The Dual Polytope: A Simple Trick for Simplifying Convex Hulls
Understanding the Dual Polytope for Hull Simplification
Simplifying a convex hull usually means merging or dropping face planes and rebuilding the hull. Cairn Overturf explains the dual polytope approach using the support function's level sets. The key insight: the polar dual is the level set of the support function, its faces correspond to the original vertices, and its vertices correspond to the original faces. This makes editing face normals equivalent to moving dual vertices, and taking their convex hull rebuilds the simplified hull.
The faces of the polar dual are the vertices of the original polytope, and the vertices of the polar dual are the faces of the original polytope.