A general numerical algorithm is proposed for the fast computation of the common volume function (CVF) of any polyhedral object, from which the diffraction pattern of a corresponding powder can be obtained. The theoretical description of the algorithm is supported by examples ranging from simple equilibrium shapes in cubic materials (Wulff polyhedra) to more exotic non-convex shapes, such as tripods or hollow cubes. Excellent agreement is shown between patterns simulated using the CVF and the corresponding ones calculated from the atomic positionsviathe Debye scattering equation.
Volume functions on blow-ups and Seshadri constants
