A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
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SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Integration of parametric geometry and non-manifold topology in geometric modeling
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
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ACM Transactions on Graphics (TOG)
A tracing algorithm for surface-surface intersections on surface boundaries
Journal of Computer Science and Technology
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Computer Aided Geometric Design
Self-intersection detection and elimination in freeform curves and surfaces
Computer-Aided Design
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International Journal of Computer Applications in Technology
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Computer Aided Geometric Design
Heterogeneous spline surface intersections
Proceedings of the 26th Spring Conference on Computer Graphics
Solving polynomial systems using no-root elimination blending schemes
Computer-Aided Design
Solving polynomial systems using no-root elimination blending schemes
Computer-Aided Design
Spline surface intersections optimized for GPUs
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
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This paper presents a theorem relating the geometry of two smooth surfaces with the topology of their intersection. Algorithms for computing intersections of surfaces are very basic to those solid-modeling systems that allow Boolean operations such as Union, Intersection, and Subtraction on solids. Recently, such an algorithm based on recursive subdivision of the surfaces has attracted a lot of attention because of its simplicity and wide applicability. However, this algorithm for intersection of surfaces fails to find all intersections for certain relative orientations of surfaces. Finer subdivision of the surfaces may result in the correct intersections but also results in many unnecessary computations. The mathematical result established in this paper is significant in that it provides a check to determine when finer subdivision will yield no new topological information for an intersection. It is shown how the check may be incorporated into the existing subdivision algorithm to compute intersections reliably and efficiently.