Space curves reconstructed from prescribed curvature $\kappa(s)$ and torsion $\tau(s)$ via the Frenet–Serret equations
The fundamental theorem of space curves states that a regular curve γ:I→R3 is uniquely determined up to isometry by its curvature κ and torsion τ. This graphing calculator lets you explore the existence direction of this theorem: given functions κ(s) and τ(s) of arc length, the program numerically integrates the Frenet-Serret equations to reconstruct a space curve with those invariants.
You can type custom expressions for curvature and torsion in the pulldown menu, using parameters a, b, c which are controlled by interactive sliders, allowing you to deform the resulting curve in real time.
Controls: Click and drag to orbit, scroll to zoom.
