.2202 -0.1617 -0.0988 -0.0332 0.0332 0.0988 0.1617 0.2202 0.2727 0.3177 0.3540 0.3808
-0.3082 -0.3040 -0.2915 -0.2711 -0.2432 -0.2087 -0.1686 -0.1238 -0.0757 -0.0255 0.0255 0.0757 0.1238 0.1686 0.2087 0.2432 0.2711 0.2915
-0.2107 -0.2078 -0.1993 -0.1853 -0.1663 -0.1427 -0.1152 -0.0846 -0.0517 -0.0174 0.0174 0.0517 0.0846 0.1152 0.1427 0.1663 0.1853 0.1993
-0.1111 -0.1095 -0.1050 -0.0977 -0.0876 -0.0752 -0.0607 -0.0446 -0.0273 -0.0092 0.0092 0.0273 0.0446 0.0607 0.0752 0.0876 0.0977 0.1050
-0.0103 -0.0101 -0.0097 -0.0090 -0.0081 -0.0070 -0.0056 -0.0041 -0.0025 -0.0008 0.0008 0.0025 0.0041 0.0056 0.0070 0.0081 0.0090 0.0097
0.0906 0.0894 0.0857 0.0797 0.0715 0.0614 0.0496 0.0364 0.0222 0.0075 -0.0075 -0.0222 -0.0364 -0.0496 -0.0614 -0.0715 -0.0797 -0.0857
0.1906 0.1880 0.1802 0.1676 0.1504 0.1291 0.1042 0.0766 0.0468 0.0157 -0.0157 -0.0468 -0.0766 -0.1042 -0.1291 -0.1504 -0.1676 -0.1802
0.2886 0.2847 0.2730 0.2538 0.2277 0.1955 0.1578 0.1159 0.0708 0.0238 -0.0238 -0.0708 -0.1159 -0.1578 -0.1955 -0.2277 -0.2538 -0.2730
0.3837 0.3784 0.3629 0.3374 0.3028 0.2598 0.2098 0.1541 0.0942 0.0317 -0.0317 -0.0942 -0.1541 -0.2098 -0.2598 -0.3028 -0.3374 -0.3629
0.4748 0.4684 0.4491 0.4176 0.3747 0.3216 0.2597 0.1907 0.1166 0.0392 -0.0392 -0.1166 -0.1907 -0.2597 -0.3216 -0.3747 -0.4176 -0.4491
0.5612 0.5535 0.5308 0.4935 0.4428 0.3801 0.3069 0.2254 0.1378 0.0463 -0.0463 -0.1378 -0.2254 -0.3069 -0.3801 -0.4428 -0.4935 -0.5308
0.6418 0.6330 0.6070 0.5644 0.5064 0.4347 0.3510 0.2578 0.1575 0.0530 -0.0530 -0.1575 -0.2578 -0.3510 -0.4347 -0.5064 -0.5644 -0.6070
0.7158 0.7061 0.6770 0.6295 0.5649 0.4848 0.3915 0.2875 0.1757 0.0591 -0.0591 -0.1757 -0.2875 -0.3915 -0.4848 -0.5649 -0.6295 -0.6770
0.7826 0.7719 0.7402 0.6883 0.6176 0.5300 0.4280 0.3144 0.1921 0.0646 -0.0646 -0.1921 -0.3144 -0.4280 -0.5300 -0.6176 -0.6883 -0.7402
0.8414 0.8299 0.7958 0.7400 0.6640 0.5698 0.4602 0.3380 0.2065 0.0695 -0.0695 -0.2065 -0.3380 -0.4602 -0.5698 -0.6640 -0.7400 -0.7958
0.8916 0.8794 0.8433 0.7841 0.7036 0.6039 0.4877 0.3581 0.2189 0.0736 -0.0736 -0.2189 -0.3581 -0.4877 -0.6039 -0.7036 -0.7841 -0.8433
0.9327 0.9200 0.8822 0.8203 0.7360 0.6317 0.5101 0.3747 0.2290 0.0770 -0.0770 -0.2290 -0.3747 -0.5101 -0.6317 -0.7360 -0.8203 -0.8822
0.9643 0.9512 0.9121 0.8481 0.7610 0.6531 0.5274 0.3874 0.2367 0.0796 -0.0796 -0.2367 -0.3874 -0.5274 -0.6531 -0.7610 -0.8481 -0.9121
0.9861 0.9726 0.9327 0.8672 0.7782 0.6679 0.5393 0.3961 0.2421 0.0814 -0.0814 -0.2421 -0.3961 -0.5393 -0.6679 -0.7782 -0.8672 -0.9327
0.9978 0.9842 0.9438 0.8776 0.7874 0.6758 0.5458 0.4008 0.2450 0.0824 -0.0824 -0.2450 -0.4008 -0.5458 -0.6758 -0.7874 -0.8776 -0.9438
0.9994 0.9858 0.9452 0.8789 0.7887 0.6769 0.5466 0.4014 0.2453 0.0825 -0.0825 -0.2453 -0.4014 -0.5466 -0.6769 -0.7887 -0.8789 -0.9452
0.9908 0.9772 0.9371 0.8713 0.7818 0.6710 0.5419 0.3980 0.2432 0.0818 -0.0818 -0.2432 -0.3980 -0.5419 -0.6710 -0.7818 -0.8713 -0.9371
0.9720 0.9588 0.9194 0.8549 0.7671 0.6583 0.5316 0.3905 0.2386 0.0803 -0.0803 -0.2386 -0.3905 -0.5316 -0.6583 -0.7671 -0.8549 -0.9194
0.9434 0.9305 0.8923 0.8297 0.7445 0.6389 0.5160 0.3790 0.2316 0.0779 -0.0779 -0.2316 -0.3790 -0.5160 -0.6389 -0.7445 -0.8297 -0.8923
0.9051 0.8928 0.8561 0.7960 0.7143 0.6130 0.4951 0.3636 0.2222 0.0747 -0.0747 -0.2222 -0.3636 -0.4951 -0.6130 -0.7143 -0.7960 -0.8561
0.8576 0.8459 0.8112 0.7543 0.6768 0.5809 0.4691 0.3445 0.2105 0.0708 -0.0708 -0.2105 -0.3445 -0.4691 -0.5809 -0.6768 -0.7543 -0.8112
0.8014 0.7905 0.7580 0.7048 0.6324 0.5428 0.4383 0.3219 0.1967 0.0662 -0.0662 -0.1967 -0.3219 -0.4383 -0.5428 -0.6324 -0.7048 -0.7580
0.7370 0.7270 0.6971 0.6482 0.5816 0.4992 0.4031 0.2961 0.1809 0.0609 -0.0609 -0.1809 -0.2961 -0.4031 -0.4992 -0.5816 -0.6482 -0.6971
0.6651 0.6560 0.6291 0.5849 0.5249 0.4505 0.3638 0.2672 0.1633 0.0549 -0.0549 -0.1633 -0.2672 -0.3638 -0.4505 -0.5249 -0.5849 -0.6291
0.5864 0.5784 0.5546 0.5157 0.4628 0.3972 0.3207 0.2356 0.1440 0.0484 -0.0484 -0.1440 -0.2356 -0.3207 -0.3972 -0.4628 -0.5157 -0.5546
0.5017 0.4949 0.4746 0.4413 0.3959 0.3398 0.2744 0.2015 0.1232 0.0414 -0.0414 -0.1232 -0.2015 -0.2744 -0.3398 -0.3959 -0.4413 -0.4746
0.4120 0.4063 0.3896 0.3623 0.3251 0.2790 0.2253 0.1655 0.1011 0.0340 -0.0340 -0.1011 -0.1655 -0.2253 -0.2790 -0.3251 -0.3623 -0.3896
0.3180 0.3136 0.3007 0.2796 0.2509 0.2154 0.1739 0.1277 0.0781 0.0263 -0.0263 -0.0781 -0.1277 -0.1739 -0.2154 -0.2509 -0.2796 -0.3007
0.2207 0.2177 0.2088 0.1941 0.1742 0.1495 0.1207 0.0887 0.0542 0.0182 -0.0182 -0.0542 -0.0887 -0.1207 -0.1495 -0.1742 -0.1941 -0.2088
0.1213 0.1196 0.1147 0.1067 0.0957 0.0821 0.0663 0.0487 0.0298 0.0100 -0.0100 -0.0298 -0.0487 -0.0663 -0.0821 -0.0957 -0.1067 -0.1147
0.0206 0.0203 0.0194 0.0181 0.0162 0.0139 0.0112 0.0083 0.0050 0.0017 -0.0017 -0.0050 -0.0083 -0.0112 -0.0139 -0.0162 -0.0181 -0.0194
-0.0804 -0.0793 -0.0760 -0.0707 -0.0634 -0.0544 -0.0440 -0.0323 -0.0197 -0.0066 0.0066 0.0197 0.0323 0.0440 0.0544 0.0634 0.0707 0.0760
-0.1805 -0.1780 -0.1707 -0.1587 -0.1424 -0.1222 -0.0987 -0.0725 -0.0443 -0.0149 0.0149 0.0443 0.0725 0.0987 0.1222 0.1424 0.1587 0.1707
-0.2787 -0.2749 -0.2636 -0.2451 -0.2200 -0.1888 -0.1525 -0.1120 -0.0684 -0.0230 0.0230 0.0684 0.1120 0.1525 0.1888 0.2200 0.2451 0.2636
-0.3742 -0.3690 -0.3539 -0.3291 -0.2953 -0.2534 -0.2046 -0.1503 -0.0918 -0.0309 0.0309 0.0918 0.1503 0.2046 0.2534 0.2953 0.3291 0.3539
-0.4658 -0.4594 -0.4405 -0.4096 -0.3675 -0.3154 -0.2547 -0.1871 -0.1143 -0.0385 0.0385 0.1143 0.1871 0.2547 0.3154 0.3675 0.4096 0.4405
-0.5526 -0.5451 -0.5227 -0.4860 -0.4361 -0.3743 -0.3023 -0.2220 -0.1357 -0.0456 0.0456 0.1357 0.2220 0.3023 0.3743 0.4361 0.4860 0.5227
-0.6338 -0.6252 -0.5995 -0.5574 -0.5002 -0.4293 -0.3467 -0.2546 -0.1556 -0.0523 0.0523 0.1556 0.2546 0.3467 0.4293 0.5002 0.5574 0.5995
-0.7086 -0.6989 -0.6702 -0.6232 -0.5592 -0.4799 -0.3876 -0.2846 -0.1740 -0.0585 0.0585 0.1740 0.2846 0.3876 0.4799 0.5592 0.6232 0.6702
-0.7761 -0.7656 -0.7341 -0.6826 -0.6125 -0.5257 -0.4245 -0.3118 -0.1905 -0.0641 0.0641 0.1905 0.3118 0.4245 0.5257 0.6125 0.6826 0.7341
-0.8358 -0.8244 -0.7905 -0.7350 -0.6595 -0.5661 -0.4571 -0.3357 -0.2052 -0.0690 0.0690 0.2052 0.3357 0.4571 0.5661 0.6595 0.7350 0.7905
-0.8869 -0.8748 -0.8388 -0.7800 -0.6999 -0.6007 -0.4851 -0.3563 -0.2177 -0.0732 0.0732 0.2177 0.3563 0.4851 0.6007 0.6999 0.7800 0.8388
-0.9289 -0.9163 -0.8786 -0.8170 -0.7331 -0.6292 -0.5081 -0.3732 -0.2280 -0.0767 0.0767 0.2280 0.3732 0.5081 0.6292 0.7331 0.8170 0.8786
-0.9615 -0.9484 -0.9094 -0.8457 -0.7588 -0.6512 -0.5259 -0.3862 -0.2360 -0.0794 0.0794 0.2360 0.3862 0.5259 0.6512 0.7588 0.8457 0.9094
-0.9843 -0.9709 -0.9310 -0.8657 -0.7768 -0.6667 -0.5384 -0.3954 -0.2416 -0.0813 0.0813 0.2416 0.3954 0.5384 0.6667 0.7768 0.8657 0.9310
-0.9971 -0.9835 -0.9431 -0.8769 -0.7869 -0.6753 -0.5454 -0.4005 -0.2448 -0.0823 0.0823 0.2448 0.4005 0.5454 0.6753 0.7869 0.8769 0.9431
-0.9997 -0.9861 -0.9455 -0.8792 -0.7889 -0.6771 -0.5468 -0.4016 -0.2454 -0.0826 0.0826 0.2454 0.4016 0.5468 0.6771 0.7889 0.8792 0.9455
-0.9921 -0.9786 -0.9383 -0.8725 -0.7829 -0.6719 -0.5426 -0.3985 -0.2435 -0.0819 0.0819 0.2435 0.3985 0.5426 0.6719 0.7829 0.8725 0.9383
-0.9744 -0.9611 -0.9216 -0.8569 -0.7689 -0.6599 -0.5329 -0.3914 -0.2392 -0.0805 0.0805 0.2392 0.3914 0.5329 0.6599 0.7689 0.8569 0.9216
-0.9467 -0.9338 -0.8954 -0.8326 -0.7471 -0.6412 -0.5178 -0.3803 -0.2324 -0.0782 0.0782 0.2324 0.3803 0.5178 0.6412 0.7471 0.8326 0.8954
-0.9094 -0.8970 -0.8602 -0.7998 -0.7177 -0.6160 -0.4974 -0.3653 -0.2233 -0.0751 0.0751 0.2233 0.3653 0.4974 0.6160 0.7177 0.7998 0.8602
-0.8629 -0.8511 -0.8161 -0.7589 -0.6809 -0.5844 -0.4720 -0.3466 -0.2118 -0.0713 0.0713 0.2118 0.3466 0.4720 0.5844 0.6809 0.7589 0.8161
-0.8075 -0.7965 -0.7638 -0.7102 -0.6372 -0.5469 -0.4417 -0.3244 -0.1982 -0.0667 0.0667 0.1982 0.3244 0.4417 0.5469 0.6372 0.7102 0.7638
-0.7439 -0.7338 -0.7036 -0.6543 -0.5871 -0.5038 -0.4069 -0.2988 -0.1826 -0.0614 0.0614 0.1826 0.2988 0.4069 0.5038 0.5871 0.6543 0.7036
-0.6727 -0.6636 -0.6363 -0.5917 -0.5309 -0.4556 -0.3680 -0.2702 -0.1651 -0.0556 0.0556 0.1651 0.2702 0.3680 0.4556 0.5309 0.5917 0.6363
-0.5947 -0.5866 -0.5625 -0.5230 -0.4693 -0.4028 -0.3253 -0.2389 -0.1460 -0.0491 0.0491 0.1460 0.2389 0.3253 0.4028 0.4693 0.5230 0.5625
-0.5106 -0.5036 -0.4829 -0.4491 -0.4029 -0.3458 -0.2793 -0.2051 -0.1253 -0.0422 0.0422 0.1253 0.2051 0.2793 0.3458 0.4029 0.4491 0.4829
-0.4213 -0.4156 -0.3985 -0.3705 -0.3325 -0.2853 -0.2304 -0.1692 -0.1034 -0.0348 0.0348 0.1034 0.1692 0.2304 0.2853 0.3325 0.3705 0.3985
-0.3277 -0.3232 -0.3099 -0.2882 -0.2586 -0.2219 -0.1792 -0.1316 -0.0804 -0.0271 0.0271 0.0804 0.1316 0.1792 0.2219 0.2586 0.2882 0.3099
-0.2308 -0.2276 -0.2183 -0.2029 -0.1821 -0.1563 -0.1262 -0.0927 -0.0566 -0.0191 0.0191 0.0566 0.0927 0.1262 0.1563 0.1821 0.2029 0.2183
-0.1315 -0.1297 -0.1243 -0.1156 -0.1037 -0.0890 -0.0719 -0.0528 -0.0323 -0.0109 0.0109 0.0323 0.0528 0.0719 0.0890 0.1037 0.1156 0.1243
-0.0308 -0.0304 -0.0292 -0.0271 -0.0243 -0.0209 -0.0169 -0.0124 -0.0076 -0.0025 0.0025 0.0076 0.0124 0.0169 0.0209 0.0243 0.0271 0.0292
0.0701 0.0692 0.0663 0.0617 0.0553 0.0475 0.0383 0.0282 0.0172 0.0058 -0.0058 -0.0172 -0.0282 -0.0383 -0.0475 -0.0553 -0.0617 -0.0663
0.1703 0.1680 0.1611 0.1498 0.1344 0.1154 0.0932 0.0684 0.0418 0.0141 -0.0141 -0.0418 -0.0684 -0.0932 -0.1154 -0.1344 -0.1498 -0.1611
0.2688 0.2652 0.2543 0.2364 0.2122 0.1821 0.1470 0.1080 0.0660 0.0222 -0.0222 -0.0660 -0.1080 -0.1470 -0.1821 -0.2122 -0.2364 -0.2543
0.3646 0.3596 0.3448 0.3207 0.2877 0.2469 0.1994 0.1465 0.0895 0.0301 -0.0301 -0.0895 -0.1465 -0.1994 -0.2469 -0.2877 -0.3207 -0.3448
0.4566 0.4504 0.4319 0.4016 0.3604 0.3093 0.2498 0.1834 0.1121 0.0377 -0.0377 -0.1121 -0.1834 -0.2498 -0.3093 -0.3604 -0.4016 -0.4319
0.5440 0.5366 0.5145 0.4785 0.4293 0.3685 0.2976 0.2185 0.1335 0.0449 -0.0449 -0.1335 -0.2185 -0.2976 -0.3685 -0.4293 -0.4785 -0.5145
Columns 19 through 20
0 0
0.0995 0.1008
0.1979 0.2006
0.2943 0.2984
0.3878 0.3931
0.4773 0.4839
0.5619 0.5696
0.6407 0.6496
0.7131 0.7230
0.7782 0.7889
0.8353 0.8469
0.8840 0.8962
0.9236 0.9364
0.9538 0.9670
0.9743 0.9878
0.9848 0.9985
0.9853 0.9990
0.9758 0.9893
0.9563 0.9696
0.9271 0.9399
0.8884 0.9007
0.8407 0.8523
0.7844 0.7952
0.7201 0.7300
0.6484 0.6574
0.5702 0.5781
0.4861 0.4928
0.3971 0.4026
0.3040 0.3082
0.2078 0.2107
0.1095 0.1111
0.0101 0.0103
-0.0894 -0.0906
-0.1880 -0.1906
-0.2847 -0.2886
-0.3784 -0.3837
-0.4684 -0.4748
-0.5535 -0.5612
-0.6330 -0.6418
-0.7061 -0.7158
-0.7719 -0.7826
-0.8299 -0.8414
-0.8794 -0.8916
-0.9200 -0.9327
-0.9512 -0.9643
-0.9726 -0.9861
-0.9842 -0.9978
-0.9858 -0.9994
-0.9772 -0.9908
-0.9588 -0.9720
-0.9305 -0.9434
-0.8928 -0.9051
-0.8459 -0.8576
-0.7905 -0.8014
-0.7270 -0.7370
-0.6560 -0.6651
-0.5784 -0.5864
-0.4949 -0.5017
-0.4063 -0.4120
-0.3136 -0.3180
-0.2177 -0.2207
-0.1196 -0.1213
-0.0203 -0.0206
0.0793 0.0804
0.1780 0.1805
0.2749 0.2787
0.3690 0.3742
0.4594 0.4658
0.5451 0.5526
0.6252 0.6338
0.6989 0.7086
0.7656 0.7761
0.8244 0.8358
0.8748 0.8869
0.9163 0.9289
0.9484 0.9615
0.9709 0.9843
0.9835 0.9971
0.9861 0.9997
0.9786 0.9921
0.9611 0.9744
0.9338 0.9467
0.8970 0.9094
0.8511 0.8629
0.7965 0.8075
0.7338 0.7439
0.6636 0.6727
0.5866 0.5947
0.5036 0.5106
0.4156 0.4213
0.3232 0.3277
0.2276 0.2308
0.1297 0.1315
0.0304 0.0308
-0.0692 -0.0701
-0.1680 -0.1703
-0.2652 -0.2688
-0.3596 -0.3646
-0.4504 -0.4566
-0.5366 -0.5440
velocity(:,:,3) =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
% where vx = cos(beta)*sin(alpha),
%
% and vy is something similar.
