Calculation of Tangent (T), Normal (N) and Binormal (B) of a continuous curve at every points of the curve.
function [T N B]=myfrenet(x,y,z,init)
% "x","y",and "z" is the coordinates of the curve. The curve also can be 2d.
% "init" is initial normal vector that user can be specified. With this input, you can freely initialize your vectors.
Although the name of the function is "myfrenet", the vectors are calculated in a different way from "frenet" equations because of some discontinuities of "frenet".
Derrivatives of the curve are calculated with spline fitting, therefore spline toolbox are required. If the toolbox are not available, users can change the derrivative calculation method such as by using "diff" or "gradient" command.
x=cos(t); y=sin(t); z=t;
Hi Walter, sorry for the late response. I have not received any notification about your comment.
This code is originally based on the paper:
"Calculation of Reference Frames along a Space Curve"- Jules Bloomenthal (published in Graphics Gems, vol. 1)
So, you can cite this paper insted.
I will run it once and then take the mean of the Tangent vectors to use as the initial Norm vector for the second pass through.
This ensures that the orientation of the normals is typically coplanar for a more-or-less 2D curve in 3D space.
How do I cite this code/method for research purposes?
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