Surface Morphing

This Demonstration shows morphing between a plane, a sphere, a torus, a cylinder, a Möbius strip, and a sine surface using a continuous transition function.

For any two surfaces which can be defined by continuous parametrizations :[, , ] →︀ , the transition function can be assigned as: π)=(1 - τ(t)) f₁+ τ(t) f₂, where τ(t) ϵ [0,1] for ∀t ϵ [0,1].

Also, we multiply a rotation matrix to the result to provide a 360° view of the morphing.