%
% The surface plot will be against beta and alpha, so I write
% vx_times_ip = vx .* ip(theta)
.
Noob
on 2 Jan 2025
Looping through beta and alpha causes issues with the functions not being matrices, and so the surface plot won't work. Let me try your suggestion above. Will report back sometime tonight. Thanks Star Strider!
My pleasure!
With respect to the surface plot, you could do something lke this —
alpha = linspace(0,pi,20)
alpha = 1×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
beta = linspace(0,10,100)
beta = 1×100
0 0.1010 0.2020 0.3030 0.4040 0.5051 0.6061 0.7071 0.8081 0.9091 1.0101 1.1111 1.2121 1.3131 1.4141 1.5152 1.6162 1.7172 1.8182 1.9192 2.0202 2.1212 2.2222 2.3232 2.4242 2.5253 2.6263 2.7273 2.8283 2.9293
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
theta = zeros(size(beta));
[Alpha, Beta] = meshgrid(alpha, beta),
Alpha = 100×20
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
0 0.1653 0.3307 0.4960 0.6614 0.8267 0.9921 1.1574 1.3228 1.4881 1.6535 1.8188 1.9842 2.1495 2.3149 2.4802 2.6456 2.8109 2.9762 3.1416
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Beta = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010 0.1010
0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020 0.2020
0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030 0.3030
0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040 0.4040
0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051 0.5051
0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061 0.6061
0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071 0.7071
0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081 0.8081
0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091 0.9091
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
i = rand
i = 0.9926
j = rand
j = 0.5299
vx = cos(Beta) .* sin(Alpha)
vx = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
vy = -sin(Beta) .* cos(Alpha)
vy = 100×20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954 0.0995 0.1008
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898 0.1979 0.2006
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822 0.2943 0.2984
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718 0.3878 0.3931
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576 0.4773 0.4839
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388 0.5619 0.5696
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144 0.6407 0.6496
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838 0.7131 0.7230
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462 0.7782 0.7889
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
ip = @(theta) [ cos(theta(:)) sin(theta(:)) zeros(size(theta(:)))]
ip = function_handle with value:
@(theta)[cos(theta(:)),sin(theta(:)),zeros(size(theta(:)))]
jp = @(theta) [-sin(theta(:)) cos(theta(:)) zeros(size(theta(:)))]
jp = function_handle with value:
@(theta)[-sin(theta(:)),cos(theta(:)),zeros(size(theta(:)))]
kp = @(theta) [zeros(size(theta(:))) zeros(size(theta(:))) ones(size(theta(:)))]
kp = function_handle with value:
@(theta)[zeros(size(theta(:))),zeros(size(theta(:))),ones(size(theta(:)))]
ipm = ip(theta)
ipm = 100×3
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
1 0 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
jpm = jp(theta)
jpm = 100×3
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
for k = 1:3
velocity(:,:,k) = vx .* ipm(:,k) + vy .* jpm(:,k) % Cell Array Or 3D Matrix Necessary Here
end
velocity = 100×20
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247 0.1646 0.0000
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230 0.1638 0.0000
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181 0.1612 0.0000
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099 0.1571 0.0000
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986 0.1513 0.0000
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842 0.1440 0.0000
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669 0.1353 0.0000
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469 0.1251 0.0000
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243 0.1137 0.0000
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995 0.1011 0.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
velocity =
velocity(:,:,1) =
Columns 1 through 18
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995
0 0.0875 0.1727 0.2531 0.3266 0.3912 0.4452 0.4870 0.5155 0.5300 0.5300 0.5155 0.4870 0.4452 0.3912 0.3266 0.2531 0.1727
0 0.0730 0.1441 0.2112 0.2725 0.3264 0.3714 0.4063 0.4301 0.4422 0.4422 0.4301 0.4063 0.3714 0.3264 0.2725 0.2112 0.1441
0 0.0578 0.1140 0.1671 0.2156 0.2583 0.2939 0.3215 0.3403 0.3498 0.3498 0.3403 0.3215 0.2939 0.2583 0.2156 0.1671 0.1140
0 0.0419 0.0827 0.1213 0.1565 0.1875 0.2133 0.2334 0.2470 0.2540 0.2540 0.2470 0.2334 0.2133 0.1875 0.1565 0.1213 0.0827
0 0.0257 0.0507 0.0743 0.0958 0.1148 0.1306 0.1429 0.1512 0.1555 0.1555 0.1512 0.1429 0.1306 0.1148 0.0958 0.0743 0.0507
0 0.0092 0.0181 0.0265 0.0342 0.0409 0.0466 0.0509 0.0539 0.0554 0.0554 0.0539 0.0509 0.0466 0.0409 0.0342 0.0265 0.0181
0 -0.0075 -0.0147 -0.0216 -0.0279 -0.0334 -0.0380 -0.0415 -0.0440 -0.0452 -0.0452 -0.0440 -0.0415 -0.0380 -0.0334 -0.0279 -0.0216 -0.0147
0 -0.0240 -0.0474 -0.0694 -0.0896 -0.1073 -0.1221 -0.1336 -0.1414 -0.1454 -0.1454 -0.1414 -0.1336 -0.1221 -0.1073 -0.0896 -0.0694 -0.0474
0 -0.0403 -0.0795 -0.1165 -0.1504 -0.1802 -0.2050 -0.2242 -0.2374 -0.2440 -0.2440 -0.2374 -0.2242 -0.2050 -0.1802 -0.1504 -0.1165 -0.0795
0 -0.0562 -0.1108 -0.1625 -0.2097 -0.2512 -0.2858 -0.3126 -0.3309 -0.3402 -0.3402 -0.3309 -0.3126 -0.2858 -0.2512 -0.2097 -0.1625 -0.1108
0 -0.0715 -0.1411 -0.2068 -0.2668 -0.3196 -0.3637 -0.3978 -0.4211 -0.4329 -0.4329 -0.4211 -0.3978 -0.3637 -0.3196 -0.2668 -0.2068 -0.1411
0 -0.0861 -0.1698 -0.2489 -0.3213 -0.3848 -0.4379 -0.4790 -0.5070 -0.5213 -0.5213 -0.5070 -0.4790 -0.4379 -0.3848 -0.3213 -0.2489 -0.1698
0 -0.0998 -0.1969 -0.2886 -0.3724 -0.4461 -0.5076 -0.5553 -0.5878 -0.6043 -0.6043 -0.5878 -0.5553 -0.5076 -0.4461 -0.3724 -0.2886 -0.1969
0 -0.1125 -0.2219 -0.3253 -0.4198 -0.5028 -0.5721 -0.6259 -0.6625 -0.6811 -0.6811 -0.6625 -0.6259 -0.5721 -0.5028 -0.4198 -0.3253 -0.2219
0 -0.1240 -0.2447 -0.3587 -0.4628 -0.5544 -0.6308 -0.6901 -0.7305 -0.7510 -0.7510 -0.7305 -0.6901 -0.6308 -0.5544 -0.4628 -0.3587 -0.2447
0 -0.1343 -0.2650 -0.3884 -0.5012 -0.6004 -0.6831 -0.7473 -0.7910 -0.8132 -0.8132 -0.7910 -0.7473 -0.6831 -0.6004 -0.5012 -0.3884 -0.2650
0 -0.1432 -0.2825 -0.4141 -0.5344 -0.6402 -0.7284 -0.7968 -0.8435 -0.8672 -0.8672 -0.8435 -0.7968 -0.7284 -0.6402 -0.5344 -0.4141 -0.2825
0 -0.1507 -0.2972 -0.4357 -0.5622 -0.6735 -0.7663 -0.8383 -0.8874 -0.9123 -0.9123 -0.8874 -0.8383 -0.7663 -0.6735 -0.5622 -0.4357 -0.2972
0 -0.1566 -0.3089 -0.4528 -0.5843 -0.6999 -0.7964 -0.8712 -0.9222 -0.9481 -0.9481 -0.9222 -0.8712 -0.7964 -0.6999 -0.5843 -0.4528 -0.3089
0 -0.1609 -0.3174 -0.4653 -0.6004 -0.7192 -0.8184 -0.8952 -0.9476 -0.9742 -0.9742 -0.9476 -0.8952 -0.8184 -0.7192 -0.6004 -0.4653 -0.3174
0 -0.1636 -0.3227 -0.4730 -0.6104 -0.7312 -0.8320 -0.9101 -0.9634 -0.9904 -0.9904 -0.9634 -0.9101 -0.8320 -0.7312 -0.6104 -0.4730 -0.3227
0 -0.1646 -0.3247 -0.4759 -0.6142 -0.7357 -0.8371 -0.9157 -0.9693 -0.9965 -0.9965 -0.9693 -0.9157 -0.8371 -0.7357 -0.6142 -0.4759 -0.3247
0 -0.1639 -0.3234 -0.4740 -0.6117 -0.7327 -0.8337 -0.9120 -0.9654 -0.9925 -0.9925 -0.9654 -0.9120 -0.8337 -0.7327 -0.6117 -0.4740 -0.3234
0 -0.1616 -0.3187 -0.4672 -0.6030 -0.7222 -0.8218 -0.8990 -0.9516 -0.9783 -0.9783 -0.9516 -0.8990 -0.8218 -0.7222 -0.6030 -0.4672 -0.3187
0 -0.1576 -0.3109 -0.4557 -0.5881 -0.7044 -0.8015 -0.8768 -0.9282 -0.9542 -0.9542 -0.9282 -0.8768 -0.8015 -0.7044 -0.5881 -0.4557 -0.3109
0 -0.1520 -0.2999 -0.4395 -0.5672 -0.6794 -0.7731 -0.8457 -0.8952 -0.9203 -0.9203 -0.8952 -0.8457 -0.7731 -0.6794 -0.5672 -0.4395 -0.2999
0 -0.1449 -0.2858 -0.4189 -0.5406 -0.6475 -0.7368 -0.8060 -0.8531 -0.8771 -0.8771 -0.8531 -0.8060 -0.7368 -0.6475 -0.5406 -0.4189 -0.2858
0 -0.1362 -0.2688 -0.3939 -0.5084 -0.6090 -0.6929 -0.7580 -0.8024 -0.8249 -0.8249 -0.8024 -0.7580 -0.6929 -0.6090 -0.5084 -0.3939 -0.2688
0 -0.1262 -0.2490 -0.3650 -0.4710 -0.5642 -0.6420 -0.7023 -0.7434 -0.7643 -0.7643 -0.7434 -0.7023 -0.6420 -0.5642 -0.4710 -0.3650 -0.2490
0 -0.1149 -0.2267 -0.3323 -0.4289 -0.5137 -0.5846 -0.6395 -0.6769 -0.6959 -0.6959 -0.6769 -0.6395 -0.5846 -0.5137 -0.4289 -0.3323 -0.2267
0 -0.1025 -0.2021 -0.2963 -0.3824 -0.4580 -0.5212 -0.5701 -0.6035 -0.6204 -0.6204 -0.6035 -0.5701 -0.5212 -0.4580 -0.3824 -0.2963 -0.2021
0 -0.0890 -0.1755 -0.2572 -0.3320 -0.3976 -0.4524 -0.4949 -0.5239 -0.5386 -0.5386 -0.5239 -0.4949 -0.4524 -0.3976 -0.3320 -0.2572 -0.1755
0 -0.0745 -0.1470 -0.2155 -0.2781 -0.3332 -0.3791 -0.4147 -0.4390 -0.4513 -0.4513 -0.4390 -0.4147 -0.3791 -0.3332 -0.2781 -0.2155 -0.1470
0 -0.0594 -0.1171 -0.1716 -0.2215 -0.2653 -0.3019 -0.3303 -0.3496 -0.3594 -0.3594 -0.3496 -0.3303 -0.3019 -0.2653 -0.2215 -0.1716 -0.1171
0 -0.0436 -0.0860 -0.1260 -0.1626 -0.1948 -0.2216 -0.2425 -0.2566 -0.2638 -0.2638 -0.2566 -0.2425 -0.2216 -0.1948 -0.1626 -0.1260 -0.0860
0 -0.0273 -0.0540 -0.0791 -0.1021 -0.1222 -0.1391 -0.1522 -0.1611 -0.1656 -0.1656 -0.1611 -0.1522 -0.1391 -0.1222 -0.1021 -0.0791 -0.0540
0 -0.0108 -0.0214 -0.0314 -0.0405 -0.0485 -0.0551 -0.0603 -0.0639 -0.0657 -0.0657 -0.0639 -0.0603 -0.0551 -0.0485 -0.0405 -0.0314 -0.0214
0 0.0058 0.0114 0.0167 0.0215 0.0258 0.0294 0.0321 0.0340 0.0350 0.0350 0.0340 0.0321 0.0294 0.0258 0.0215 0.0167 0.0114
0 0.0223 0.0441 0.0646 0.0833 0.0998 0.1136 0.1242 0.1315 0.1352 0.1352 0.1315 0.1242 0.1136 0.0998 0.0833 0.0646 0.0441
0 0.0387 0.0763 0.1118 0.1443 0.1728 0.1966 0.2151 0.2277 0.2341 0.2341 0.2277 0.2151 0.1966 0.1728 0.1443 0.1118 0.0763
0 0.0546 0.1077 0.1579 0.2037 0.2440 0.2777 0.3038 0.3216 0.3306 0.3306 0.3216 0.3038 0.2777 0.2440 0.2037 0.1579 0.1077
0 0.0700 0.1380 0.2023 0.2611 0.3128 0.3559 0.3893 0.4121 0.4237 0.4237 0.4121 0.3893 0.3559 0.3128 0.2611 0.2023 0.1380
0 0.0846 0.1670 0.2448 0.3159 0.3783 0.4305 0.4709 0.4985 0.5125 0.5125 0.4985 0.4709 0.4305 0.3783 0.3159 0.2448 0.1670
0 0.0984 0.1942 0.2847 0.3674 0.4400 0.5007 0.5477 0.5798 0.5961 0.5961 0.5798 0.5477 0.5007 0.4400 0.3674 0.2847 0.1942
