In this paper we present a new, morphological criterion for determining whether a geometric solid is suitable for voxelization at a given resolution. The criterion embodies two conditions, namely that the curvature of the solid must be bounded and the critical points of the distance field must be at a certain distance from the boundary of the solid. For solids that fulfill this criterion, we present an analytic and an empirical bound for the trilinear reconstruction error. Additionally, we give a theoretical argument as to why the distance field approach to voxelization is more sound than the prefiltering technique. The essence of the argument is that while sampling and interpolation must always introduce some error, the latter method (but not the former) introduces an error in the surface position independently of the sampling.
|Title of host publication||Winter School of Computer Graphics (WSCG) 2000|
|Publisher||University of West Bohemia, Plzen, Czech Republic|
|Publication status||Published - 2000|
|Event||Winter School of Computer Graphics 2000 - University of West Bohemia, Plzen, Czech Republic|
Duration: 7 Feb 2000 → 11 Feb 2000
|Course||Winter School of Computer Graphics 2000|
|Location||University of West Bohemia|
|Period||07/02/2000 → 11/02/2000|
Bærentzen, J. A., Sramek, M., & Christensen, N. J. (2000). A Morphological Approach to the Voxelization of Solids. In Winter School of Computer Graphics (WSCG) 2000 (pp. 44-51). University of West Bohemia, Plzen, Czech Republic.