Chapter 25

Intersection Problems

Nicholas M. Patrikalakis and Takashi Maekawa

25.1 INTRODUCTION

Intersections are fundamental in computational geometry, geometric modeling and design, analysis and manufacturing applications [4],[33],[67]. Examples of intersection problems include: (1) Contouring of surfaces through intersection with a series of parallel planes or coaxial cylinders for visualization. (2) Numerical control machining (milling) involving intersection of offset surfaces with a series of parallel planes, to create machining paths for ball (spherical) cutters. (3) Representation of complex geometries in the Boundary Representation (B-rep) scheme using a process called boundary evaluation, in which the Boundary Representation is ...

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