0 0.1112 0.2195 0.3217 0.4151 0.4973 0.5658 0.6190 0.6552 0.6736 0.6736 0.6552 0.6190 0.5658 0.4973 0.4151 0.3217 0.2195
0 0.1229 0.2425 0.3554 0.4587 0.5494 0.6252 0.6839 0.7239 0.7442 0.7442 0.7239 0.6839 0.6252 0.5494 0.4587 0.3554 0.2425
0 0.1333 0.2630 0.3855 0.4975 0.5959 0.6781 0.7418 0.7852 0.8072 0.8072 0.7852 0.7418 0.6781 0.5959 0.4975 0.3855 0.2630
0 0.1424 0.2809 0.4117 0.5313 0.6364 0.7242 0.7922 0.8385 0.8621 0.8621 0.8385 0.7922 0.7242 0.6364 0.5313 0.4117 0.2809
0 0.1500 0.2959 0.4337 0.5597 0.6704 0.7628 0.8345 0.8833 0.9081 0.9081 0.8833 0.8345 0.7628 0.6704 0.5597 0.4337 0.2959
0 0.1561 0.3078 0.4512 0.5823 0.6975 0.7937 0.8682 0.9191 0.9449 0.9449 0.9191 0.8682 0.7937 0.6975 0.5823 0.4512 0.3078
0 0.1605 0.3167 0.4642 0.5991 0.7176 0.8165 0.8932 0.9455 0.9720 0.9720 0.9455 0.8932 0.8165 0.7176 0.5991 0.4642 0.3167
0 0.1634 0.3223 0.4724 0.6097 0.7303 0.8310 0.9090 0.9622 0.9892 0.9892 0.9622 0.9090 0.8310 0.7303 0.6097 0.4724 0.3223
0 0.1646 0.3246 0.4758 0.6141 0.7356 0.8370 0.9156 0.9692 0.9964 0.9964 0.9692 0.9156 0.8370 0.7356 0.6141 0.4758 0.3246
0 0.1641 0.3236 0.4744 0.6122 0.7333 0.8345 0.9128 0.9663 0.9934 0.9934 0.9663 0.9128 0.8345 0.7333 0.6122 0.4744 0.3236
0 0.1619 0.3194 0.4681 0.6041 0.7236 0.8234 0.9007 0.9535 0.9802 0.9802 0.9535 0.9007 0.8234 0.7236 0.6041 0.4681 0.3194
0 0.1581 0.3118 0.4571 0.5899 0.7066 0.8040 0.8795 0.9310 0.9571 0.9571 0.9310 0.8795 0.8040 0.7066 0.5899 0.4571 0.3118
0 0.1526 0.3011 0.4414 0.5696 0.6823 0.7764 0.8493 0.8990 0.9242 0.9242 0.8990 0.8493 0.7764 0.6823 0.5696 0.4414 0.3011
0 0.1457 0.2873 0.4212 0.5435 0.6511 0.7408 0.8104 0.8578 0.8819 0.8819 0.8578 0.8104 0.7408 0.6511 0.5435 0.4212 0.2873
0 0.1372 0.2706 0.3967 0.5119 0.6132 0.6977 0.7632 0.8079 0.8306 0.8306 0.8079 0.7632 0.6977 0.6132 0.5119 0.3967 0.2706
0 0.1273 0.2511 0.3681 0.4751 0.5691 0.6475 0.7083 0.7498 0.7708 0.7708 0.7498 0.7083 0.6475 0.5691 0.4751 0.3681 0.2511
0 0.1161 0.2291 0.3358 0.4334 0.5191 0.5907 0.6462 0.6840 0.7032 0.7032 0.6840 0.6462 0.5907 0.5191 0.4334 0.3358 0.2291
0 0.1038 0.2047 0.3001 0.3873 0.4639 0.5279 0.5774 0.6113 0.6284 0.6284 0.6113 0.5774 0.5279 0.4639 0.3873 0.3001 0.2047
0 0.0904 0.1783 0.2613 0.3372 0.4040 0.4597 0.5028 0.5323 0.5472 0.5472 0.5323 0.5028 0.4597 0.4040 0.3372 0.2613 0.1783
0 0.0760 0.1500 0.2199 0.2838 0.3399 0.3868 0.4231 0.4479 0.4604 0.4604 0.4479 0.4231 0.3868 0.3399 0.2838 0.2199 0.1500
0 0.0609 0.1202 0.1762 0.2274 0.2724 0.3099 0.3390 0.3589 0.3689 0.3689 0.3589 0.3390 0.3099 0.2724 0.2274 0.1762 0.1202
0 0.0452 0.0892 0.1307 0.1687 0.2021 0.2299 0.2515 0.2662 0.2737 0.2737 0.2662 0.2515 0.2299 0.2021 0.1687 0.1307 0.0892
0 0.0290 0.0572 0.0839 0.1083 0.1297 0.1476 0.1614 0.1709 0.1757 0.1757 0.1709 0.1614 0.1476 0.1297 0.1083 0.0839 0.0572
0 0.0125 0.0247 0.0362 0.0468 0.0560 0.0637 0.0697 0.0738 0.0759 0.0759 0.0738 0.0697 0.0637 0.0560 0.0468 0.0362 0.0247
0 -0.0041 -0.0081 -0.0118 -0.0152 -0.0182 -0.0208 -0.0227 -0.0240 -0.0247 -0.0247 -0.0240 -0.0227 -0.0208 -0.0182 -0.0152 -0.0118 -0.0081
0 -0.0207 -0.0407 -0.0597 -0.0771 -0.0923 -0.1051 -0.1149 -0.1216 -0.1251 -0.1251 -0.1216 -0.1149 -0.1051 -0.0923 -0.0771 -0.0597 -0.0407
0 -0.0370 -0.0730 -0.1070 -0.1381 -0.1655 -0.1883 -0.2059 -0.2180 -0.2241 -0.2241 -0.2180 -0.2059 -0.1883 -0.1655 -0.1381 -0.1070 -0.0730
0 -0.0530 -0.1046 -0.1533 -0.1978 -0.2369 -0.2696 -0.2949 -0.3121 -0.3209 -0.3209 -0.3121 -0.2949 -0.2696 -0.2369 -0.1978 -0.1533 -0.1046
0 -0.0684 -0.1350 -0.1979 -0.2554 -0.3059 -0.3481 -0.3808 -0.4031 -0.4144 -0.4144 -0.4031 -0.3808 -0.3481 -0.3059 -0.2554 -0.1979 -0.1350
0 -0.0832 -0.1641 -0.2405 -0.3104 -0.3718 -0.4231 -0.4628 -0.4899 -0.5037 -0.5037 -0.4899 -0.4628 -0.4231 -0.3718 -0.3104 -0.2405 -0.1641
0 -0.0971 -0.1915 -0.2807 -0.3623 -0.4340 -0.4938 -0.5402 -0.5718 -0.5878 -0.5878 -0.5718 -0.5402 -0.4938 -0.4340 -0.3623 -0.2807 -0.1915
0 -0.1100 -0.2170 -0.3181 -0.4105 -0.4917 -0.5595 -0.6120 -0.6478 -0.6660 -0.6660 -0.6478 -0.6120 -0.5595 -0.4917 -0.4105 -0.3181 -0.2170
0 -0.1218 -0.2402 -0.3521 -0.4544 -0.5443 -0.6194 -0.6776 -0.7172 -0.7373 -0.7373 -0.7172 -0.6776 -0.6194 -0.5443 -0.4544 -0.3521 -0.2402
0 -0.1323 -0.2610 -0.3826 -0.4938 -0.5915 -0.6730 -0.7362 -0.7793 -0.8012 -0.8012 -0.7793 -0.7362 -0.6730 -0.5915 -0.4938 -0.3826 -0.2610
0 -0.1415 -0.2792 -0.4092 -0.5281 -0.6326 -0.7198 -0.7874 -0.8335 -0.8569 -0.8569 -0.8335 -0.7874 -0.7198 -0.6326 -0.5281 -0.4092 -0.2792
0 -0.1493 -0.2945 -0.4316 -0.5570 -0.6672 -0.7592 -0.8305 -0.8792 -0.9038 -0.9038 -0.8792 -0.8305 -0.7592 -0.6672 -0.5570 -0.4316 -0.2945
0 -0.1555 -0.3068 -0.4497 -0.5803 -0.6951 -0.7909 -0.8652 -0.9159 -0.9416 -0.9416 -0.9159 -0.8652 -0.7909 -0.6951 -0.5803 -0.4497 -0.3068
0 -0.1602 -0.3159 -0.4631 -0.5976 -0.7159 -0.8146 -0.8911 -0.9432 -0.9697 -0.9697 -0.9432 -0.8911 -0.8146 -0.7159 -0.5976 -0.4631 -0.3159
0 -0.1632 -0.3219 -0.4718 -0.6089 -0.7293 -0.8299 -0.9078 -0.9610 -0.9879 -0.9879 -0.9610 -0.9078 -0.8299 -0.7293 -0.6089 -0.4718 -0.3219
0 -0.1645 -0.3245 -0.4757 -0.6139 -0.7354 -0.8368 -0.9153 -0.9689 -0.9961 -0.9961 -0.9689 -0.9153 -0.8368 -0.7354 -0.6139 -0.4757 -0.3245
0 -0.1642 -0.3239 -0.4748 -0.6127 -0.7339 -0.8351 -0.9135 -0.9670 -0.9941 -0.9941 -0.9670 -0.9135 -0.8351 -0.7339 -0.6127 -0.4748 -0.3239
0 -0.1622 -0.3200 -0.4690 -0.6052 -0.7250 -0.8249 -0.9024 -0.9552 -0.9820 -0.9820 -0.9552 -0.9024 -0.8249 -0.7250 -0.6052 -0.4690 -0.3200
0 -0.1585 -0.3127 -0.4584 -0.5916 -0.7086 -0.8063 -0.8821 -0.9337 -0.9599 -0.9599 -0.9337 -0.8821 -0.8063 -0.7086 -0.5916 -0.4584 -0.3127
0 -0.1533 -0.3023 -0.4432 -0.5719 -0.6851 -0.7795 -0.8527 -0.9027 -0.9280 -0.9280 -0.9027 -0.8527 -0.7795 -0.6851 -0.5719 -0.4432 -0.3023
0 -0.1464 -0.2889 -0.4234 -0.5464 -0.6545 -0.7448 -0.8147 -0.8624 -0.8866 -0.8866 -0.8624 -0.8147 -0.7448 -0.6545 -0.5464 -0.4234 -0.2889
0 -0.1381 -0.2724 -0.3994 -0.5154 -0.6173 -0.7024 -0.7684 -0.8134 -0.8362 -0.8362 -0.8134 -0.7684 -0.7024 -0.6173 -0.5154 -0.3994 -0.2724
Columns 19 through 20
0.1646 0.0000
0.1638 0.0000
0.1612 0.0000
0.1571 0.0000
0.1513 0.0000
0.1440 0.0000
0.1353 0.0000
0.1251 0.0000
0.1137 0.0000
0.1011 0.0000
0.0875 0.0000
0.0730 0.0000
0.0578 0.0000
0.0419 0.0000
0.0257 0.0000
0.0092 0.0000
-0.0075 -0.0000
-0.0240 -0.0000
-0.0403 -0.0000
-0.0562 -0.0000
-0.0715 -0.0000
-0.0861 -0.0000
-0.0998 -0.0000
-0.1125 -0.0000
-0.1240 -0.0000
-0.1343 -0.0000
-0.1432 -0.0000
-0.1507 -0.0000
-0.1566 -0.0000
-0.1609 -0.0000
-0.1636 -0.0000
-0.1646 -0.0000
-0.1639 -0.0000
-0.1616 -0.0000
-0.1576 -0.0000
-0.1520 -0.0000
-0.1449 -0.0000
-0.1362 -0.0000
-0.1262 -0.0000
-0.1149 -0.0000
-0.1025 -0.0000
-0.0890 -0.0000
-0.0745 -0.0000
-0.0594 -0.0000
-0.0436 -0.0000
-0.0273 -0.0000
-0.0108 -0.0000
0.0058 0.0000
0.0223 0.0000
0.0387 0.0000
0.0546 0.0000
0.0700 0.0000
0.0846 0.0000
0.0984 0.0000
0.1112 0.0000
0.1229 0.0000
0.1333 0.0000
0.1424 0.0000
0.1500 0.0000
0.1561 0.0000
0.1605 0.0000
0.1634 0.0000
0.1646 0.0000
0.1641 0.0000
0.1619 0.0000
0.1581 0.0000
0.1526 0.0000
0.1457 0.0000
0.1372 0.0000
0.1273 0.0000
0.1161 0.0000
0.1038 0.0000
0.0904 0.0000
0.0760 0.0000
0.0609 0.0000
0.0452 0.0000
0.0290 0.0000
0.0125 0.0000
-0.0041 -0.0000
-0.0207 -0.0000
-0.0370 -0.0000
-0.0530 -0.0000
-0.0684 -0.0000
-0.0832 -0.0000
-0.0971 -0.0000
-0.1100 -0.0000
-0.1218 -0.0000
-0.1323 -0.0000
-0.1415 -0.0000
-0.1493 -0.0000
-0.1555 -0.0000
-0.1602 -0.0000
-0.1632 -0.0000
-0.1645 -0.0000
-0.1642 -0.0000
-0.1622 -0.0000
-0.1585 -0.0000
-0.1533 -0.0000
-0.1464 -0.0000
-0.1381 -0.0000
velocity(:,:,2) =
Columns 1 through 18
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462
-0.8469 -0.8353 -0.8010 -0.7448 -0.6683 -0.5736 -0.4632 -0.3402 -0.2079 -0.0699 0.0699 0.2079 0.3402 0.4632 0.5736 0.6683 0.7448 0.8010
-0.8962 -0.8840 -0.8476 -0.7882 -0.7072 -0.6070 -0.4902 -0.3600 -0.2200 -0.0740 0.0740 0.2200 0.3600 0.4902 0.6070 0.7072 0.7882 0.8476
-0.9364 -0.9236 -0.8856 -0.8235 -0.7389 -0.6342 -0.5121 -0.3761 -0.2299 -0.0773 0.0773 0.2299 0.3761 0.5121 0.6342 0.7389 0.8235 0.8856
-0.9670 -0.9538 -0.9146 -0.8504 -0.7631 -0.6549 -0.5289 -0.3884 -0.2374 -0.0799 0.0799 0.2374 0.3884 0.5289 0.6549 0.7631 0.8504 0.9146
-0.9878 -0.9743 -0.9342 -0.8687 -0.7795 -0.6690 -0.5403 -0.3968 -0.2425 -0.0816 0.0816 0.2425 0.3968 0.5403 0.6690 0.7795 0.8687 0.9342
-0.9985 -0.9848 -0.9444 -0.8781 -0.7879 -0.6762 -0.5461 -0.4011 -0.2451 -0.0825 0.0825 0.2451 0.4011 0.5461 0.6762 0.7879 0.8781 0.9444
-0.9990 -0.9853 -0.9448 -0.8786 -0.7883 -0.6766 -0.5464 -0.4013 -0.2452 -0.0825 0.0825 0.2452 0.4013 0.5464 0.6766 0.7883 0.8786 0.9448
-0.9893 -0.9758 -0.9357 -0.8701 -0.7807 -0.6700 -0.5411 -0.3974 -0.2429 -0.0817 0.0817 0.2429 0.3974 0.5411 0.6700 0.7807 0.8701 0.9357
-0.9696 -0.9563 -0.9170 -0.8527 -0.7651 -0.6567 -0.5303 -0.3895 -0.2380 -0.0801 0.0801 0.2380 0.3895 0.5303 0.6567 0.7651 0.8527 0.9170
-0.9399 -0.9271 -0.8890 -0.8266 -0.7417 -0.6366 -0.5141 -0.3776 -0.2307 -0.0776 0.0776 0.2307 0.3776 0.5141 0.6366 0.7417 0.8266 0.8890
-0.9007 -0.8884 -0.8519 -0.7921 -0.7108 -0.6100 -0.4926 -0.3618 -0.2211 -0.0744 0.0744 0.2211 0.3618 0.4926 0.6100 0.7108 0.7921 0.8519
-0.8523 -0.8407 -0.8061 -0.7496 -0.6726 -0.5773 -0.4662 -0.3424 -0.2092 -0.0704 0.0704 0.2092 0.3424 0.4662 0.5773 0.6726 0.7496 0.8061
-0.7952 -0.7844 -0.7521 -0.6994 -0.6275 -0.5386 -0.4349 -0.3194 -0.1952 -0.0657 0.0657 0.1952 0.3194 0.4349 0.5386 0.6275 0.6994 0.7521
-0.7300 -0.7201 -0.6905 -0.6420 -0.5761 -0.4944 -0.3993 -0.2932 -0.1792 -0.0603 0.0603 0.1792 0.2932 0.3993 0.4944 0.5761 0.6420 0.6905
-0.6574 -0.6484 -0.6218 -0.5782 -0.5188 -0.4452 -0.3596 -0.2641 -0.1614 -0.0543 0.0543 0.1614 0.2641 0.3596 0.4452 0.5188 0.5782 0.6218
-0.5781 -0.5702 -0.5467 -0.5084 -0.4562 -0.3915 -0.3162 -0.2322 -0.1419 -0.0477 0.0477 0.1419 0.2322 0.3162 0.3915 0.4562 0.5084 0.5467
-0.4928 -0.4861 -0.4661 -0.4334 -0.3889 -0.3338 -0.2695 -0.1980 -0.1210 -0.0407 0.0407 0.1210 0.1980 0.2695 0.3338 0.3889 0.4334 0.4661
-0.4026 -0.3971 -0.3808 -0.3540 -0.3177 -0.2727 -0.2202 -0.1617 -0.0988 -0.0332 0.0332 0.0988 0.1617 0.2202 0.2727 0.3177 0.3540 0.3808
-0.3082 -0.3040 -0.2915 -0.2711 -0.2432 -0.2087 -0.1686 -0.1238 -0.0757 -0.0255 0.0255 0.0757 0.1238 0.1686 0.2087 0.2432 0.2711 0.2915
-0.2107 -0.2078 -0.1993 -0.1853 -0.1663 -0.1427 -0.1152 -0.0846 -0.0517 -0.0174 0.0174 0.0517 0.0846 0.1152 0.1427 0.1663 0.1853 0.1993
