Projectively Invariant Intersection Detections for Solid Modeling

Abstract

An intersection detection method for solid modeling which is invariant under projective transformations is presented. We redefine the fundamental geometric figures necessary to describe solid models and their dual figures in a homogeneous coordinate representation. Then we derive conditions, which are projectively invariant, for intersections between these primitives. We will show that a geometric processor based on the 4 x 4 determinant method is applicable to a wide range of problems with little modification. This method has applications in intersection detections of rational parametric curves and surfaces and hidden-line/surface removal algorithms. © 1994, ACM. All rights reserved.