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Title: Bi-conic subdivision of surfaces of revolution and its applications in intersection problems
Authors: Jia, Jinyuan
Tang, Kai
Joneja, Ajay
Keywords: Quadric decomposition
Bi-conic arc fitting
Surfaces of revolution
Revolute quadrics
Issue Date: Aug-2004
Citation: The visual computer, v. 20, no. 7, Aug. 2004, p. 457-478
Abstract: This paper presents a novel method for subdivision of surfaces of revolutions. Such surfaces occur in a wide variety of applications. Our method approximates the surface by a series of revolute quadrics. To do this transformation, we develop a new technique for approximating the generatrix by a series of pairs of conic sections. By the use of an error estimate based on convex combinations, an efficient least-squares approach is proposed that yields near-optimum fitting. Due to the versatility of the approximating curves, the resulting surface approximation is shown to be significantly more efficient than other tessellation methods in terms of the number of segments required at a given precision level. This in turn allows us to implement efficient and robust algorithms for some of the fundamental intersection problems related to such surfaces. In particular, novel intersection techniques based on the proposed subdivision method are introduced in this paper for the two most fundamental types of intersection in geometric modeling and computer graphics - line/surface and surface/surface intersections. Both use a tight bounding volume called a cylindrical bounding shell, and employ efficient, binary tree based data structures. Several examples are provided for each type of the intersections in the paper. The experimental results show that our method outperforms conventional methods significantly in both computing time and memory cost.
Rights: The original publication is available at
Appears in Collections:MECH Journal/Magazine Articles
IELM Journal/Magazine Articles
CSE Journal/Magazine Articles

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