-0.1111 -0.1095 -0.1050 -0.0977 -0.0876 -0.0752 -0.0607 -0.0446 -0.0273 -0.0092 0.0092 0.0273 0.0446 0.0607 0.0752 0.0876 0.0977 0.1050
-0.0103 -0.0101 -0.0097 -0.0090 -0.0081 -0.0070 -0.0056 -0.0041 -0.0025 -0.0008 0.0008 0.0025 0.0041 0.0056 0.0070 0.0081 0.0090 0.0097
0.0906 0.0894 0.0857 0.0797 0.0715 0.0614 0.0496 0.0364 0.0222 0.0075 -0.0075 -0.0222 -0.0364 -0.0496 -0.0614 -0.0715 -0.0797 -0.0857
0.1906 0.1880 0.1802 0.1676 0.1504 0.1291 0.1042 0.0766 0.0468 0.0157 -0.0157 -0.0468 -0.0766 -0.1042 -0.1291 -0.1504 -0.1676 -0.1802
0.2886 0.2847 0.2730 0.2538 0.2277 0.1955 0.1578 0.1159 0.0708 0.0238 -0.0238 -0.0708 -0.1159 -0.1578 -0.1955 -0.2277 -0.2538 -0.2730
0.3837 0.3784 0.3629 0.3374 0.3028 0.2598 0.2098 0.1541 0.0942 0.0317 -0.0317 -0.0942 -0.1541 -0.2098 -0.2598 -0.3028 -0.3374 -0.3629
0.4748 0.4684 0.4491 0.4176 0.3747 0.3216 0.2597 0.1907 0.1166 0.0392 -0.0392 -0.1166 -0.1907 -0.2597 -0.3216 -0.3747 -0.4176 -0.4491
0.5612 0.5535 0.5308 0.4935 0.4428 0.3801 0.3069 0.2254 0.1378 0.0463 -0.0463 -0.1378 -0.2254 -0.3069 -0.3801 -0.4428 -0.4935 -0.5308
0.6418 0.6330 0.6070 0.5644 0.5064 0.4347 0.3510 0.2578 0.1575 0.0530 -0.0530 -0.1575 -0.2578 -0.3510 -0.4347 -0.5064 -0.5644 -0.6070
0.7158 0.7061 0.6770 0.6295 0.5649 0.4848 0.3915 0.2875 0.1757 0.0591 -0.0591 -0.1757 -0.2875 -0.3915 -0.4848 -0.5649 -0.6295 -0.6770
0.7826 0.7719 0.7402 0.6883 0.6176 0.5300 0.4280 0.3144 0.1921 0.0646 -0.0646 -0.1921 -0.3144 -0.4280 -0.5300 -0.6176 -0.6883 -0.7402
0.8414 0.8299 0.7958 0.7400 0.6640 0.5698 0.4602 0.3380 0.2065 0.0695 -0.0695 -0.2065 -0.3380 -0.4602 -0.5698 -0.6640 -0.7400 -0.7958
0.8916 0.8794 0.8433 0.7841 0.7036 0.6039 0.4877 0.3581 0.2189 0.0736 -0.0736 -0.2189 -0.3581 -0.4877 -0.6039 -0.7036 -0.7841 -0.8433
0.9327 0.9200 0.8822 0.8203 0.7360 0.6317 0.5101 0.3747 0.2290 0.0770 -0.0770 -0.2290 -0.3747 -0.5101 -0.6317 -0.7360 -0.8203 -0.8822
0.9643 0.9512 0.9121 0.8481 0.7610 0.6531 0.5274 0.3874 0.2367 0.0796 -0.0796 -0.2367 -0.3874 -0.5274 -0.6531 -0.7610 -0.8481 -0.9121
0.9861 0.9726 0.9327 0.8672 0.7782 0.6679 0.5393 0.3961 0.2421 0.0814 -0.0814 -0.2421 -0.3961 -0.5393 -0.6679 -0.7782 -0.8672 -0.9327
0.9978 0.9842 0.9438 0.8776 0.7874 0.6758 0.5458 0.4008 0.2450 0.0824 -0.0824 -0.2450 -0.4008 -0.5458 -0.6758 -0.7874 -0.8776 -0.9438
0.9994 0.9858 0.9452 0.8789 0.7887 0.6769 0.5466 0.4014 0.2453 0.0825 -0.0825 -0.2453 -0.4014 -0.5466 -0.6769 -0.7887 -0.8789 -0.9452
0.9908 0.9772 0.9371 0.8713 0.7818 0.6710 0.5419 0.3980 0.2432 0.0818 -0.0818 -0.2432 -0.3980 -0.5419 -0.6710 -0.7818 -0.8713 -0.9371
0.9720 0.9588 0.9194 0.8549 0.7671 0.6583 0.5316 0.3905 0.2386 0.0803 -0.0803 -0.2386 -0.3905 -0.5316 -0.6583 -0.7671 -0.8549 -0.9194
0.9434 0.9305 0.8923 0.8297 0.7445 0.6389 0.5160 0.3790 0.2316 0.0779 -0.0779 -0.2316 -0.3790 -0.5160 -0.6389 -0.7445 -0.8297 -0.8923
0.9051 0.8928 0.8561 0.7960 0.7143 0.6130 0.4951 0.3636 0.2222 0.0747 -0.0747 -0.2222 -0.3636 -0.4951 -0.6130 -0.7143 -0.7960 -0.8561
0.8576 0.8459 0.8112 0.7543 0.6768 0.5809 0.4691 0.3445 0.2105 0.0708 -0.0708 -0.2105 -0.3445 -0.4691 -0.5809 -0.6768 -0.7543 -0.8112
0.8014 0.7905 0.7580 0.7048 0.6324 0.5428 0.4383 0.3219 0.1967 0.0662 -0.0662 -0.1967 -0.3219 -0.4383 -0.5428 -0.6324 -0.7048 -0.7580
0.7370 0.7270 0.6971 0.6482 0.5816 0.4992 0.4031 0.2961 0.1809 0.0609 -0.0609 -0.1809 -0.2961 -0.4031 -0.4992 -0.5816 -0.6482 -0.6971
0.6651 0.6560 0.6291 0.5849 0.5249 0.4505 0.3638 0.2672 0.1633 0.0549 -0.0549 -0.1633 -0.2672 -0.3638 -0.4505 -0.5249 -0.5849 -0.6291
0.5864 0.5784 0.5546 0.5157 0.4628 0.3972 0.3207 0.2356 0.1440 0.0484 -0.0484 -0.1440 -0.2356 -0.3207 -0.3972 -0.4628 -0.5157 -0.5546
0.5017 0.4949 0.4746 0.4413 0.3959 0.3398 0.2744 0.2015 0.1232 0.0414 -0.0414 -0.1232 -0.2015 -0.2744 -0.3398 -0.3959 -0.4413 -0.4746
0.4120 0.4063 0.3896 0.3623 0.3251 0.2790 0.2253 0.1655 0.1011 0.0340 -0.0340 -0.1011 -0.1655 -0.2253 -0.2790 -0.3251 -0.3623 -0.3896
0.3180 0.3136 0.3007 0.2796 0.2509 0.2154 0.1739 0.1277 0.0781 0.0263 -0.0263 -0.0781 -0.1277 -0.1739 -0.2154 -0.2509 -0.2796 -0.3007
0.2207 0.2177 0.2088 0.1941 0.1742 0.1495 0.1207 0.0887 0.0542 0.0182 -0.0182 -0.0542 -0.0887 -0.1207 -0.1495 -0.1742 -0.1941 -0.2088
0.1213 0.1196 0.1147 0.1067 0.0957 0.0821 0.0663 0.0487 0.0298 0.0100 -0.0100 -0.0298 -0.0487 -0.0663 -0.0821 -0.0957 -0.1067 -0.1147
0.0206 0.0203 0.0194 0.0181 0.0162 0.0139 0.0112 0.0083 0.0050 0.0017 -0.0017 -0.0050 -0.0083 -0.0112 -0.0139 -0.0162 -0.0181 -0.0194
-0.0804 -0.0793 -0.0760 -0.0707 -0.0634 -0.0544 -0.0440 -0.0323 -0.0197 -0.0066 0.0066 0.0197 0.0323 0.0440 0.0544 0.0634 0.0707 0.0760
-0.1805 -0.1780 -0.1707 -0.1587 -0.1424 -0.1222 -0.0987 -0.0725 -0.0443 -0.0149 0.0149 0.0443 0.0725 0.0987 0.1222 0.1424 0.1587 0.1707
-0.2787 -0.2749 -0.2636 -0.2451 -0.2200 -0.1888 -0.1525 -0.1120 -0.0684 -0.0230 0.0230 0.0684 0.1120 0.1525 0.1888 0.2200 0.2451 0.2636
-0.3742 -0.3690 -0.3539 -0.3291 -0.2953 -0.2534 -0.2046 -0.1503 -0.0918 -0.0309 0.0309 0.0918 0.1503 0.2046 0.2534 0.2953 0.3291 0.3539
-0.4658 -0.4594 -0.4405 -0.4096 -0.3675 -0.3154 -0.2547 -0.1871 -0.1143 -0.0385 0.0385 0.1143 0.1871 0.2547 0.3154 0.3675 0.4096 0.4405
-0.5526 -0.5451 -0.5227 -0.4860 -0.4361 -0.3743 -0.3023 -0.2220 -0.1357 -0.0456 0.0456 0.1357 0.2220 0.3023 0.3743 0.4361 0.4860 0.5227
-0.6338 -0.6252 -0.5995 -0.5574 -0.5002 -0.4293 -0.3467 -0.2546 -0.1556 -0.0523 0.0523 0.1556 0.2546 0.3467 0.4293 0.5002 0.5574 0.5995
-0.7086 -0.6989 -0.6702 -0.6232 -0.5592 -0.4799 -0.3876 -0.2846 -0.1740 -0.0585 0.0585 0.1740 0.2846 0.3876 0.4799 0.5592 0.6232 0.6702
-0.7761 -0.7656 -0.7341 -0.6826 -0.6125 -0.5257 -0.4245 -0.3118 -0.1905 -0.0641 0.0641 0.1905 0.3118 0.4245 0.5257 0.6125 0.6826 0.7341
-0.8358 -0.8244 -0.7905 -0.7350 -0.6595 -0.5661 -0.4571 -0.3357 -0.2052 -0.0690 0.0690 0.2052 0.3357 0.4571 0.5661 0.6595 0.7350 0.7905
-0.8869 -0.8748 -0.8388 -0.7800 -0.6999 -0.6007 -0.4851 -0.3563 -0.2177 -0.0732 0.0732 0.2177 0.3563 0.4851 0.6007 0.6999 0.7800 0.8388
-0.9289 -0.9163 -0.8786 -0.8170 -0.7331 -0.6292 -0.5081 -0.3732 -0.2280 -0.0767 0.0767 0.2280 0.3732 0.5081 0.6292 0.7331 0.8170 0.8786
-0.9615 -0.9484 -0.9094 -0.8457 -0.7588 -0.6512 -0.5259 -0.3862 -0.2360 -0.0794 0.0794 0.2360 0.3862 0.5259 0.6512 0.7588 0.8457 0.9094
-0.9843 -0.9709 -0.9310 -0.8657 -0.7768 -0.6667 -0.5384 -0.3954 -0.2416 -0.0813 0.0813 0.2416 0.3954 0.5384 0.6667 0.7768 0.8657 0.9310
-0.9971 -0.9835 -0.9431 -0.8769 -0.7869 -0.6753 -0.5454 -0.4005 -0.2448 -0.0823 0.0823 0.2448 0.4005 0.5454 0.6753 0.7869 0.8769 0.9431
-0.9997 -0.9861 -0.9455 -0.8792 -0.7889 -0.6771 -0.5468 -0.4016 -0.2454 -0.0826 0.0826 0.2454 0.4016 0.5468 0.6771 0.7889 0.8792 0.9455
-0.9921 -0.9786 -0.9383 -0.8725 -0.7829 -0.6719 -0.5426 -0.3985 -0.2435 -0.0819 0.0819 0.2435 0.3985 0.5426 0.6719 0.7829 0.8725 0.9383
-0.9744 -0.9611 -0.9216 -0.8569 -0.7689 -0.6599 -0.5329 -0.3914 -0.2392 -0.0805 0.0805 0.2392 0.3914 0.5329 0.6599 0.7689 0.8569 0.9216
-0.9467 -0.9338 -0.8954 -0.8326 -0.7471 -0.6412 -0.5178 -0.3803 -0.2324 -0.0782 0.0782 0.2324 0.3803 0.5178 0.6412 0.7471 0.8326 0.8954
-0.9094 -0.8970 -0.8602 -0.7998 -0.7177 -0.6160 -0.4974 -0.3653 -0.2233 -0.0751 0.0751 0.2233 0.3653 0.4974 0.6160 0.7177 0.7998 0.8602
-0.8629 -0.8511 -0.8161 -0.7589 -0.6809 -0.5844 -0.4720 -0.3466 -0.2118 -0.0713 0.0713 0.2118 0.3466 0.4720 0.5844 0.6809 0.7589 0.8161
-0.8075 -0.7965 -0.7638 -0.7102 -0.6372 -0.5469 -0.4417 -0.3244 -0.1982 -0.0667 0.0667 0.1982 0.3244 0.4417 0.5469 0.6372 0.7102 0.7638
-0.7439 -0.7338 -0.7036 -0.6543 -0.5871 -0.5038 -0.4069 -0.2988 -0.1826 -0.0614 0.0614 0.1826 0.2988 0.4069 0.5038 0.5871 0.6543 0.7036
-0.6727 -0.6636 -0.6363 -0.5917 -0.5309 -0.4556 -0.3680 -0.2702 -0.1651 -0.0556 0.0556 0.1651 0.2702 0.3680 0.4556 0.5309 0.5917 0.6363
-0.5947 -0.5866 -0.5625 -0.5230 -0.4693 -0.4028 -0.3253 -0.2389 -0.1460 -0.0491 0.0491 0.1460 0.2389 0.3253 0.4028 0.4693 0.5230 0.5625
-0.5106 -0.5036 -0.4829 -0.4491 -0.4029 -0.3458 -0.2793 -0.2051 -0.1253 -0.0422 0.0422 0.1253 0.2051 0.2793 0.3458 0.4029 0.4491 0.4829
-0.4213 -0.4156 -0.3985 -0.3705 -0.3325 -0.2853 -0.2304 -0.1692 -0.1034 -0.0348 0.0348 0.1034 0.1692 0.2304 0.2853 0.3325 0.3705 0.3985
-0.3277 -0.3232 -0.3099 -0.2882 -0.2586 -0.2219 -0.1792 -0.1316 -0.0804 -0.0271 0.0271 0.0804 0.1316 0.1792 0.2219 0.2586 0.2882 0.3099
-0.2308 -0.2276 -0.2183 -0.2029 -0.1821 -0.1563 -0.1262 -0.0927 -0.0566 -0.0191 0.0191 0.0566 0.0927 0.1262 0.1563 0.1821 0.2029 0.2183
-0.1315 -0.1297 -0.1243 -0.1156 -0.1037 -0.0890 -0.0719 -0.0528 -0.0323 -0.0109 0.0109 0.0323 0.0528 0.0719 0.0890 0.1037 0.1156 0.1243
-0.0308 -0.0304 -0.0292 -0.0271 -0.0243 -0.0209 -0.0169 -0.0124 -0.0076 -0.0025 0.0025 0.0076 0.0124 0.0169 0.0209 0.0243 0.0271 0.0292
0.0701 0.0692 0.0663 0.0617 0.0553 0.0475 0.0383 0.0282 0.0172 0.0058 -0.0058 -0.0172 -0.0282 -0.0383 -0.0475 -0.0553 -0.0617 -0.0663
0.1703 0.1680 0.1611 0.1498 0.1344 0.1154 0.0932 0.0684 0.0418 0.0141 -0.0141 -0.0418 -0.0684 -0.0932 -0.1154 -0.1344 -0.1498 -0.1611
0.2688 0.2652 0.2543 0.2364 0.2122 0.1821 0.1470 0.1080 0.0660 0.0222 -0.0222 -0.0660 -0.1080 -0.1470 -0.1821 -0.2122 -0.2364 -0.2543
0.3646 0.3596 0.3448 0.3207 0.2877 0.2469 0.1994 0.1465 0.0895 0.0301 -0.0301 -0.0895 -0.1465 -0.1994 -0.2469 -0.2877 -0.3207 -0.3448
0.4566 0.4504 0.4319 0.4016 0.3604 0.3093 0.2498 0.1834 0.1121 0.0377 -0.0377 -0.1121 -0.1834 -0.2498 -0.3093 -0.3604 -0.4016 -0.4319
0.5440 0.5366 0.5145 0.4785 0.4293 0.3685 0.2976 0.2185 0.1335 0.0449 -0.0449 -0.1335 -0.2185 -0.2976 -0.3685 -0.4293 -0.4785 -0.5145
Columns 19 through 20
0 0
0.0995 0.1008
0.1979 0.2006
0.2943 0.2984
0.3878 0.3931
0.4773 0.4839
0.5619 0.5696
0.6407 0.6496
0.7131 0.7230
0.7782 0.7889
0.8353 0.8469
0.8840 0.8962
0.9236 0.9364
0.9538 0.9670
0.9743 0.9878
0.9848 0.9985
0.9853 0.9990
0.9758 0.9893
0.9563 0.9696
0.9271 0.9399
0.8884 0.9007
0.8407 0.8523
0.7844 0.7952
0.7201 0.7300
0.6484 0.6574
0.5702 0.5781
0.4861 0.4928
0.3971 0.4026
0.3040 0.3082
0.2078 0.2107
0.1095 0.1111
0.0101 0.0103
-0.0894 -0.0906
-0.1880 -0.1906
-0.2847 -0.2886
-0.3784 -0.3837
-0.4684 -0.4748
-0.5535 -0.5612
-0.6330 -0.6418
-0.7061 -0.7158
-0.7719 -0.7826
-0.8299 -0.8414
-0.8794 -0.8916
-0.9200 -0.9327
-0.9512 -0.9643
-0.9726 -0.9861
-0.9842 -0.9978
-0.9858 -0.9994
-0.9772 -0.9908
