Understanding the Dual Polytope for Hull Simplification

Automated excerpt

Let’s look at the level sets of \(\boldsymbol{h}\). The vertices of \(\boldsymbol{P^{\circ}}\) are the faces of \(\boldsymbol{P}\). A face of \(\boldsymbol{P}\) with plane \(\boldsymbol{n \cdot x = d}\) becomes the vertex \(\boldsymbol{n/d}\), and projecting the edges of \(\boldsymbol{P^{\circ}}\) onto the sphere gives the Gauss map.

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