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
Surfaces of Rotation
Surfaces of rotation are generated from a planar curve by rotating the curve around an axis.
The shape of the surface of rotation depends on the given meridian curve, the position of the axis. Let c(s)= (c1(s),c2(s),c3(s)) be a curve in the xz-plane, then the expression of a surface of rotation with respect to the z-axis is given by
Rotation[c,z-axis](s, t) = (cos(t)*c1(s), sin(t)*c2(s), c3(s)).