movingTrihedron

The function computes the 'moving trihedron' in terms of the unit tangent, normal and binormal.

Given a curve in 'd' spatial coordinates, the function computes the associated 'moving trihedron' in terms of the unit tangent, -normal and -binormal at each point of the curve 'x'. The function returns the frame ['t', 'p','b'], corresponding to the tangent, normal and binormal, respectively.

To check that it works, compute e.g.

N = 100; nwinds = 2;
theta = linspace(0,nwinds*2*pi,N)';
L = theta/nwinds;

x = [cos(theta), sin(theta), L];

[t,p,b] = movingTrihedron(x);
refinement_factor = 10;

plot3(x(:,1),x(:,2),x(:,3),'k-')
hold on
quiver3(x(1:10:end,1),x(1:10:end,2),x(1:10:end,3),t(1:10:end,1),t(1:10:end,2),t(1:10:end,3))
quiver3(x(1:10:end,1),x(1:10:end,2),x(1:10:end,3),p(1:10:end,1),p(1:10:end,2),p(1:10:end,3))
quiver3(x(1:10:end,1),x(1:10:end,2),x(1:10:end,3),b(1:10:end,1),b(1:10:end,2),b(1:10:end,3))