Numerically stable form factor of any polygon and polyhedron

Abstract

Coordinate‐free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small‐angle scattering by nanocrystals.

Coordinate‐free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Series expansions are used to ensure numeric precision close to apparent singularities. image