-0.9588 -0.9720
-0.9305 -0.9434
-0.8928 -0.9051
-0.8459 -0.8576
-0.7905 -0.8014
-0.7270 -0.7370
-0.6560 -0.6651
-0.5784 -0.5864
-0.4949 -0.5017
-0.4063 -0.4120
-0.3136 -0.3180
-0.2177 -0.2207
-0.1196 -0.1213
-0.0203 -0.0206
0.0793 0.0804
0.1780 0.1805
0.2749 0.2787
0.3690 0.3742
0.4594 0.4658
0.5451 0.5526
0.6252 0.6338
0.6989 0.7086
0.7656 0.7761
0.8244 0.8358
0.8748 0.8869
0.9163 0.9289
0.9484 0.9615
0.9709 0.9843
0.9835 0.9971
0.9861 0.9997
0.9786 0.9921
0.9611 0.9744
0.9338 0.9467
0.8970 0.9094
0.8511 0.8629
0.7965 0.8075
0.7338 0.7439
0.6636 0.6727
0.5866 0.5947
0.5036 0.5106
0.4156 0.4213
0.3232 0.3277
0.2276 0.2308
0.1297 0.1315
0.0304 0.0308
-0.0692 -0.0701
-0.1680 -0.1703
-0.2652 -0.2688
-0.3596 -0.3646
-0.4504 -0.4566
-0.5366 -0.5440
velocity =
velocity(:,:,1) =
Columns 1 through 18
0 0.1646 0.3247 0.4759 0.6142 0.7357 0.8372 0.9158 0.9694 0.9966 0.9966 0.9694 0.9158 0.8372 0.7357 0.6142 0.4759 0.3247
0 0.1638 0.3230 0.4735 0.6111 0.7320 0.8329 0.9111 0.9645 0.9915 0.9915 0.9645 0.9111 0.8329 0.7320 0.6111 0.4735 0.3230
0 0.1612 0.3181 0.4663 0.6017 0.7208 0.8201 0.8971 0.9497 0.9763 0.9763 0.9497 0.8971 0.8201 0.7208 0.6017 0.4663 0.3181
0 0.1571 0.3099 0.4543 0.5862 0.7022 0.7990 0.8740 0.9252 0.9512 0.9512 0.9252 0.8740 0.7990 0.7022 0.5862 0.4543 0.3099
0 0.1513 0.2986 0.4376 0.5648 0.6765 0.7698 0.8420 0.8913 0.9163 0.9163 0.8913 0.8420 0.7698 0.6765 0.5648 0.4376 0.2986
0 0.1440 0.2842 0.4165 0.5375 0.6439 0.7326 0.8014 0.8484 0.8722 0.8722 0.8484 0.8014 0.7326 0.6439 0.5375 0.4165 0.2842
0 0.1353 0.2669 0.3912 0.5048 0.6047 0.6881 0.7527 0.7967 0.8191 0.8191 0.7967 0.7527 0.6881 0.6047 0.5048 0.3912 0.2669
0 0.1251 0.2469 0.3618 0.4670 0.5593 0.6365 0.6962 0.7370 0.7577 0.7577 0.7370 0.6962 0.6365 0.5593 0.4670 0.3618 0.2469
0 0.1137 0.2243 0.3288 0.4244 0.5083 0.5784 0.6327 0.6697 0.6885 0.6885 0.6697 0.6327 0.5784 0.5083 0.4244 0.3288 0.2243
0 0.1011 0.1995 0.2925 0.3774 0.4521 0.5144 0.5627 0.5957 0.6124 0.6124 0.5957 0.5627 0.5144 0.4521 0.3774 0.2925 0.1995
0 0.0875 0.1727 0.2531 0.3266 0.3912 0.4452 0.4870 0.5155 0.5300 0.5300 0.5155 0.4870 0.4452 0.3912 0.3266 0.2531 0.1727
0 0.0730 0.1441 0.2112 0.2725 0.3264 0.3714 0.4063 0.4301 0.4422 0.4422 0.4301 0.4063 0.3714 0.3264 0.2725 0.2112 0.1441
0 0.0578 0.1140 0.1671 0.2156 0.2583 0.2939 0.3215 0.3403 0.3498 0.3498 0.3403 0.3215 0.2939 0.2583 0.2156 0.1671 0.1140
0 0.0419 0.0827 0.1213 0.1565 0.1875 0.2133 0.2334 0.2470 0.2540 0.2540 0.2470 0.2334 0.2133 0.1875 0.1565 0.1213 0.0827
0 0.0257 0.0507 0.0743 0.0958 0.1148 0.1306 0.1429 0.1512 0.1555 0.1555 0.1512 0.1429 0.1306 0.1148 0.0958 0.0743 0.0507
0 0.0092 0.0181 0.0265 0.0342 0.0409 0.0466 0.0509 0.0539 0.0554 0.0554 0.0539 0.0509 0.0466 0.0409 0.0342 0.0265 0.0181
0 -0.0075 -0.0147 -0.0216 -0.0279 -0.0334 -0.0380 -0.0415 -0.0440 -0.0452 -0.0452 -0.0440 -0.0415 -0.0380 -0.0334 -0.0279 -0.0216 -0.0147
0 -0.0240 -0.0474 -0.0694 -0.0896 -0.1073 -0.1221 -0.1336 -0.1414 -0.1454 -0.1454 -0.1414 -0.1336 -0.1221 -0.1073 -0.0896 -0.0694 -0.0474
0 -0.0403 -0.0795 -0.1165 -0.1504 -0.1802 -0.2050 -0.2242 -0.2374 -0.2440 -0.2440 -0.2374 -0.2242 -0.2050 -0.1802 -0.1504 -0.1165 -0.0795
0 -0.0562 -0.1108 -0.1625 -0.2097 -0.2512 -0.2858 -0.3126 -0.3309 -0.3402 -0.3402 -0.3309 -0.3126 -0.2858 -0.2512 -0.2097 -0.1625 -0.1108
0 -0.0715 -0.1411 -0.2068 -0.2668 -0.3196 -0.3637 -0.3978 -0.4211 -0.4329 -0.4329 -0.4211 -0.3978 -0.3637 -0.3196 -0.2668 -0.2068 -0.1411
0 -0.0861 -0.1698 -0.2489 -0.3213 -0.3848 -0.4379 -0.4790 -0.5070 -0.5213 -0.5213 -0.5070 -0.4790 -0.4379 -0.3848 -0.3213 -0.2489 -0.1698
0 -0.0998 -0.1969 -0.2886 -0.3724 -0.4461 -0.5076 -0.5553 -0.5878 -0.6043 -0.6043 -0.5878 -0.5553 -0.5076 -0.4461 -0.3724 -0.2886 -0.1969
0 -0.1125 -0.2219 -0.3253 -0.4198 -0.5028 -0.5721 -0.6259 -0.6625 -0.6811 -0.6811 -0.6625 -0.6259 -0.5721 -0.5028 -0.4198 -0.3253 -0.2219
0 -0.1240 -0.2447 -0.3587 -0.4628 -0.5544 -0.6308 -0.6901 -0.7305 -0.7510 -0.7510 -0.7305 -0.6901 -0.6308 -0.5544 -0.4628 -0.3587 -0.2447
0 -0.1343 -0.2650 -0.3884 -0.5012 -0.6004 -0.6831 -0.7473 -0.7910 -0.8132 -0.8132 -0.7910 -0.7473 -0.6831 -0.6004 -0.5012 -0.3884 -0.2650
0 -0.1432 -0.2825 -0.4141 -0.5344 -0.6402 -0.7284 -0.7968 -0.8435 -0.8672 -0.8672 -0.8435 -0.7968 -0.7284 -0.6402 -0.5344 -0.4141 -0.2825
0 -0.1507 -0.2972 -0.4357 -0.5622 -0.6735 -0.7663 -0.8383 -0.8874 -0.9123 -0.9123 -0.8874 -0.8383 -0.7663 -0.6735 -0.5622 -0.4357 -0.2972
0 -0.1566 -0.3089 -0.4528 -0.5843 -0.6999 -0.7964 -0.8712 -0.9222 -0.9481 -0.9481 -0.9222 -0.8712 -0.7964 -0.6999 -0.5843 -0.4528 -0.3089
0 -0.1609 -0.3174 -0.4653 -0.6004 -0.7192 -0.8184 -0.8952 -0.9476 -0.9742 -0.9742 -0.9476 -0.8952 -0.8184 -0.7192 -0.6004 -0.4653 -0.3174
0 -0.1636 -0.3227 -0.4730 -0.6104 -0.7312 -0.8320 -0.9101 -0.9634 -0.9904 -0.9904 -0.9634 -0.9101 -0.8320 -0.7312 -0.6104 -0.4730 -0.3227
0 -0.1646 -0.3247 -0.4759 -0.6142 -0.7357 -0.8371 -0.9157 -0.9693 -0.9965 -0.9965 -0.9693 -0.9157 -0.8371 -0.7357 -0.6142 -0.4759 -0.3247
0 -0.1639 -0.3234 -0.4740 -0.6117 -0.7327 -0.8337 -0.9120 -0.9654 -0.9925 -0.9925 -0.9654 -0.9120 -0.8337 -0.7327 -0.6117 -0.4740 -0.3234
0 -0.1616 -0.3187 -0.4672 -0.6030 -0.7222 -0.8218 -0.8990 -0.9516 -0.9783 -0.9783 -0.9516 -0.8990 -0.8218 -0.7222 -0.6030 -0.4672 -0.3187
0 -0.1576 -0.3109 -0.4557 -0.5881 -0.7044 -0.8015 -0.8768 -0.9282 -0.9542 -0.9542 -0.9282 -0.8768 -0.8015 -0.7044 -0.5881 -0.4557 -0.3109
0 -0.1520 -0.2999 -0.4395 -0.5672 -0.6794 -0.7731 -0.8457 -0.8952 -0.9203 -0.9203 -0.8952 -0.8457 -0.7731 -0.6794 -0.5672 -0.4395 -0.2999
0 -0.1449 -0.2858 -0.4189 -0.5406 -0.6475 -0.7368 -0.8060 -0.8531 -0.8771 -0.8771 -0.8531 -0.8060 -0.7368 -0.6475 -0.5406 -0.4189 -0.2858
0 -0.1362 -0.2688 -0.3939 -0.5084 -0.6090 -0.6929 -0.7580 -0.8024 -0.8249 -0.8249 -0.8024 -0.7580 -0.6929 -0.6090 -0.5084 -0.3939 -0.2688
0 -0.1262 -0.2490 -0.3650 -0.4710 -0.5642 -0.6420 -0.7023 -0.7434 -0.7643 -0.7643 -0.7434 -0.7023 -0.6420 -0.5642 -0.4710 -0.3650 -0.2490
0 -0.1149 -0.2267 -0.3323 -0.4289 -0.5137 -0.5846 -0.6395 -0.6769 -0.6959 -0.6959 -0.6769 -0.6395 -0.5846 -0.5137 -0.4289 -0.3323 -0.2267
0 -0.1025 -0.2021 -0.2963 -0.3824 -0.4580 -0.5212 -0.5701 -0.6035 -0.6204 -0.6204 -0.6035 -0.5701 -0.5212 -0.4580 -0.3824 -0.2963 -0.2021
0 -0.0890 -0.1755 -0.2572 -0.3320 -0.3976 -0.4524 -0.4949 -0.5239 -0.5386 -0.5386 -0.5239 -0.4949 -0.4524 -0.3976 -0.3320 -0.2572 -0.1755
0 -0.0745 -0.1470 -0.2155 -0.2781 -0.3332 -0.3791 -0.4147 -0.4390 -0.4513 -0.4513 -0.4390 -0.4147 -0.3791 -0.3332 -0.2781 -0.2155 -0.1470
0 -0.0594 -0.1171 -0.1716 -0.2215 -0.2653 -0.3019 -0.3303 -0.3496 -0.3594 -0.3594 -0.3496 -0.3303 -0.3019 -0.2653 -0.2215 -0.1716 -0.1171
0 -0.0436 -0.0860 -0.1260 -0.1626 -0.1948 -0.2216 -0.2425 -0.2566 -0.2638 -0.2638 -0.2566 -0.2425 -0.2216 -0.1948 -0.1626 -0.1260 -0.0860
0 -0.0273 -0.0540 -0.0791 -0.1021 -0.1222 -0.1391 -0.1522 -0.1611 -0.1656 -0.1656 -0.1611 -0.1522 -0.1391 -0.1222 -0.1021 -0.0791 -0.0540
0 -0.0108 -0.0214 -0.0314 -0.0405 -0.0485 -0.0551 -0.0603 -0.0639 -0.0657 -0.0657 -0.0639 -0.0603 -0.0551 -0.0485 -0.0405 -0.0314 -0.0214
0 0.0058 0.0114 0.0167 0.0215 0.0258 0.0294 0.0321 0.0340 0.0350 0.0350 0.0340 0.0321 0.0294 0.0258 0.0215 0.0167 0.0114
0 0.0223 0.0441 0.0646 0.0833 0.0998 0.1136 0.1242 0.1315 0.1352 0.1352 0.1315 0.1242 0.1136 0.0998 0.0833 0.0646 0.0441
0 0.0387 0.0763 0.1118 0.1443 0.1728 0.1966 0.2151 0.2277 0.2341 0.2341 0.2277 0.2151 0.1966 0.1728 0.1443 0.1118 0.0763
0 0.0546 0.1077 0.1579 0.2037 0.2440 0.2777 0.3038 0.3216 0.3306 0.3306 0.3216 0.3038 0.2777 0.2440 0.2037 0.1579 0.1077
0 0.0700 0.1380 0.2023 0.2611 0.3128 0.3559 0.3893 0.4121 0.4237 0.4237 0.4121 0.3893 0.3559 0.3128 0.2611 0.2023 0.1380
0 0.0846 0.1670 0.2448 0.3159 0.3783 0.4305 0.4709 0.4985 0.5125 0.5125 0.4985 0.4709 0.4305 0.3783 0.3159 0.2448 0.1670
0 0.0984 0.1942 0.2847 0.3674 0.4400 0.5007 0.5477 0.5798 0.5961 0.5961 0.5798 0.5477 0.5007 0.4400 0.3674 0.2847 0.1942
0 0.1112 0.2195 0.3217 0.4151 0.4973 0.5658 0.6190 0.6552 0.6736 0.6736 0.6552 0.6190 0.5658 0.4973 0.4151 0.3217 0.2195
0 0.1229 0.2425 0.3554 0.4587 0.5494 0.6252 0.6839 0.7239 0.7442 0.7442 0.7239 0.6839 0.6252 0.5494 0.4587 0.3554 0.2425
0 0.1333 0.2630 0.3855 0.4975 0.5959 0.6781 0.7418 0.7852 0.8072 0.8072 0.7852 0.7418 0.6781 0.5959 0.4975 0.3855 0.2630
0 0.1424 0.2809 0.4117 0.5313 0.6364 0.7242 0.7922 0.8385 0.8621 0.8621 0.8385 0.7922 0.7242 0.6364 0.5313 0.4117 0.2809
0 0.1500 0.2959 0.4337 0.5597 0.6704 0.7628 0.8345 0.8833 0.9081 0.9081 0.8833 0.8345 0.7628 0.6704 0.5597 0.4337 0.2959
0 0.1561 0.3078 0.4512 0.5823 0.6975 0.7937 0.8682 0.9191 0.9449 0.9449 0.9191 0.8682 0.7937 0.6975 0.5823 0.4512 0.3078
0 0.1605 0.3167 0.4642 0.5991 0.7176 0.8165 0.8932 0.9455 0.9720 0.9720 0.9455 0.8932 0.8165 0.7176 0.5991 0.4642 0.3167
0 0.1634 0.3223 0.4724 0.6097 0.7303 0.8310 0.9090 0.9622 0.9892 0.9892 0.9622 0.9090 0.8310 0.7303 0.6097 0.4724 0.3223
0 0.1646 0.3246 0.4758 0.6141 0.7356 0.8370 0.9156 0.9692 0.9964 0.9964 0.9692 0.9156 0.8370 0.7356 0.6141 0.4758 0.3246
0 0.1641 0.3236 0.4744 0.6122 0.7333 0.8345 0.9128 0.9663 0.9934 0.9934 0.9663 0.9128 0.8345 0.7333 0.6122 0.4744 0.3236
0 0.1619 0.3194 0.4681 0.6041 0.7236 0.8234 0.9007 0.9535 0.9802 0.9802 0.9535 0.9007 0.8234 0.7236 0.6041 0.4681 0.3194
0 0.1581 0.3118 0.4571 0.5899 0.7066 0.8040 0.8795 0.9310 0.9571 0.9571 0.9310 0.8795 0.8040 0.7066 0.5899 0.4571 0.3118
0 0.1526 0.3011 0.4414 0.5696 0.6823 0.7764 0.8493 0.8990 0.9242 0.9242 0.8990 0.8493 0.7764 0.6823 0.5696 0.4414 0.3011
0 0.1457 0.2873 0.4212 0.5435 0.6511 0.7408 0.8104 0.8578 0.8819 0.8819 0.8578 0.8104 0.7408 0.6511 0.5435 0.4212 0.2873
0 0.1372 0.2706 0.3967 0.5119 0.6132 0.6977 0.7632 0.8079 0.8306 0.8306 0.8079 0.7632 0.6977 0.6132 0.5119 0.3967 0.2706
0 0.1273 0.2511 0.3681 0.4751 0.5691 0.6475 0.7083 0.7498 0.7708 0.7708 0.7498 0.7083 0.6475 0.5691 0.4751 0.3681 0.2511
0 0.1161 0.2291 0.3358 0.4334 0.5191 0.5907 0.6462 0.6840 0.7032 0.7032 0.6840 0.6462 0.5907 0.5191 0.4334 0.3358 0.2291
0 0.1038 0.2047 0.3001 0.3873 0.4639 0.5279 0.5774 0.6113 0.6284 0.6284 0.6113 0.5774 0.5279 0.4639 0.3873 0.3001 0.2047
0 0.0904 0.1783 0.2613 0.3372 0.4040 0.4597 0.5028 0.5323 0.5472 0.5472 0.5323 0.5028 0.4597 0.4040 0.3372 0.2613 0.1783
0 0.0760 0.1500 0.2199 0.2838 0.3399 0.3868 0.4231 0.4479 0.4604 0.4604 0.4479 0.4231 0.3868 0.3399 0.2838 0.2199 0.1500
