Shape interrogation is the process of extraction of information from a
geometric model. Shape interrogation is a fundamental component of
Computer Aided Design and Manufacturing (CAD/CAM) systems. In this
book the authors focus on shape interrogation of geometric models
bounded by free-form surfaces. Free-form surfaces, also called
sculptured surfaces, are widely used in the bodies of ships,
automobiles and aircraft, which have both functionality and attractive
shape requirements. Many electronic devices as well as consumer
products are designed with aesthetic shapes, which involve free-form
surfaces.
This book provides a bridge between the areas of geometric modeling and
solid modeling. Apart from the
differential geometry topics covered, the entire book is based on the
unifying concept of recasting all shape interrogation problems to the
solution of a nonlinear system. It provides the mathematical
fundamentals as well as algorithms for various shape interrogation
methods including nonlinear polynomial solvers, intersection problems,
differential geometry of intersection curves, distance functions,
curve and surface interrogation, umbilics and lines of curvature,
geodesics, and offset curves and surfaces.
The book can serve as a textbook for teaching advanced topics of
geometric modeling for graduate students as well as professionals in
industry.