Frenet basis for 3D torsion-curvature based curves

Given torsion and curvature functions, it computes the curve by solving Frenet differential system.

Description

Given 2 continuous functions of t as curvature and torsion, there is a unique 3D curve that is the solution to the system of 3 vector differential equations, known as Frenet's equations, one equation for each basic vector.

Each equation can be split into 3 scalar equations whose unknown are the coordinates on the final point of the vector. The resulting system is linear with an antisymmetric matrix.

1. Run the GUI file frenetgui.m
2. edit Curvature and Torsion as constant or functions of t.
3. Click the "Compute Orbit Curve" button
4. Click on the "Frenet Bases Motion" button.
5. You can freeze the motion, resize the size of basis vectors and then resume the motion.
6. You can change the temporal span.

• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other requirements: MATLAB R14 at least

[Tan Nguyen]

 

[tan nguyen]