3D scan conversion of CSG models into distance volumes

A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the object being represented by the volume. Distance volumes are a useful representation in a number of computer graphics applications. We present a technique for generating a distance volume with sub-voxel accuracy from one type of geometric model, a constructive solid geometry (CSG) model consisting of superellipsoid primitives. The distance volume is generated in a two step process. The first step calculates the shortest distance to the CSG model at a set of points within a narrow band around the evaluated surface. Additionally, a second set of points, labeled the zero set, which lies on the CSG model´s surface are computed. A point in the zero set is associated with each point in the narrow band. Once the narrow band and zero set are calculated, a fast marching method is employed to propagate the shortest distance and closest point information out to the remaining voxels in the volume. Our technique has been used to scan convert a number of CSG models, producing distance volumes which have been utilized in a variety of computer graphics applications, e.g. CSG surface evaluation, offset surface generation, and 3D model morphing.