Quadric decomposition for computing the intersections of surfaces of revolution

摘要

Surface subdivision has been one of the most efficient techniques for surface representation, rendering, and intersection problems. General triangular and quadrilateral subdivision schemes often lead to data proliferation and increased computational load. In this paper, we propose a novel quadric decomposition method for computing intersection curves and present an efficient algorithm for solving the intersection problem of general surfaces of revolution. In our method, we decompose surfaces of revolution into a sequence of coaxial revolute quad-rics and reduce the intersection problem for two surfaces of revolution to the intersection problem for two revolute quadrics. We present the performance of our method in the context of some of the most efficient and well-known solutions proposed so far by Kim and our previous method based on truncated cone decomposition. We give the performance characterization and show that this method is significantly more robust and efficient than previous methods.