  This paper presents a novel approach for the differentiable rendering of
convex polyhedra, addressing the limitations of recent methods that rely on
implicit field supervision. Our technique introduces a strategy that combines
non-differentiable computation of hyperplane intersection through duality
transform with differentiable optimization for vertex positioning with
three-plane intersection, enabling gradient-based optimization without the need
for 3D implicit fields. This allows for efficient shape representation across a
range of applications, from shape parsing to compact mesh reconstruction. This
work not only overcomes the challenges of previous approaches but also sets a
new standard for representing shapes with convex polyhedra.
