Numerical Method for 3D Quantification of Glenoid Bone Loss

Abstract

Let a three-dimensional ball intersect a three-dimensional polyhedron given by its triangulated boundary with outward unit normals. We propose a numerical method for approximate computation of the intersection volume by using voxelization of the interior of the polyhedron. The approximation error is verified by comparison with the exact volume of the polyhedron provided by the Gauss divergence theorem. Voxelization of the polyhedron interior is achieved by the aid of an indicator function, which is very similar to the signed distance to the boundary of the polyhedron. The proposed numerical method can be used in 3D quantification of glenoid bone loss.