Kernels from hulls

The kernel of a polygon has long been an object of study in computational geometry, especially in the context of art gallery theorems. In this paper, we present two new algorithms for computing the kernel of a plane curve. We show that the computation of the kernel of a plane curve can be reduced to the computation of the convex hull of a plane curve, revealing the computational and structural similarity of these two fundamental geometric objects. The kernel of a curve is studied in dual space, by applying the geometric duality between lines and points to the curve’s tangent space. The kernel in primal space becomes the convex hull in dual space.