0 0.0609 0.1202 0.1762 0.2274 0.2724 0.3099 0.3390 0.3589 0.3689 0.3689 0.3589 0.3390 0.3099 0.2724 0.2274 0.1762 0.1202
0 0.0452 0.0892 0.1307 0.1687 0.2021 0.2299 0.2515 0.2662 0.2737 0.2737 0.2662 0.2515 0.2299 0.2021 0.1687 0.1307 0.0892
0 0.0290 0.0572 0.0839 0.1083 0.1297 0.1476 0.1614 0.1709 0.1757 0.1757 0.1709 0.1614 0.1476 0.1297 0.1083 0.0839 0.0572
0 0.0125 0.0247 0.0362 0.0468 0.0560 0.0637 0.0697 0.0738 0.0759 0.0759 0.0738 0.0697 0.0637 0.0560 0.0468 0.0362 0.0247
0 -0.0041 -0.0081 -0.0118 -0.0152 -0.0182 -0.0208 -0.0227 -0.0240 -0.0247 -0.0247 -0.0240 -0.0227 -0.0208 -0.0182 -0.0152 -0.0118 -0.0081
0 -0.0207 -0.0407 -0.0597 -0.0771 -0.0923 -0.1051 -0.1149 -0.1216 -0.1251 -0.1251 -0.1216 -0.1149 -0.1051 -0.0923 -0.0771 -0.0597 -0.0407
0 -0.0370 -0.0730 -0.1070 -0.1381 -0.1655 -0.1883 -0.2059 -0.2180 -0.2241 -0.2241 -0.2180 -0.2059 -0.1883 -0.1655 -0.1381 -0.1070 -0.0730
0 -0.0530 -0.1046 -0.1533 -0.1978 -0.2369 -0.2696 -0.2949 -0.3121 -0.3209 -0.3209 -0.3121 -0.2949 -0.2696 -0.2369 -0.1978 -0.1533 -0.1046
0 -0.0684 -0.1350 -0.1979 -0.2554 -0.3059 -0.3481 -0.3808 -0.4031 -0.4144 -0.4144 -0.4031 -0.3808 -0.3481 -0.3059 -0.2554 -0.1979 -0.1350
0 -0.0832 -0.1641 -0.2405 -0.3104 -0.3718 -0.4231 -0.4628 -0.4899 -0.5037 -0.5037 -0.4899 -0.4628 -0.4231 -0.3718 -0.3104 -0.2405 -0.1641
0 -0.0971 -0.1915 -0.2807 -0.3623 -0.4340 -0.4938 -0.5402 -0.5718 -0.5878 -0.5878 -0.5718 -0.5402 -0.4938 -0.4340 -0.3623 -0.2807 -0.1915
0 -0.1100 -0.2170 -0.3181 -0.4105 -0.4917 -0.5595 -0.6120 -0.6478 -0.6660 -0.6660 -0.6478 -0.6120 -0.5595 -0.4917 -0.4105 -0.3181 -0.2170
0 -0.1218 -0.2402 -0.3521 -0.4544 -0.5443 -0.6194 -0.6776 -0.7172 -0.7373 -0.7373 -0.7172 -0.6776 -0.6194 -0.5443 -0.4544 -0.3521 -0.2402
0 -0.1323 -0.2610 -0.3826 -0.4938 -0.5915 -0.6730 -0.7362 -0.7793 -0.8012 -0.8012 -0.7793 -0.7362 -0.6730 -0.5915 -0.4938 -0.3826 -0.2610
0 -0.1415 -0.2792 -0.4092 -0.5281 -0.6326 -0.7198 -0.7874 -0.8335 -0.8569 -0.8569 -0.8335 -0.7874 -0.7198 -0.6326 -0.5281 -0.4092 -0.2792
0 -0.1493 -0.2945 -0.4316 -0.5570 -0.6672 -0.7592 -0.8305 -0.8792 -0.9038 -0.9038 -0.8792 -0.8305 -0.7592 -0.6672 -0.5570 -0.4316 -0.2945
0 -0.1555 -0.3068 -0.4497 -0.5803 -0.6951 -0.7909 -0.8652 -0.9159 -0.9416 -0.9416 -0.9159 -0.8652 -0.7909 -0.6951 -0.5803 -0.4497 -0.3068
0 -0.1602 -0.3159 -0.4631 -0.5976 -0.7159 -0.8146 -0.8911 -0.9432 -0.9697 -0.9697 -0.9432 -0.8911 -0.8146 -0.7159 -0.5976 -0.4631 -0.3159
0 -0.1632 -0.3219 -0.4718 -0.6089 -0.7293 -0.8299 -0.9078 -0.9610 -0.9879 -0.9879 -0.9610 -0.9078 -0.8299 -0.7293 -0.6089 -0.4718 -0.3219
0 -0.1645 -0.3245 -0.4757 -0.6139 -0.7354 -0.8368 -0.9153 -0.9689 -0.9961 -0.9961 -0.9689 -0.9153 -0.8368 -0.7354 -0.6139 -0.4757 -0.3245
0 -0.1642 -0.3239 -0.4748 -0.6127 -0.7339 -0.8351 -0.9135 -0.9670 -0.9941 -0.9941 -0.9670 -0.9135 -0.8351 -0.7339 -0.6127 -0.4748 -0.3239
0 -0.1622 -0.3200 -0.4690 -0.6052 -0.7250 -0.8249 -0.9024 -0.9552 -0.9820 -0.9820 -0.9552 -0.9024 -0.8249 -0.7250 -0.6052 -0.4690 -0.3200
0 -0.1585 -0.3127 -0.4584 -0.5916 -0.7086 -0.8063 -0.8821 -0.9337 -0.9599 -0.9599 -0.9337 -0.8821 -0.8063 -0.7086 -0.5916 -0.4584 -0.3127
0 -0.1533 -0.3023 -0.4432 -0.5719 -0.6851 -0.7795 -0.8527 -0.9027 -0.9280 -0.9280 -0.9027 -0.8527 -0.7795 -0.6851 -0.5719 -0.4432 -0.3023
0 -0.1464 -0.2889 -0.4234 -0.5464 -0.6545 -0.7448 -0.8147 -0.8624 -0.8866 -0.8866 -0.8624 -0.8147 -0.7448 -0.6545 -0.5464 -0.4234 -0.2889
0 -0.1381 -0.2724 -0.3994 -0.5154 -0.6173 -0.7024 -0.7684 -0.8134 -0.8362 -0.8362 -0.8134 -0.7684 -0.7024 -0.6173 -0.5154 -0.3994 -0.2724
Columns 19 through 20
0.1646 0.0000
0.1638 0.0000
0.1612 0.0000
0.1571 0.0000
0.1513 0.0000
0.1440 0.0000
0.1353 0.0000
0.1251 0.0000
0.1137 0.0000
0.1011 0.0000
0.0875 0.0000
0.0730 0.0000
0.0578 0.0000
0.0419 0.0000
0.0257 0.0000
0.0092 0.0000
-0.0075 -0.0000
-0.0240 -0.0000
-0.0403 -0.0000
-0.0562 -0.0000
-0.0715 -0.0000
-0.0861 -0.0000
-0.0998 -0.0000
-0.1125 -0.0000
-0.1240 -0.0000
-0.1343 -0.0000
-0.1432 -0.0000
-0.1507 -0.0000
-0.1566 -0.0000
-0.1609 -0.0000
-0.1636 -0.0000
-0.1646 -0.0000
-0.1639 -0.0000
-0.1616 -0.0000
-0.1576 -0.0000
-0.1520 -0.0000
-0.1449 -0.0000
-0.1362 -0.0000
-0.1262 -0.0000
-0.1149 -0.0000
-0.1025 -0.0000
-0.0890 -0.0000
-0.0745 -0.0000
-0.0594 -0.0000
-0.0436 -0.0000
-0.0273 -0.0000
-0.0108 -0.0000
0.0058 0.0000
0.0223 0.0000
0.0387 0.0000
0.0546 0.0000
0.0700 0.0000
0.0846 0.0000
0.0984 0.0000
0.1112 0.0000
0.1229 0.0000
0.1333 0.0000
0.1424 0.0000
0.1500 0.0000
0.1561 0.0000
0.1605 0.0000
0.1634 0.0000
0.1646 0.0000
0.1641 0.0000
0.1619 0.0000
0.1581 0.0000
0.1526 0.0000
0.1457 0.0000
0.1372 0.0000
0.1273 0.0000
0.1161 0.0000
0.1038 0.0000
0.0904 0.0000
0.0760 0.0000
0.0609 0.0000
0.0452 0.0000
0.0290 0.0000
0.0125 0.0000
-0.0041 -0.0000
-0.0207 -0.0000
-0.0370 -0.0000
-0.0530 -0.0000
-0.0684 -0.0000
-0.0832 -0.0000
-0.0971 -0.0000
-0.1100 -0.0000
-0.1218 -0.0000
-0.1323 -0.0000
-0.1415 -0.0000
-0.1493 -0.0000
-0.1555 -0.0000
-0.1602 -0.0000
-0.1632 -0.0000
-0.1645 -0.0000
-0.1642 -0.0000
-0.1622 -0.0000
-0.1585 -0.0000
-0.1533 -0.0000
-0.1464 -0.0000
-0.1381 -0.0000
velocity(:,:,2) =
Columns 1 through 18
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.1008 -0.0995 -0.0954 -0.0887 -0.0796 -0.0683 -0.0552 -0.0405 -0.0248 -0.0083 0.0083 0.0248 0.0405 0.0552 0.0683 0.0796 0.0887 0.0954
-0.2006 -0.1979 -0.1898 -0.1765 -0.1583 -0.1359 -0.1097 -0.0806 -0.0493 -0.0166 0.0166 0.0493 0.0806 0.1097 0.1359 0.1583 0.1765 0.1898
-0.2984 -0.2943 -0.2822 -0.2624 -0.2355 -0.2021 -0.1632 -0.1199 -0.0733 -0.0246 0.0246 0.0733 0.1199 0.1632 0.2021 0.2355 0.2624 0.2822
-0.3931 -0.3878 -0.3718 -0.3458 -0.3102 -0.2663 -0.2150 -0.1579 -0.0965 -0.0325 0.0325 0.0965 0.1579 0.2150 0.2663 0.3102 0.3458 0.3718
-0.4839 -0.4773 -0.4576 -0.4255 -0.3818 -0.3277 -0.2646 -0.1944 -0.1188 -0.0400 0.0400 0.1188 0.1944 0.2646 0.3277 0.3818 0.4255 0.4576
-0.5696 -0.5619 -0.5388 -0.5010 -0.4495 -0.3858 -0.3116 -0.2288 -0.1398 -0.0470 0.0470 0.1398 0.2288 0.3116 0.3858 0.4495 0.5010 0.5388
-0.6496 -0.6407 -0.6144 -0.5713 -0.5126 -0.4400 -0.3553 -0.2609 -0.1595 -0.0536 0.0536 0.1595 0.2609 0.3553 0.4400 0.5126 0.5713 0.6144
-0.7230 -0.7131 -0.6838 -0.6358 -0.5705 -0.4896 -0.3954 -0.2904 -0.1775 -0.0597 0.0597 0.1775 0.2904 0.3954 0.4896 0.5705 0.6358 0.6838
-0.7889 -0.7782 -0.7462 -0.6939 -0.6226 -0.5343 -0.4315 -0.3169 -0.1937 -0.0652 0.0652 0.1937 0.3169 0.4315 0.5343 0.6226 0.6939 0.7462
-0.8469 -0.8353 -0.8010 -0.7448 -0.6683 -0.5736 -0.4632 -0.3402 -0.2079 -0.0699 0.0699 0.2079 0.3402 0.4632 0.5736 0.6683 0.7448 0.8010
-0.8962 -0.8840 -0.8476 -0.7882 -0.7072 -0.6070 -0.4902 -0.3600 -0.2200 -0.0740 0.0740 0.2200 0.3600 0.4902 0.6070 0.7072 0.7882 0.8476
-0.9364 -0.9236 -0.8856 -0.8235 -0.7389 -0.6342 -0.5121 -0.3761 -0.2299 -0.0773 0.0773 0.2299 0.3761 0.5121 0.6342 0.7389 0.8235 0.8856
-0.9670 -0.9538 -0.9146 -0.8504 -0.7631 -0.6549 -0.5289 -0.3884 -0.2374 -0.0799 0.0799 0.2374 0.3884 0.5289 0.6549 0.7631 0.8504 0.9146
-0.9878 -0.9743 -0.9342 -0.8687 -0.7795 -0.6690 -0.5403 -0.3968 -0.2425 -0.0816 0.0816 0.2425 0.3968 0.5403 0.6690 0.7795 0.8687 0.9342
-0.9985 -0.9848 -0.9444 -0.8781 -0.7879 -0.6762 -0.5461 -0.4011 -0.2451 -0.0825 0.0825 0.2451 0.4011 0.5461 0.6762 0.7879 0.8781 0.9444
-0.9990 -0.9853 -0.9448 -0.8786 -0.7883 -0.6766 -0.5464 -0.4013 -0.2452 -0.0825 0.0825 0.2452 0.4013 0.5464 0.6766 0.7883 0.8786 0.9448
-0.9893 -0.9758 -0.9357 -0.8701 -0.7807 -0.6700 -0.5411 -0.3974 -0.2429 -0.0817 0.0817 0.2429 0.3974 0.5411 0.6700 0.7807 0.8701 0.9357
-0.9696 -0.9563 -0.9170 -0.8527 -0.7651 -0.6567 -0.5303 -0.3895 -0.2380 -0.0801 0.0801 0.2380 0.3895 0.5303 0.6567 0.7651 0.8527 0.9170
-0.9399 -0.9271 -0.8890 -0.8266 -0.7417 -0.6366 -0.5141 -0.3776 -0.2307 -0.0776 0.0776 0.2307 0.3776 0.5141 0.6366 0.7417 0.8266 0.8890
-0.9007 -0.8884 -0.8519 -0.7921 -0.7108 -0.6100 -0.4926 -0.3618 -0.2211 -0.0744 0.0744 0.2211 0.3618 0.4926 0.6100 0.7108 0.7921 0.8519
-0.8523 -0.8407 -0.8061 -0.7496 -0.6726 -0.5773 -0.4662 -0.3424 -0.2092 -0.0704 0.0704 0.2092 0.3424 0.4662 0.5773 0.6726 0.7496 0.8061
-0.7952 -0.7844 -0.7521 -0.6994 -0.6275 -0.5386 -0.4349 -0.3194 -0.1952 -0.0657 0.0657 0.1952 0.3194 0.4349 0.5386 0.6275 0.6994 0.7521
-0.7300 -0.7201 -0.6905 -0.6420 -0.5761 -0.4944 -0.3993 -0.2932 -0.1792 -0.0603 0.0603 0.1792 0.2932 0.3993 0.4944 0.5761 0.6420 0.6905
-0.6574 -0.6484 -0.6218 -0.5782 -0.5188 -0.4452 -0.3596 -0.2641 -0.1614 -0.0543 0.0543 0.1614 0.2641 0.3596 0.4452 0.5188 0.5782 0.6218
-0.5781 -0.5702 -0.5467 -0.5084 -0.4562 -0.3915 -0.3162 -0.2322 -0.1419 -0.0477 0.0477 0.1419 0.2322 0.3162 0.3915 0.4562 0.5084 0.5467
-0.4928 -0.4861 -0.4661 -0.4334 -0.3889 -0.3338 -0.2695 -0.1980 -0.1210 -0.0407 0.0407 0.1210 0.1980 0.2695 0.3338 0.3889 0.4334 0.4661
-0.4026 -0.3971 -0.3808 -0.3540 -0.3177 -0.2727 -0.2202 -0.1617 -0.0988 -0.0332 0.0332 0.0988 0.1617 0.2202 0.2727 0.3177 0.3540 0.3808
-0.3082 -0.3040 -0.2915 -0.2711 -0.2432 -0.2087 -0.1686 -0.1238 -0.0757 -0.0255 0.0255 0.0757 0.1238 0.1686 0.2087 0.2432 0.2711 0.2915
-0.2107 -0.2078 -0.1993 -0.1853 -0.1663 -0.1427 -0.1152 -0.0846 -0.0517 -0.0174 0.0174 0.0517 0.0846 0.1152 0.1427 0.1663 0.1853 0.1993
-0.1111 -0.1095 -0.1050 -0.0977 -0.0876 -0.0752 -0.0607 -0.0446 -0.0273 -0.0092 0.0092 0.0273 0.0446 0.0607 0.0752 0.0876 0.0977 0.1050
-0.0103 -0.0101 -0.0097 -0.0090 -0.0081 -0.0070 -0.0056 -0.0041 -0.0025 -0.0008 0.0008 0.0025 0.0041 0.0056 0.0070 0.0081 0.0090 0.0097
0.0906 0.0894 0.0857 0.0797 0.0715 0.0614 0.0496 0.0364 0.0222 0.0075 -0.0075 -0.0222 -0.0364 -0.0496 -0.0614 -0.0715 -0.0797 -0.0857
0.1906 0.1880 0.1802 0.1676 0.1504 0.1291 0.1042 0.0766 0.0468 0.0157 -0.0157 -0.0468 -0.0766 -0.1042 -0.1291 -0.1504 -0.1676 -0.1802
0.2886 0.2847 0.2730 0.2538 0.2277 0.1955 0.1578 0.1159 0.0708 0.0238 -0.0238 -0.0708 -0.1159 -0.1578 -0.1955 -0.2277 -0.2538 -0.2730
0.3837 0.3784 0.3629 0.3374 0.3028 0.2598 0.2098 0.1541 0.0942 0.0317 -0.0317 -0.0942 -0.1541 -0.2098 -0.2598 -0.3028 -0.3374 -0.3629
0.4748 0.4684 0.4491 0.4176 0.3747 0.3216 0.2597 0.1907 0.1166 0.0392 -0.0392 -0.1166 -0.1907 -0.2597 -0.3216 -0.3747 -0.4176 -0.4491
0.5612 0.5535 0.5308 0.4935 0.4428 0.3801 0.3069 0.2254 0.1378 0.0463 -0.0463 -0.1378 -0.2254 -0.3069 -0.3801 -0.4428 -0.4935 -0.5308
