M-Reps: A New Object Representation for Graphics
Stephen M. Pizer, Andrew Thall, David Chen · 1999
M-reps are a multiscale approach to the modeling and rendering of 3D solid geometry. Traditional geometric models, whether b-reps or CSG, are represented at infinitesimal spatial scale and then require simplification to meet needs requiring coarser scale or smaller data sets. We have developed a model that is designed at successively smaller scales and supports a coarse-to-fine hierarchy in design, rendering, physical deformation, and other graphics operations. We base our representation on figural models, defined at coarse scale by a hierarchy of figures -- protrusions, indentations, corners, neighboring figures, and included figures -- which simultaneously represent solid regions and their boundaries. To capture local shape at scale and thus local zoom-invariance, the figural components imply a fuzzy, i.e., probabilistically described boundary position with a width- and scale-proportional tolerance. At small scale these figures are made precise by displacement maps, geometric texture...