Abstract
This chapter classifies the intersection problems by dimension, type of geometric specification, and the number system used. It describes various examples of intersection problems, including (1) contouring of surfaces through intersection with a series of parallel planes or coaxial cylinders for visualization, (2) numerical control machining involving intersection of offset surfaces with a series of parallel planes, to create machining paths for ball cutters, and (3) representation of complex geometries in the boundary representation (B-rep) scheme using a process called boundary evaluation, in which the B-rep is created by evaluating a constructive solid geometry (CSG) model of the object. During this process, intersections of the surfaces of primitives must be found during Boolean operations between primitives. The chapter provides an overview of the solution methods for systems of nonlinear polynomial equations. It discusses curve/surface intersection problems followed by surface/surface intersection problems.
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