Book Chapter10.1007/3-540-27157-0_2
Challenges in Surface-Surface Intersections
Vibeke Skytt
- 01 Jan 2005
- pp 11-26
10
TL;DR: Solutions which use the possibility of representing a parametric surface as an algebraic surface through the use of approximate implicitization, are in focus, to transform an intersection between two parametric surfaces to the problem of finding zeroes of a function of two parameters.
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Abstract: Tangential and singular situations are still challenges in a system for surface-surface intersections. This paper presents several real world examples of hard intersection problems, and proposes methods on how to deal with them. In particular, solutions which use the possibility of representing a parametric surface as an algebraic surface through the use of approximate implicitization, are in focus. This allows us to transform an intersection between two parametric surfaces to the problem of finding zeroes of a function of two parameters.
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Citations
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Self-Intersection Problems and Approximate Implicitization
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24
Three-dimensional adaptive limit analysis of masonry arch bridges interacting with the backfill
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Spline surface intersections optimized for GPUs
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Mathematical Methods for Curves and Surfaces
Michael S. Floater,Tom Lyche,Marie-Laurence Mazure,Knut Mørken,Larry L. Schumaker +4 more
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TL;DR: A construction of rational isotropic curves with a prescribed tangent field which leads to the description of all rational minimal surfaces is presented.
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Implicit representation of parametric curves and surfaces
TL;DR: It is shown that a two-dimensional curve defined parametrically in terms of rational degree n polynomials in t can be expressed implicitly as a degree n POlynomial in z and y and it is demonstrated that a “bi-m-ic” parametric surface can be written implicitly as an implicit polynomial of degree 2m2.
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Mathematical Methods in Computer Aided Geometric Design.
Tom Lyche,Larry L. Schumaker +1 more
TL;DR: Symmetrizing multiaffine polynomials, P. Brunet and A. Goldman wavelets and multiscale interpolation, C. DeRose and S. Degen an approximately G1 cubic surface interpolant, T. Chui and X. Yuen Bezier curves and surface patches on quadrics, J. Farouki and J.-C.
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