0.6418 0.6330 0.6070 0.5644 0.5064 0.4347 0.3510 0.2578 0.1575 0.0530 -0.0530 -0.1575 -0.2578 -0.3510 -0.4347 -0.5064 -0.5644 -0.6070
0.7158 0.7061 0.6770 0.6295 0.5649 0.4848 0.3915 0.2875 0.1757 0.0591 -0.0591 -0.1757 -0.2875 -0.3915 -0.4848 -0.5649 -0.6295 -0.6770
0.7826 0.7719 0.7402 0.6883 0.6176 0.5300 0.4280 0.3144 0.1921 0.0646 -0.0646 -0.1921 -0.3144 -0.4280 -0.5300 -0.6176 -0.6883 -0.7402
0.8414 0.8299 0.7958 0.7400 0.6640 0.5698 0.4602 0.3380 0.2065 0.0695 -0.0695 -0.2065 -0.3380 -0.4602 -0.5698 -0.6640 -0.7400 -0.7958
0.8916 0.8794 0.8433 0.7841 0.7036 0.6039 0.4877 0.3581 0.2189 0.0736 -0.0736 -0.2189 -0.3581 -0.4877 -0.6039 -0.7036 -0.7841 -0.8433
0.9327 0.9200 0.8822 0.8203 0.7360 0.6317 0.5101 0.3747 0.2290 0.0770 -0.0770 -0.2290 -0.3747 -0.5101 -0.6317 -0.7360 -0.8203 -0.8822
0.9643 0.9512 0.9121 0.8481 0.7610 0.6531 0.5274 0.3874 0.2367 0.0796 -0.0796 -0.2367 -0.3874 -0.5274 -0.6531 -0.7610 -0.8481 -0.9121
0.9861 0.9726 0.9327 0.8672 0.7782 0.6679 0.5393 0.3961 0.2421 0.0814 -0.0814 -0.2421 -0.3961 -0.5393 -0.6679 -0.7782 -0.8672 -0.9327
0.9978 0.9842 0.9438 0.8776 0.7874 0.6758 0.5458 0.4008 0.2450 0.0824 -0.0824 -0.2450 -0.4008 -0.5458 -0.6758 -0.7874 -0.8776 -0.9438
0.9994 0.9858 0.9452 0.8789 0.7887 0.6769 0.5466 0.4014 0.2453 0.0825 -0.0825 -0.2453 -0.4014 -0.5466 -0.6769 -0.7887 -0.8789 -0.9452
0.9908 0.9772 0.9371 0.8713 0.7818 0.6710 0.5419 0.3980 0.2432 0.0818 -0.0818 -0.2432 -0.3980 -0.5419 -0.6710 -0.7818 -0.8713 -0.9371
0.9720 0.9588 0.9194 0.8549 0.7671 0.6583 0.5316 0.3905 0.2386 0.0803 -0.0803 -0.2386 -0.3905 -0.5316 -0.6583 -0.7671 -0.8549 -0.9194
0.9434 0.9305 0.8923 0.8297 0.7445 0.6389 0.5160 0.3790 0.2316 0.0779 -0.0779 -0.2316 -0.3790 -0.5160 -0.6389 -0.7445 -0.8297 -0.8923
0.9051 0.8928 0.8561 0.7960 0.7143 0.6130 0.4951 0.3636 0.2222 0.0747 -0.0747 -0.2222 -0.3636 -0.4951 -0.6130 -0.7143 -0.7960 -0.8561
0.8576 0.8459 0.8112 0.7543 0.6768 0.5809 0.4691 0.3445 0.2105 0.0708 -0.0708 -0.2105 -0.3445 -0.4691 -0.5809 -0.6768 -0.7543 -0.8112
0.8014 0.7905 0.7580 0.7048 0.6324 0.5428 0.4383 0.3219 0.1967 0.0662 -0.0662 -0.1967 -0.3219 -0.4383 -0.5428 -0.6324 -0.7048 -0.7580
0.7370 0.7270 0.6971 0.6482 0.5816 0.4992 0.4031 0.2961 0.1809 0.0609 -0.0609 -0.1809 -0.2961 -0.4031 -0.4992 -0.5816 -0.6482 -0.6971
0.6651 0.6560 0.6291 0.5849 0.5249 0.4505 0.3638 0.2672 0.1633 0.0549 -0.0549 -0.1633 -0.2672 -0.3638 -0.4505 -0.5249 -0.5849 -0.6291
0.5864 0.5784 0.5546 0.5157 0.4628 0.3972 0.3207 0.2356 0.1440 0.0484 -0.0484 -0.1440 -0.2356 -0.3207 -0.3972 -0.4628 -0.5157 -0.5546
0.5017 0.4949 0.4746 0.4413 0.3959 0.3398 0.2744 0.2015 0.1232 0.0414 -0.0414 -0.1232 -0.2015 -0.2744 -0.3398 -0.3959 -0.4413 -0.4746
0.4120 0.4063 0.3896 0.3623 0.3251 0.2790 0.2253 0.1655 0.1011 0.0340 -0.0340 -0.1011 -0.1655 -0.2253 -0.2790 -0.3251 -0.3623 -0.3896
0.3180 0.3136 0.3007 0.2796 0.2509 0.2154 0.1739 0.1277 0.0781 0.0263 -0.0263 -0.0781 -0.1277 -0.1739 -0.2154 -0.2509 -0.2796 -0.3007
0.2207 0.2177 0.2088 0.1941 0.1742 0.1495 0.1207 0.0887 0.0542 0.0182 -0.0182 -0.0542 -0.0887 -0.1207 -0.1495 -0.1742 -0.1941 -0.2088
0.1213 0.1196 0.1147 0.1067 0.0957 0.0821 0.0663 0.0487 0.0298 0.0100 -0.0100 -0.0298 -0.0487 -0.0663 -0.0821 -0.0957 -0.1067 -0.1147
0.0206 0.0203 0.0194 0.0181 0.0162 0.0139 0.0112 0.0083 0.0050 0.0017 -0.0017 -0.0050 -0.0083 -0.0112 -0.0139 -0.0162 -0.0181 -0.0194
-0.0804 -0.0793 -0.0760 -0.0707 -0.0634 -0.0544 -0.0440 -0.0323 -0.0197 -0.0066 0.0066 0.0197 0.0323 0.0440 0.0544 0.0634 0.0707 0.0760
-0.1805 -0.1780 -0.1707 -0.1587 -0.1424 -0.1222 -0.0987 -0.0725 -0.0443 -0.0149 0.0149 0.0443 0.0725 0.0987 0.1222 0.1424 0.1587 0.1707
-0.2787 -0.2749 -0.2636 -0.2451 -0.2200 -0.1888 -0.1525 -0.1120 -0.0684 -0.0230 0.0230 0.0684 0.1120 0.1525 0.1888 0.2200 0.2451 0.2636
-0.3742 -0.3690 -0.3539 -0.3291 -0.2953 -0.2534 -0.2046 -0.1503 -0.0918 -0.0309 0.0309 0.0918 0.1503 0.2046 0.2534 0.2953 0.3291 0.3539
-0.4658 -0.4594 -0.4405 -0.4096 -0.3675 -0.3154 -0.2547 -0.1871 -0.1143 -0.0385 0.0385 0.1143 0.1871 0.2547 0.3154 0.3675 0.4096 0.4405
-0.5526 -0.5451 -0.5227 -0.4860 -0.4361 -0.3743 -0.3023 -0.2220 -0.1357 -0.0456 0.0456 0.1357 0.2220 0.3023 0.3743 0.4361 0.4860 0.5227
-0.6338 -0.6252 -0.5995 -0.5574 -0.5002 -0.4293 -0.3467 -0.2546 -0.1556 -0.0523 0.0523 0.1556 0.2546 0.3467 0.4293 0.5002 0.5574 0.5995
-0.7086 -0.6989 -0.6702 -0.6232 -0.5592 -0.4799 -0.3876 -0.2846 -0.1740 -0.0585 0.0585 0.1740 0.2846 0.3876 0.4799 0.5592 0.6232 0.6702
-0.7761 -0.7656 -0.7341 -0.6826 -0.6125 -0.5257 -0.4245 -0.3118 -0.1905 -0.0641 0.0641 0.1905 0.3118 0.4245 0.5257 0.6125 0.6826 0.7341
-0.8358 -0.8244 -0.7905 -0.7350 -0.6595 -0.5661 -0.4571 -0.3357 -0.2052 -0.0690 0.0690 0.2052 0.3357 0.4571 0.5661 0.6595 0.7350 0.7905
-0.8869 -0.8748 -0.8388 -0.7800 -0.6999 -0.6007 -0.4851 -0.3563 -0.2177 -0.0732 0.0732 0.2177 0.3563 0.4851 0.6007 0.6999 0.7800 0.8388
-0.9289 -0.9163 -0.8786 -0.8170 -0.7331 -0.6292 -0.5081 -0.3732 -0.2280 -0.0767 0.0767 0.2280 0.3732 0.5081 0.6292 0.7331 0.8170 0.8786
-0.9615 -0.9484 -0.9094 -0.8457 -0.7588 -0.6512 -0.5259 -0.3862 -0.2360 -0.0794 0.0794 0.2360 0.3862 0.5259 0.6512 0.7588 0.8457 0.9094
-0.9843 -0.9709 -0.9310 -0.8657 -0.7768 -0.6667 -0.5384 -0.3954 -0.2416 -0.0813 0.0813 0.2416 0.3954 0.5384 0.6667 0.7768 0.8657 0.9310
-0.9971 -0.9835 -0.9431 -0.8769 -0.7869 -0.6753 -0.5454 -0.4005 -0.2448 -0.0823 0.0823 0.2448 0.4005 0.5454 0.6753 0.7869 0.8769 0.9431
-0.9997 -0.9861 -0.9455 -0.8792 -0.7889 -0.6771 -0.5468 -0.4016 -0.2454 -0.0826 0.0826 0.2454 0.4016 0.5468 0.6771 0.7889 0.8792 0.9455
-0.9921 -0.9786 -0.9383 -0.8725 -0.7829 -0.6719 -0.5426 -0.3985 -0.2435 -0.0819 0.0819 0.2435 0.3985 0.5426 0.6719 0.7829 0.8725 0.9383
-0.9744 -0.9611 -0.9216 -0.8569 -0.7689 -0.6599 -0.5329 -0.3914 -0.2392 -0.0805 0.0805 0.2392 0.3914 0.5329 0.6599 0.7689 0.8569 0.9216
-0.9467 -0.9338 -0.8954 -0.8326 -0.7471 -0.6412 -0.5178 -0.3803 -0.2324 -0.0782 0.0782 0.2324 0.3803 0.5178 0.6412 0.7471 0.8326 0.8954
-0.9094 -0.8970 -0.8602 -0.7998 -0.7177 -0.6160 -0.4974 -0.3653 -0.2233 -0.0751 0.0751 0.2233 0.3653 0.4974 0.6160 0.7177 0.7998 0.8602
-0.8629 -0.8511 -0.8161 -0.7589 -0.6809 -0.5844 -0.4720 -0.3466 -0.2118 -0.0713 0.0713 0.2118 0.3466 0.4720 0.5844 0.6809 0.7589 0.8161
-0.8075 -0.7965 -0.7638 -0.7102 -0.6372 -0.5469 -0.4417 -0.3244 -0.1982 -0.0667 0.0667 0.1982 0.3244 0.4417 0.5469 0.6372 0.7102 0.7638
-0.7439 -0.7338 -0.7036 -0.6543 -0.5871 -0.5038 -0.4069 -0.2988 -0.1826 -0.0614 0.0614 0.1826 0.2988 0.4069 0.5038 0.5871 0.6543 0.7036
-0.6727 -0.6636 -0.6363 -0.5917 -0.5309 -0.4556 -0.3680 -0.2702 -0.1651 -0.0556 0.0556 0.1651 0.2702 0.3680 0.4556 0.5309 0.5917 0.6363
-0.5947 -0.5866 -0.5625 -0.5230 -0.4693 -0.4028 -0.3253 -0.2389 -0.1460 -0.0491 0.0491 0.1460 0.2389 0.3253 0.4028 0.4693 0.5230 0.5625
-0.5106 -0.5036 -0.4829 -0.4491 -0.4029 -0.3458 -0.2793 -0.2051 -0.1253 -0.0422 0.0422 0.1253 0.2051 0.2793 0.3458 0.4029 0.4491 0.4829
-0.4213 -0.4156 -0.3985 -0.3705 -0.3325 -0.2853 -0.2304 -0.1692 -0.1034 -0.0348 0.0348 0.1034 0.1692 0.2304 0.2853 0.3325 0.3705 0.3985
-0.3277 -0.3232 -0.3099 -0.2882 -0.2586 -0.2219 -0.1792 -0.1316 -0.0804 -0.0271 0.0271 0.0804 0.1316 0.1792 0.2219 0.2586 0.2882 0.3099
-0.2308 -0.2276 -0.2183 -0.2029 -0.1821 -0.1563 -0.1262 -0.0927 -0.0566 -0.0191 0.0191 0.0566 0.0927 0.1262 0.1563 0.1821 0.2029 0.2183
-0.1315 -0.1297 -0.1243 -0.1156 -0.1037 -0.0890 -0.0719 -0.0528 -0.0323 -0.0109 0.0109 0.0323 0.0528 0.0719 0.0890 0.1037 0.1156 0.1243
-0.0308 -0.0304 -0.0292 -0.0271 -0.0243 -0.0209 -0.0169 -0.0124 -0.0076 -0.0025 0.0025 0.0076 0.0124 0.0169 0.0209 0.0243 0.0271 0.0292
0.0701 0.0692 0.0663 0.0617 0.0553 0.0475 0.0383 0.0282 0.0172 0.0058 -0.0058 -0.0172 -0.0282 -0.0383 -0.0475 -0.0553 -0.0617 -0.0663
0.1703 0.1680 0.1611 0.1498 0.1344 0.1154 0.0932 0.0684 0.0418 0.0141 -0.0141 -0.0418 -0.0684 -0.0932 -0.1154 -0.1344 -0.1498 -0.1611
0.2688 0.2652 0.2543 0.2364 0.2122 0.1821 0.1470 0.1080 0.0660 0.0222 -0.0222 -0.0660 -0.1080 -0.1470 -0.1821 -0.2122 -0.2364 -0.2543
0.3646 0.3596 0.3448 0.3207 0.2877 0.2469 0.1994 0.1465 0.0895 0.0301 -0.0301 -0.0895 -0.1465 -0.1994 -0.2469 -0.2877 -0.3207 -0.3448
0.4566 0.4504 0.4319 0.4016 0.3604 0.3093 0.2498 0.1834 0.1121 0.0377 -0.0377 -0.1121 -0.1834 -0.2498 -0.3093 -0.3604 -0.4016 -0.4319
0.5440 0.5366 0.5145 0.4785 0.4293 0.3685 0.2976 0.2185 0.1335 0.0449 -0.0449 -0.1335 -0.2185 -0.2976 -0.3685 -0.4293 -0.4785 -0.5145
Columns 19 through 20
0 0
0.0995 0.1008
0.1979 0.2006
0.2943 0.2984
0.3878 0.3931
0.4773 0.4839
0.5619 0.5696
0.6407 0.6496
0.7131 0.7230
0.7782 0.7889
0.8353 0.8469
0.8840 0.8962
0.9236 0.9364
0.9538 0.9670
0.9743 0.9878
0.9848 0.9985
0.9853 0.9990
0.9758 0.9893
0.9563 0.9696
0.9271 0.9399
0.8884 0.9007
0.8407 0.8523
0.7844 0.7952
0.7201 0.7300
0.6484 0.6574
0.5702 0.5781
0.4861 0.4928
0.3971 0.4026
0.3040 0.3082
0.2078 0.2107
0.1095 0.1111
0.0101 0.0103
-0.0894 -0.0906
-0.1880 -0.1906
-0.2847 -0.2886
-0.3784 -0.3837
-0.4684 -0.4748
-0.5535 -0.5612
-0.6330 -0.6418
-0.7061 -0.7158
-0.7719 -0.7826
-0.8299 -0.8414
-0.8794 -0.8916
-0.9200 -0.9327
-0.9512 -0.9643
-0.9726 -0.9861
-0.9842 -0.9978
-0.9858 -0.9994
-0.9772 -0.9908
-0.9588 -0.9720
-0.9305 -0.9434
-0.8928 -0.9051
-0.8459 -0.8576
-0.7905 -0.8014
-0.7270 -0.7370
-0.6560 -0.6651
-0.5784 -0.5864
-0.4949 -0.5017
-0.4063 -0.4120
-0.3136 -0.3180
-0.2177 -0.2207
-0.1196 -0.1213
-0.0203 -0.0206
0.0793 0.0804
0.1780 0.1805
0.2749 0.2787
0.3690 0.3742
0.4594 0.4658
0.5451 0.5526
0.6252 0.6338
0.6989 0.7086
0.7656 0.7761
0.8244 0.8358
0.8748 0.8869
0.9163 0.9289
0.9484 0.9615
0.9709 0.9843
0.9835 0.9971
0.9861 0.9997
0.9786 0.9921
0.9611 0.9744
0.9338 0.9467
0.8970 0.9094
0.8511 0.8629
0.7965 0.8075
0.7338 0.7439
0.6636 0.6727
0.5866 0.5947
0.5036 0.5106
0.4156 0.4213
0.3232 0.3277
0.2276 0.2308
0.1297 0.1315
0.0304 0.0308
-0.0692 -0.0701
-0.1680 -0.1703
-0.2652 -0.2688
-0.3596 -0.3646
-0.4504 -0.4566
-0.5366 -0.5440
velocity(:,:,3) =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
figure
hold on
for k = 1:size(velocity,3)
surfc(vx, vy, velocity(:,:,k))
end
Warning: Contour not rendered for constant ZData
view(-27,30)
colormap(turbo)
colorbar
grid on
axis('equal')
xlabel('v_x')
ylabel('V_y')
zlabel('velocity')
% where vx = cos(beta)*sin(alpha),
%
% and vy is something similar.
