Overview
Animation
Classic Surfaces
Parm Surfaces
Curves on Surfaces
Discrete Geodesics
ODE
Platonic Solids
Cycloid
Root Finder
Harmonic Maps
Rivara Bisection
Scalar Field
Weierstrass
Closed Polygon
Elastic Curve
Billiard in an Ellipse
LIC Visualization
Discrete VF
Hodge Splitting
Textured Surface
Surfaces of Rotation
Mean Curvature Flow
Pythagoraen Tree
Julia Sets
Continuous Generalized Elastic curves
Generalized elastic curves are solutions of the differential equation
K'' = b + (a - 1/2 * K*K)*K
where K is the curvature of the curve. The curve itself is then the solution of
c'' = K*Jc'
where J denotes the anti-clockwise rotation by 90°. Change the initial values K, K', initial point, initial direction and/or parameters a or b to get another elastic curve. Parameter 'Stepsize K' is used for the integration of equation K''=..., parameter 'Stepsize' is used for equation c''=... .