Fast Differentiable Polygon Overlap Using Edge-Edge Kernel

Abstract

In this paper, we introduce a differentiable geometry framework for computing polygon overlap areas. Our approach relies on exploiting an existing representation of polygons through edge-based border functions, which collectively define the interior of the shape. Using this formulation, the area of a polygon is expressed as a sum over each edge. For pairs of polygons, the intersection overlap area is derived from simple edge-to-edge kernel functions, defined by integrating border contributions. In addition, our technique can be used to compute differentials of the overlap with respect to polygon vertex coordinates. Our formulation results in a simple branchless expression that naturally supports concave and holed polygons.