Adaptively Represented Complete Distance Fields of Polygonal Models

Abstract

Distance fields are an important volume representation. However, distance fields constructed by straightforward discrete sampling can neither provide a quantitative measure of error nor fully capture detailed distance fields caused by corners in 3D geometries. We discuss here a complete distance field representation (CDFR) of polygonal models that does not rely on Nyquist sampling theory. In a CDFR volume, each voxel has a complete description of all surface polygons that affect the local distance field. CDFR can be adaptively represented without compromising accuracy. The adaptively represented complete distance field is shorted for ARCDF. For any desired distance, we can extract a surface contour in Euclidean distance, at any levels of accuracy, from the same CDFR or ARCDF representation. We further show any example of applying CDFR to a cutting edge CAD application involving high-complexity parts at un-precedented accuracy using only commonly available computational resources. Finally, although the general concepts presented here may be extended for parametric models as well, our current method can only handle polygonal models.