ConceptDual Polytope / 极点对偶
Dual Polyhedron
A classical concept in computational and algebraic geometry that applies polar duality transforms to interchange the vertices and faces of a convex polyhedron, enabling conversion between vertex representation (V-representation) and half-space representation (H-representation). The concept is widely applied in convex hull simplification and optimization algorithm design.
Timeline (last 90 days)
Sep 30
The polar dual transformation maps each face of the original polyhedron to a vertex of the dual, and each vertex to a face of the dual.
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Sep 30
The dual transformation can convert the problem of "simplifying vertices" into the problem of "simplifying faces," and vice versa.
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