How to convert X, Y, Z cartesian coordinates into a surface.

Hello,

I have three vectors representing x, y, and z cartesian coordinates of half of a nosecone shape. I need to convert the z data into a "matrix of z heights", as as described in the documentation for Grid Surfaces used in Simscape Multibody (https://www.mathworks.com/help/sm/ref/gridsurface.html#mw_e7b9ffe5-592d-4971-9715-092dba7fd93a).

I tried to use the diag() command and surf() to check things, but it isn't quite right; there are valleys between rows of points and some of the negative space outside the nosecone is also included. Additionally, Simscape grid surfaces need x and y vectors that are monotonic and increasing. I can sort these vectors in Matlab easily enough, I can't seem to get my z matrix quite right when I sort x and y.

Sample code below. The x_coords, y_coords, and z_coords are pulled in from a .mat file.

Thank you!

load('cone_data - Copy.mat');
x = x_coords(:);
y = y_coords(:);
z = z_coords(:);
z = diag(z);
fullset = [x y z];
surf(x, y, z); 

[Voss]

Can you upload the mat file, using the paperclip button?

[Kylen]

Hi, thanks for asking. I added a .mat file. It's the x, y, z data in three columns. My original .mat was given to me unsorted (many columns for each x, y, z), so I uploaded the version that's a bit less cumbersome.

Anyway, my attachment is x, y, z. The z column is giving me trouble. I think I might need to interpolate between points to get a surface. I've tried using diag() to kind of fill in the "empty" spots with zeros. That was helpful, but not quite right.

If you hadn't guessed, this is a little outside of my wheelhouse, so I appreciate the help.

[Cris LaPierre]

Please upload the same data you are working with.

The mat file you uploaded does not appear to have the same variables your code uses.

load nosecone.mat
whos

  Name                Size            Bytes  Class             Attributes

  ans                 1x36               72  char                        
  cmdout              1x33               66  char                        
  full              675x3             16200  double                      
  gdsCacheDir         1x14               28  char                        
  gdsCacheFlag        1x1                 8  double                      
  i                   0x0                 0  double                      
  managers            1x0                 0  cell                        
  managersMap         0x1                 8  containers.Map              

[Kylen]

Attached. Thanks.

Answer 1

[Voss]

load('cone_data - Copy.mat');

Here's how the surface looks. This is using the matrices x_coords, y_coords, and z_coords.

% a surface based on x, y, and z matrices
figure
surf(x_coords,y_coords,z_coords)

I understand that for Simscape Multibody you need to specify the surface as a matrix z based on x and y being monotonically increasing vectors, instead of matrices. That constraint is the same as requiring the surface to have a footprint (i.e., its projection on the x-y plane) that is a rectangle. Obviously the surface above does not have a rectangular footprint; it's more like a filled-in parabola kind of shape. In order to define your surface on a rectangular footprint, you'll need to fill in some z values outside the parabola. Using zeros is a natural choice for those values, which can be done something like this:

% need to interpolate x/y/z_coords over some rectangular 
% grid, so use a scatteredInterpolant
SI = scatteredInterpolant(x_coords(:),y_coords(:),z_coords(:));

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

% define the grid with some equally-spaced x values
x = linspace(min(x_coords(:)),max(x_coords(:)),25);

% and non-equally-spaced y values (because y_coords is already grid-like)
y = y_coords(:,1);

% interpolate to get z on that grid
[X,Y] = meshgrid(x,y);
Z = max(0,SI(X,Y));

% surface based on x, y vectors, and matrix z
figure
surf(x,y,Z);

Another choice might be NaNs (I have no idea what Simscape Multibody will do with NaN z values, but it's worth a shot, I guess), which can be done like this:

% using the same x-y grid as before, but
Z = SI(X,Y);
Z(Z < 0) = NaN;

% surface based on x, y vectors, and matrix z
figure
surf(x,y,Z);

I guess I would try the one with the zeros first.

[Kylen]

Hello, and thank you so much! This is the closest I've gotten so far. I think your first version with the zeros will work for my purposes. I'll be contact modeling on the top contours of the curve, so the "flat" underside shouldn't really come into play.

Do you happen to have a suggestion for the following Simscape error?

• ['untitled/Grid Surface']: The number of elements in the X Grid Vector parameter must equal the number of rows in the Z Heights matrix parameter. Resolve this issue in order to simulate the model.
• ['untitled/Grid Surface']: The number of elements in the Y Grid Vector parameter must equal the number of columns in the Z Heights matrix parameter. Resolve this issue in order to simulate the model.

I tried to take transpose x and y such that the dimensions match that of the Z matrix, but that didn't seem to work either.

Again, thanks for helping!

[Voss]

You're welcome!

Transpose Z or use ndgrid rather than meshgrid to get rid of those errors.

Double-checking:

load('cone_data - Copy.mat');

% need to interpolate x/y/z_coords over some rectangular 
% grid, so use a scatteredInterpolant
SI = scatteredInterpolant(x_coords(:),y_coords(:),z_coords(:));

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

% define the grid with some equally-spaced x values
x = linspace(min(x_coords(:)),max(x_coords(:)),25);

% and non-equally-spaced y values (because y_coords is already grid-like)
y = y_coords(:,1);

Z is numel(y)-by-numel(x) because that's convenient for plotting a surface

% interpolate to get z on that grid
[X,Y] = meshgrid(x,y);
Z = max(0,SI(X,Y));

whos x y Z

  Name       Size            Bytes  Class     Attributes

  Z         27x25             5400  double              
  x          1x25              200  double              
  y         27x1               216  double              

But Simscape Multibody expects Z to be numel(x)-by-numel(y)

% interpolate to get z on that grid
[X,Y] = ndgrid(x,y);
Z = max(0,SI(X,Y));

whos x y Z

  Name       Size            Bytes  Class     Attributes

  Z         25x27             5400  double              
  x          1x25              200  double              
  y         27x1               216  double              

[Kylen]

Thank you! This should be more than adequate for my purposes.

My teammate and I are eternally grateful!

[Voss]

You're welcome! Please "Accept" this answer if it ends up working.