Geometric method of intersecting natural quadrics represented in trimmed surface form
Computer-Aided Design
Smooth piecewise quadric surfaces
Mathematical methods in computer aided geometric design
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
The intersection of two ringed surfaces and some related problems
Graphical Models
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
Classifying the Nonsingular Intersection Curve of Two Quadric Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
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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 quadrics 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 [11] and our previous method based on truncated cone decomposition [1]. We give the performance characterization and show that this method is significantly more robust and efficient than previous methods.