Rotate Normal Around Tangent
8 views (last 30 days)
Show older comments
I want to rotate a normal vector around a tangent vector to create a circle. I have not been able to find anything to do this. Does such a function exist? Or how would I generate one?
Thanks.
2 Comments
Matt J
on 5 Oct 2012
Clarify what this is supposed to do. What data are you given and in what form? What will the output data be, and in what form?
Accepted Answer
Matt J
on 6 Oct 2012
Edited: Matt J
on 6 Oct 2012
I'm assuming you're choosing the radius, R, of this circle. Then if T and N are the tangent and normal vectors at point P on the curve (all in column vector form):
n=1000;
theta=linspace(0,2*pi,n+1);
theta(end)=[];
refcircle = [R*cos(theta);R*sin(theta);zeros(1,n);ones(1,n)] ;
T=T/norm(T);
N=N/norm(N);
E=cross(N,T);
A=[0 0 0; R 0 0; 0 R 0].';
B=[P,P+R*N,P+R*E];
params=absor(A,B); %get this function from FEX
C = params.M*refcircle; %circle points at 3D curve
plot3(C(1,:), C(2,:), C(3,:)) %plot the circle
The above uses ABSOR, available here
8 Comments
Matt J
on 7 Oct 2012
Edited: Matt J
on 7 Oct 2012
Clarify whether the plot you're talking about is from the code as I gave it to you, or the result of you adapting/inserting it into your larger problem. If the latter, I'd have to see what you did.
However, when I run it in isolation with the sample data P,T,N,R data below, I definitely get a plot of a circle floating in 3D space. Verify first that you can reproduce this.
P=[1;1;1];
T=[1;1;1];
N=[-1;2;-1];
R=3;
n=1000;
theta=linspace(0,2*pi,n+1);
theta(end)=[];
refcircle = [R*cos(theta);R*sin(theta)] ;
T=T/norm(T);
N=N/norm(N);
E=cross(N,T);
C=bsxfun(@plus, [N,E]*refcircle, P);
plot3(C(1,:), C(2,:), C(3,:)) %plot the circle
More Answers (2)
Muthu Annamalai
on 5 Oct 2012
Paul, You need to find the points of a 2D rotation transform using the equations, for example affine transformation http://en.wikipedia.org/wiki/Rotation_(mathematics), and then you may visualize it using plot() commands. HTH, -Muthu
Image Analyst
on 6 Oct 2012
Edited: Image Analyst
on 6 Oct 2012
Sounds like the streamtube() function. Could that be used? Or maybe morphological dilation, imdilate(). For morphological dilation, imagine a sphere whose center is tracing out your 3D curve. The dilated volumetric image is the volume swept out by that sphere as it travels along your curve.
0 Comments
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!