A novel algorithm for computing intersections of two surfaces of revolution

Authors:
Jinyuan Jia;Kai Tang;Ki-wan Kwok
Affiliations:
Department of Computer Science, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Mechanical Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Venue:
Geometric modeling
Year:
2004

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Abstract

This chapter presents a novel method for computing the intersection curves of two surfaces of revolution RSIC. In this method, each surface of revolution is decomposed into a collection of coaxial spherical stripes along the generatrix, by subdividing its generatrix into a collection of C0 or C1 coaxial circular arcs centered on the revolute axis. Thus, computing intersections of two surfaces of revolution RSIC is reduced to computing intersection curves of two spherical stripes SSIC. RSIC can be represented as a piecewise C0 or C1 circular approximation, which is quite convenient for various operations such as offsetting, blending and so on, To avoid the unnecessary intersection computations, cylindrical bounding shell CBS is devised and valid intersection intervals VII is introduced. Finally, a simple algorithm is designed to trace RSIC for classification.