# Frenet-Serret MatLab Function

1. Jan 21, 2010

### mpassman

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));
end

% 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);
end

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);
end

% 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);
end

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