3D scan conversion of CSG models into distance volumes

Abstract

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. In this paper 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.

Designing with distance fields

“…Others reduce processing by restricting evaluation of the distance field to a 'shell' or 'narrow band' around the object surface [Curless 1996, Jones 1996, Desbrun and Cani-Gascuel 1998]. In some cases, accurate distance values evaluated in the shell are then propagated to voxels outside the shell using fast distance transforms [Jones andSatherley 2001, Zhao et al 2001] or fast marching methods from level sets [Kimmel and Sethian 1996, Breen et al 1998, Whitaker 1998, and Fisher 2001. [Szeliski and Lavalle 1996, Wheeler 1998, and Strain 1999 evaluate distance values at cell vertices of a classic or '3-color' octree (i.e., an octree where all cells containing the surface are subdivided to the maximum octree level) to reduce the number of distance evaluations over regular sampling.…”

A Selective Refinement Approach for Computing the Distance Functions of Curves

“…The closest point propagation technique of Breen [1] is based on the fast marching method of Sethian [10]. The main advantages of propagation algorithms are speed and simplicity which offsets the fact that they are usually applied to sampled volumes for which only a subset of the samples will be used.…”

“…A propagation algorithm such as that of Breen [1] is the most commonly used method for obtaining an approximate distance function of a shape. These algorithms initialize a sampled scalar field with closest point information near the boundary of a shape and propagate this information throughout the volume.…”

A higher dimensional formulation for robust and interactive distance queries

“…Minimum distance queries on computer models are one of the most important geometric operations in simulation [Baraff 1990], haptics [II et al 1997], robotics [Quinlan 1994], registration [Pottmann et al 2003], and distance volume computation [Breen et al 1998]. Often, efficiency and robustness are important for these applications, yet prior formulations have not been able to combine the efficiency of numerical solutions with robustness and global convergence.…”