On the completeness and conversion of ray representations of arbitrary solids
Jai P. Menon, H. Voelcker · 1995
A ray representation (ray-rep) of a solid is a set of line segments that lie inside the solid, obtained by classifying a grid of parallel lines with respect to the solid.Enhanced rayreps contain tags, which are symbolic data associated with each line segment.Tags may carry properties of the interior of a solid or may descrilx characteristics of a solid's txrundary locaf to a segment's endpoint.Ray-reps, enhanced or not, are proving to be powerful tools in attacking some difficult applications, such as those involving general sweeping and Minkowski operations.Ray-reps are popularly perceived as 'approximate' representations, incapable of representing a solid completely (unambiguously).This paper shows, in its first set of results, that ray-reps can be complete representations of solids when enhanced with h-fags, and when generated with suitable ray grids.h-tags designate halfspaces that model the local geometries of solids at ray-segment endpoints.Ray grid suitability is determined from mathematical conditions for disambiguating spatial decompositions induced from halfspaces identified by h-tags.Complete ray-reps can be viewed as a new representation scheme within a family of complete sampling represenfafions not covered by Requicha's 1980 six-family taxonomy of complete representation schemes for solids.The paper's second set of results covers representation conversion.Conditions and procedures are given for bilateral ray-rep-to/from-Brep and ray-rep-to/from-CSG conversion; these conversions enable ray-reps to be used as working representations in CAD/CAM systems having boundary or CSG primary representations.Methods for using ray-reps to accelerate conversions (e.g.Brep-to-CSG) are discussed.