Rotate Normal Around Tangent

9 vues (au cours des 30 derniers jours)
Paul Huter
Paul Huter le 5 Oct 2012
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 commentaires
Matt J
Matt J le 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?
Paul Huter
Paul Huter le 5 Oct 2012
I have a 3D curve, and I have calculated normal and tangent vectors at each point on the curve based on a velocity (I am using Frenet-frame here). I want to be able to draw a 3D circle that is normal to the curve at some points (not all...there are a lot of points...). I figured the best way would be to rotate the normal vector about the tangent vector.

Connectez-vous pour commenter.

Réponse acceptée

Matt J
Matt J le 6 Oct 2012
Modifié(e) : Matt J le 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 commentaires
Matt J
Matt J le 7 Oct 2012
Modifié(e) : Matt J le 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
Paul Huter
Paul Huter le 7 Oct 2012
Turns out the way I was calculating my tangent/normal vectors was doing them as row-vectors, not columns. Looking at the way you did it (with columns) got it to work.
Thanks for your help.

Connectez-vous pour commenter.

Plus de réponses (2)

Muthu Annamalai
Muthu Annamalai le 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
  1 commentaire
Paul Huter
Paul Huter le 5 Oct 2012
As stated above, I am calculating Frenet-frame vectors, which I have (in the past) used to generate a rotation matrix (3D). Is this same rotation matrix going to allow me to draw a circle perpendicular to the curve (i.e. by multiplying the x, y, z points of a circle by the rotation matrix)?

Connectez-vous pour commenter.


Image Analyst
Image Analyst le 6 Oct 2012
Modifié(e) : Image Analyst le 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.

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by