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Frenet-Serret MatLab Function

  1. Jan 21, 2010 #1
    Hello, I have a function to return the Normal, Binormal and Tangent vectors of a curve defined by lots of x,y,z coordinates. It should also return torsion and curvature but I know that the curvature is certainly not correct. I'm pretty sure the vectors are right, but the curvature and possible torsion is not right. Any help much, much appreciated.

    Code (Text):

    function [T,N,B,k,t] = frenet(x,y,z),
    % Frenet - Serret Vecotrs
    % T = Tangent
    % N = Normal
    % B = Binormal
    % k = curvature
    % t = torsion

    % If only x and y inputted, set z to all zeros
    if nargin == 2,
        z = zeros(size(x));

    % If x, y and z are row vectors, make them colums
    x = x(:);
    y = y(:);
    z = z(:);

    %Set up a dr vector
    dx = gradient(x);
    dy = gradient(y);
    dz = gradient(z);
    dr = [dx dy dz];

    % The tangent vector
    for i=1:size(x)
    T(i,:) = dr(i,:)/norm(dr(i,:),2);

    dTx =  gradient(T(:,1));
    dTy =  gradient(T(:,2));
    dTz =  gradient(T(:,3));

    dT = [dTx dTy dTz];

    % The Normal vecotr
    for j=1:size(x)
    N(j,:) = dT(j,:)/norm(dT(j,:),2);

    % The binormal vector
    B = cross(T,N);

    dBx = gradient(B(:,1));
    dBy = gradient(B(:,2));
    dBz = gradient(B(:,3));

    dB = [dBx dBy dBz];

    % Curvature

    for i=1:length(x)
    k(i) = norm(dT(i,:),2);
    t(i) = norm(dB(i,:),2);
  2. jcsd
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