Solving point and plane vs. orthogonal polyhedra using the extreme vertices model (EVM)

Abstract

In a previous work, Orthogonal Polyhedra (OP) were proposed as geometric bounds in CSG. Primitives in the CSG model were approximated by their respective bounding boxes. The polyhedrical bound for the CSG object was obtained by applying the corresponding Boolean Algebra to those boxes. Also in that paper, a specific and very concise model for representing and handling OP was presented: the Extreme Vertices Model (EVM). The EVM allows simple and robust algorithms for performing the most usual and demanding tasks. This paper deals with the classification of point, and plane vs. OP. These operations can be done on the EVM in linear time. Furthermore, a very important feature of EVM algorithms is that, even though their input data (i.e., vertices' coordinates) can be floating-point values, no time-consuming floating-point arithmetic is ever performed (except when explicitly noted), so there are absolutely no propagation errors due to partial results (which do not exist). All results are obtained by just classifying and selecting vertices' coordinates of the initial data.