Computer algebra: systems and algorithms for algebraic computation
Computer algebra: systems and algorithms for algebraic computation
Automatic parsing of degenerate quadric-surface intersections
ACM Transactions on Graphics (TOG)
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Graphical Models and Image Processing
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
The virtual mesh: a geometric abstraction for efficiently computing radiosity
ACM Transactions on Graphics (TOG)
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Solid Modeling: A Historical Summary and Contemporary Assessment
IEEE Computer Graphics and Applications
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
A reliable extended octree representation of CSG objects with an adaptive subdivision depth
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Centroidal Voronoi Tessellation of Line Segments and Graphs
Computer Graphics Forum
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We present the first complete, exact, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the near-optimal algorithm recently introduced by Dupont et al. [L. Dupont, D. Lazard, S. Lazard, S. Petitjean, Near-optimal parameterization of the intersection of quadrics, in: Proc. of SoCG, ACM Symposium on Computational Geometry, San Diego, 2003, pp. 246-255] and builds upon Levin's seminal work [J. Levin, A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces, Comm. ACM 19 (10) (1976) 555-563]. Unlike existing implementations, it correctly identifies and parameterizes all the connected components of the intersection in all cases, returning parameterizations with rational functions whenever such parameterizations exist. In addition, the field of the coefficients of the parameterizations is either of minimal degree or involves one possibly unneeded square root. We prove upper bounds on the size of the coefficients of the output parameterizations and compare these bounds to observed values. We give other experimental results and present some examples.