%
% The surface plot will be against beta and alpha, so I write
% vx_times_ip = vx .* ip(theta)
.
Hi Star Strider!
Can I loop through both beta and alpha? Also, my function is in a separate function file, which my surface plotting code calls. Does this cause issues? Should I instead keep my function locally defined within my surface plotting code? Thanks!
‘’Can I loop through both beta and alpha?
You have my permission! :-)
I‘m not certain whether you’re referring to the vectors or the matrices. The matrices will be duplicates of the original vectors, with ‘Alpha’ duplicating ‘alpha’ row-wise, and ‘Beta’ duplicating ‘beta’ column-wise.
I’m not certain about the rest, since I cannot even visualise what you want to do. One option is to plot each ‘page’ of your array (if it has separate pages — I’m not sure what you’re doing) as separate surf plots.
Plotting different results in different figures would not cause issues, and could be a solution.
(Note that I’m responding to hypothetical problems with hypothetical replies.)
.
Noob
on 3 Jan 2025
Hi Star Strider,
For making surface plots, I have to use Beta and Alpha, the outputs from meshgrid(alpha, beta), as inputs to the functions. But before I get to the functions I want to code up terms, which are vectors, as linear combinations of rotating basis vectors. Matlab is telling me about arrays having incompatible sizes, when I try to do this, because Beta is a vector, Alpha is a vector, and a rotating basis vector is a vector. This is tricky to get right, in contrast to making simple line plots, where I didn’t have much issues. I’m a little frustrated with myself. I’m going to try again tomorrow. Goodnight, and thanks for your time!
My pleasure!
I’m obviously not able to understand what you are doing (since you haven’t revealed what that is), however if you have a function that takes the vectors α and β (or similarly-sized vectors for one or both) as arguments, the functions need to produce an appropriate-size matrix as an output that you can plot against α and β. To create an appropriate-size matrix from an argument vector, one option is to use the repmat function. That should make this easier.
.
Hi Star Strider!
So, just to describe my workflow a bit more clearly:
I loop through beta and then calculate values of F (a scalar-valued function) for all alpha = linspace(0, 2pi, 1001). I am only looping through beta, not alpha, which I really like.
I might choose 10 or 11 evenly spaced values of beta to loop through, using linspace( ).
Then, I made nice line plots, going from subplots to tiled layouts, which seems to be advantageous; e.g. global title, global colorbar, etc. are made easy using tiledLayout rather than with subplot.
In my 2D line plots, each tile would have the 11 curves, with alpha being the independent variable, and I use colors from a colormap to show the variation in beta. This figure of 6 tiles, I think, is really pretty -- and communicative.
Now, instead of 2D line plots, I want to present this exact same information using 3D surface plots, just to compare and see which figure is more communicative.
However, since my functions that I am plotting are scalar-valued functions, I am getting the error that my functions need to be matrices.
By the way, I have plenty of vectors expressed as linear combinations of basis vectors, but the final functions to be plotted are all scalar-valued, gotten from using dot products.
So, as of now, I can basically write a poor man's version of a code that gives the surface plots (very pretty), but this is not good and systematic:
- I would like to continue looping through beta;
- To keep things organized and de-cluttered, I would like to continue calling my functions which are stored in separate files; and
- For doing careful mathematics, I would like to continue expressing vectors as linear combinations of basis vectors, etc.
It seems if in the beginning of my surface-plotting code I define a meshgrid [Alpha,Beta] = meshgrid(alpha,beta), and use the variables Alpha and Beta as inputs, then I start running into issues with arrays having incompatible sizes.
I have one current guess at a solution, as of now:
Maybe define my functions locally in the same file as my surface-plotting code, rather than call them from another separate file? I would rather not do this, because my intuition is that my errors should be easy enough to fix.
I look forward to hearing from you.
Thanks for your time!
You can create matrices from the lines in the line plots by concatenating them into a matrix. They all have to have the same number of points (be the same size), and are functions of the inidepenedent variable at the same points.
There are ways to get around these restrictions (probably using the scatteredInterpolant function), however it impossiible to describe that process wiith only the information thus far provided.
x = linspace(0, pi/2, 333).';
f = [1 3 7 11 17];
y = sin(2*pi*x*f);
figure
plot(x, y)
grid
title('Line Plots of ‘y’')
legend(compose('Frequency %4.1f',f), Location='best')
figure
surfc(f, x, y)
grid
title('Surface Plot of ‘y’')
colormap(turbo)
colorbar
xlabel('Frequency')
ylabel('X')
zlabel('Function Value')
set(gca, 'XScale','log')
Same data, different representations.
.
I loop through beta and then calculate values of F (a scalar-valued function) for all alpha = linspace(0, 2pi, 1001). I am only looping through beta, not alpha, which I really like.
At this stage, save the scalar values for F in a 2d-matrix Fmat where Fmat(i,j) is the value you obtain for F if you evaluate it for (alpha(i),beta(j)). That's all you need for a later 3d-surface plot.
This works! And, now I've learned how to write scalar values to matrices.
Thanks so much!
Noob
on 3 Jan 2025
Hi Star Strider!
I am OK now, I think! Let me go ahead and accept your answer. Thanks and have a great day!
I just have two lingering issues now:
While my entire 2D line-plot workflow is now preserved (really great) -- by pre-allocating and filling in matrices with function values, like Torsten indicated -- I still have array-size compatibility issues when I try to write vectors as linear combinations of basis vectors. Thus, I am able to make surface plots for some functions, but not for others. So, what size do you think the basis vectors should be?
Also, with regard to colors, they seem to be coloring a solid, sort of like filling a volume, and I think that's incorrect, because the 2D version of this 3D plot would then be wrong. The colors from a colormap should only be filling the curvy cross sections, not filling in the area underneath, for example, so that the 2D version vs. all alpha, should look exactly the same as the line plots vs. alpha. As is, the area underneath, say, a sine wave, is being filled in with color, which is not correct.
Torsten
on 3 Jan 2025
Before using the "surf"-command, check the sizes of the arrays/matrices involved to conform with the requirements explicitly given in the documentation of "surf":
Input Arguments
X — x-coordinates
matrix | vector
x-coordinates, specified as a matrix the same size as Z, or as a vector with length n, where [m,n] = size(Z). If you do not specify values for X and Y, surf uses the vectors (1:n) and (1:m).
The XData property of the Surface object stores the x-coordinates.
Example: X = 1:10
Example: X = [1 2 3; 1 2 3; 1 2 3]
Example: [X,Y] = meshgrid(-5:0.5:5)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration
Y — y-coordinates
matrix | vector
y-coordinates, specified as a matrix the same size as Z or as a vector with length m, where [m,n] = size(Z). If you do not specify values for X and Y, surf uses the vectors (1:n) and (1:m).
The YData property of the surface object stores the y -coordinates.
Example: Y = 1:10
Example: Y = [1 1 1; 2 2 2; 3 3 3]
Example: [X,Y] = meshgrid(-5:0.5:5)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration
Z — z-coordinates
matrix
z-coordinates, specified as a matrix. Z must have at least two rows and two columns.
Z specifies the height of the surface plot at each x-y coordinate. If you do not specify the colors, then Z also specifies the surface colors.
The ZData property of the surface object stores the z -coordinates.
Example: Z = [1 2 3; 4 5 6]
Example: Z = sin(x) + cos(y)
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | categorical | datetime | duration
The basis vectors should span the space they define. For example, in 3-space, there are three basis vectors. However to define a 3D plot, you can have as many (x,y,z) triplets to define what you want to plot as you have available memory in your computer.
I can’t envision what you want to do with the colours. One optiion would be to use logical indexing so that only the parts you want are coloured. The second is to do something similar to Create Multicolored Line however I have no iiidea what you are doing, so I can be no more specific.
Hi Star Strider!
So, the parameter Beta essentially expresses the amount of rotation that's in my system of interest, which is crucial. Thus, I want colors from a colormap to vary with Beta, not with function value or surface height. I had started with:
alpha = linspace( ... )
Beta = linspace( ... ),
and then looping through beta = Beta(z), and, for each beta, computing function values for all alpha.
I also wrote:
[X, Y] = meshgrid(alpha, Beta),
but later, if I write:
surf(X,Y,FL_hat,Beta),
I get an error the error:
Warning: Error creating or updating Surface
Error in value of property CData
Array is wrong shape or size.
If I instead write:
surf(X,Y,FL_hat,Y),
Then I seem to sort of get what I want; only now that the area underneath the curves are also being filled in with color, so that the 2D version of this surface plot, i.e. a line plot vs. all alpha, would be wrong; the 2D version should be a bunch of colored curves, not filled-in solids.
If I store scalar function values into a matrix, and, with this matrix, denoted by FL_hat, which has size 11 X 1001, I want to write linear combinations of FL_hat, say with FD_hat so that
Net force = FL_hat * ip + FD_hat * jp,
where ip and jp are basis vectors such as:
ip = cos(theta)*i + sin(theta)*j + 0*k
jp = -sin(theta)*i + cos(theta)*j + 0*k,
then how can I write such a linear combination without getting array-size compatibility issues?
In that patch example, ‘c’ is set equal to ‘y’. You can set it equal to whatever you want, providing (in this instance) that it has the same dimensions as the other arguments.
The colour array C has to be the same size as ‘Z’. In your quoted code, ‘Beta’ iis a vector, and that iis not going to work for ‘C’. In the context of your meshgrid call, you probably have to calculate the values of ‘Beta’ you use in the surf call from ‘X’, ‘Y’, or both. Since I’m not sure how you calculate the ‘Beta’ you want to use in your surf call, that’s as far as I can go with this for the time being.
Perhaps ‘Beta’ should be the value of ‘Y’ that you return from meshgrid? (Just a guess.)
.
You mean
ip = [cos(theta);sin(theta);0]
jp = [-sin(theta);cos(theta);0]
where theta is a scalar ?
Then FL_hat and FD_hat must have 3 columns, not 1001.
Hi Star Strider,
It is indeed Y, returned from meshgrid. Only that ... while the color variation is correct, the colors seem to be filling in solids, when (I think) they should only be filling in the surface area, so that the 2D version vs. all alpha should simply be colored curves / lines, not colored solids. The 2D version, rotated around, should recover the 2D line plot, I think. So, a sine wave seems to be colored underneath it, too, which is strange, and likely not correct, because the 2D version will be wrong. Hmm ...
Noob
on 3 Jan 2025
Hi Star Strider!
I fixed this! Use NaN to create the pre-allocated matrices, not Zeros.
Not sure why, but this fixed the issue.
I think I have good working surface plots / tiles now, and I'll take a much-needed break for now, before jumping back in to work on this stuff.
Thanks again for your time and help!
With respect to filling in the patches, perhaps using mesh instead of surf will do what you want. (I’m stiill not sure what that is.)
Both zeros and NaN (or ones or rand or randn, etc.) will work for preallocation. The difference is that NaN values do not plot, and all the others, each having a finite value for every element, will plot.
More Answers (1)
Hi
To solve your problem of writing a scalar-valued function using meshgrid and linear combinations of rotating basis vectors, you need to ensure that all operations are element-wise and that the dimensions match properly.
function v_norm = velocity_norm(alpha, beta, theta)
% rotating basis vectors
ip = [cos(theta); sin(theta); 0];
jp = [-sin(theta); cos(theta); 0];
kp = [0; 0; 1]; % Not used in this example, but defined for completeness
% Calculate velocity components
vx = cos(alpha) * ip(1) + sin(beta) * jp(1);
vy = cos(alpha) * ip(2) + sin(beta) * jp(2);
vz = cos(alpha) * ip(3) + sin(beta) * jp(3);
% Calculate the norm of the velocity vector
v_norm = sqrt(vx.^2 + vy.^2 + vz.^2);
end
alpha = linspace(0, pi, 20);
beta = linspace(0, 10, 100);
[Alpha, Beta] = meshgrid(alpha, beta);
% Define the angle theta
theta = 0;
% Calculate the velocity norm for each alpha and beta
V_norm = velocity_norm(Alpha, Beta, theta);
figure;
surf(Alpha, Beta, V_norm);
xlabel('\alpha');
ylabel('\beta');
zlabel('Velocity Norm');
title('3D Surface Plot of Velocity Norm');
Hope this helps!
Categories
Find more on Matrix Indexing in Help Center and File Exchange
Tags
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)