Extrude a ribbon/tube and fly through it!

Extrude a 2D curve along a 3D path to create tubes/ribbons and then fly though it

Description

Sweeps out a 2D cross section (a circle, square, whatever, doesn't even have to be a closed path) through a 3D curve, and returns the generated surface as [X,Y,Z] for use with SURF.

Also, as a fun option, it will fly through the path generated, which looks really cool if you have a fast computer and you maximize the figure. In the DEMO mode, the ROAD cross-section is my favorite. Try changing the colormap as well.

• MATLAB release: MATLAB 7.8 (R2009a)

[Francis Chen]

 

[Steeve A.]

 

[ashwin devotta]

Hi Teja,
That is a great work.
I have a slightly different problem at hand. I am trying to parametrically model a twist drill.
http://en.wikipedia.org/wiki/Drill_bit
In order to create this, I have a 2 dimensional curve in a plane (A). Plane A is obtained by rotating X-Z Plane about Y axis by theta degree. In this case, my base curve contains points in X,Y and Z.
In my case, the trajectory curve is a helical curve.
I want to take the resulting the 3 d curve and obtain a 2 d section in the X-Y plane.

Is there a way to accomodate this situation in your program. I would be using the Algorithm 2 for this purpose. I want this for academic purpose.
Thanks in advance
Ashwin.

[Ramana Govindasamy]

Hi Guys, modification of the code to create a narrowing tube along the axis of extrusion: Additional lines are 169 and 170. Pretty simple!

if norm(z) ~= 0
z = z/norm(z);
q = real(acos(dot(dCvec_prev,dCvec)/norm(dCvec_prev)/norm(dCvec)));

Z = repmat(z,1,npt);
base = base*cos(q) + cross(Z,base)*sin(q)+Z*(1-cos(q))*diag(dot(Z,base));
redr = 0.005*base;
base = base-redr;
camdata = camdata*cos(q) + cross([z z],camdata)*sin(q)+[z z]*(1-cos(q))*diag(dot([z z],camdata));

dCvec_prev = dCvec;
end

[Ramana Govindasamy]

Thanks Teja! It is the latter that I am trying to achieve i.e. a curved axis. The curve is defined by 12 (x,y,z) data points which I have interpolated to generate a curve. I will look at modifying the code and give feedback!

Ramana

[Teja Muppirala]

Hi Ramana,
I guess there are a couple of things you could do.

If the line to extrude along is straight, you could do something like this using basic MATLAB commands:

[Z,P] = meshgrid(0:1:100,linspace(0,2*pi,101));
R0 = 0.1;
X = R0 * (100-Z) .* cos(P);
Y = R0 * (100-Z) .* sin(P);
h = surf(X,Y,Z)
rotate(h,[0,0],45)
axis equal

This is an example that just makes a cone along a constant axis.
If you needed the cone to twist around, then I think you would probably have to modify my program a little bit to make the base curve change (get smaller) as you build the surface.

Teja

[Ramana Govindasamy]

Hey Teja! Great work. Quick question, how could one extrude a cone along the newly defined 'z' axis? i'.e. I want the radius of the tube to vary along the length of 'z'.

Thanks!

Ramana

[daf]

Thanks a lot. Teja.

[Teja Muppirala]

Hi daf,
That line of code is Rodrigues' Rotation Formula:

http://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

Look at the first equation on that wikipedia page. It is how you rotate a point around an axis of unit length. In my case, instead of using a loop to go over all the base the points one by one, I have kind of vectorized it and done it in one line with a little bit of linear algebra.

Teja

[daf]

sorry! This message should be to Teja. sorry about that

[daf]

Hi Yuval, thank you for your sharing.But would you please help me the explain the principle of the followwing code:
base = base*cos(q) + cross(Z,base)*sin(q)+Z*(1-cos(q))*diag(dot(Z,base));
Thank you very much!

[Rob Campbell]

Very clever!

[Teja Muppirala]

Hi Yuval, thanks for the feedback. I'll update this when I get a chance in the next few days, but all that you need to do to add caps to the ends is add the following in at line 175.

SUR = cat(3,repmat(C(:,1),1,npt),SUR,repmat(C(:,K),1,npt));

[Yuval]

Super useful tool for making 3D figures !

Thanks Teja, may the gods of graphics smile upon you.

Feature request: The option to "cap" the end of the tube, so it doesn't look hollow.

[Andreas]

Wicked Sick!