Texture Mapping a Double Torus

The figure-eight objects in the picture below are identical copies of a double torus that has been cut and flattened into the irregular square sheet at the top left. Texture detail is finer at the edges of this shape than in the interior, reflecting the fact that surfaces of genus 2 or greater have overall negative curvature.

Ellipsoidal Texture Mapping

The series of objects in the picture below show (from top to bottom) an ellipsoid being sliced open and flattened into a rectangle. The image in the rectangle (i.e. the April 1999 calendar page) has been used to texture map the ellipsoid.