Implicitization using moving curves and surfaces

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Implicitization using moving curves and surfaces

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International Conference on Computer Graphics and Interactive Techniques archive
Proceedings of the 22nd annual conference on Computer graphics and interactive techniques table of contents

Pages: 301 - 308

Year of Publication: 1995

ISBN:0-89791-701-4

Authors

Thomas W. Sederberg	Brigham Young University, 368 Clyde Building, Brigham Young University, Provo UT
Falai Chen	Dept. of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, P. R. China

Sponsor

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 13, Downloads (12 Months): 47, Citation Count: 40

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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	4	Eng-Wee Chionh , Ronald N. Goldman, Using multivariate resultants to find the implicit equation of a rational surface, The Visual Computer: International Journal of Computer Graphics, v.8 n.3, p.171-180, March 1992 [doi>10.1007/BF01902137]
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CITED BY 40

	Thomas W. Sederberg , Jianmin Zheng, Towards the &mgr;-basis of a rational surface, Mathematical Methods for Curves and Surfaces: Oslo 2000, Vanderbilt University, Nashville, TN, 2001
	Falai Chen , Tom Sederberg, A new implicit representation of a planar rational curve with high order singularity, Computer Aided Geometric Design, v.19 n.2, p.151-167, February 2002
	Falai Chen , Lin Deng, Interval implicitization of rational curves, Computer Aided Geometric Design, v.21 n.4, p.401-415, April 2004
	Tor Dokken, Approximate implicitization, Mathematical Methods for Curves and Surfaces: Oslo 2000, Vanderbilt University, Nashville, TN, 2001
	Laurent Busé, Residual resultant over the projective plane and the implicitization problem, Proceedings of the 2001 international symposium on Symbolic and algebraic computation, p.48-55, July 2001, London, Ontario, Canada
	Falai Chen, Reparametrization of a rational ruled surface using the μ-basis, Computer Aided Geometric Design, v.20 n.1, p.11-17, March 2003
	Yongli Sun , Jianping Yu, Implicitization of Parametric Curves via Lagrange Interpolation, Computing, v.77 n.4, p.379-386, June 2006
	Falai Chen , Wenping Wang, The µ-basis of a planar rational curve: properties and computation, Graphical Models, v.64 n.6, p.368-381, November 2002
	Falai Chen , Wenping Wang, Revisiting the µ-basis of a rational ruled surface, Journal of Symbolic Computation, v.36 n.5, p.699-716, November 2003
	Xiao-Shan Gao, Implicitization of differential rational parametric equations, Journal of Symbolic Computation, v.36 n.5, p.811-824, November 2003
	E. Wurm , B. Jüttler, Approximate implicitization via curve fitting, Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, June 23-25, 2003, Aachen, Germany
	Tim Culver , John Keyser , Dinesh Manocha, Exact computation of the medial axis of a polyhedron, Computer Aided Geometric Design, v.21 n.1, p.65-98, January 2004
	Quoc-Nam Tran, Efficient Groebner walk conversion for implicitization of geometric objects, Computer Aided Geometric Design, v.21 n.9, p.837-857, November 2004
	Arpan Biswas , Vadim Shapiro, Approximate distance fields with non-vanishing gradients, Graphical Models, v.66 n.3, p.133-159, May 2004
	Ioana Boier-Martin , Denis Zorin, Differentiable parameterization of Catmull-Clark subdivision surfaces, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, July 08-10, 2004, Nice, France
	Hulya Yalcin , Mustafa Unel , William Wolovich, Implicitization of Parametric Curves by Matrix Annihilation, International Journal of Computer Vision, v.54 n.1-3, p.105-115, August-September 2003
	Jiansong Deng , Falai Chen , Liyong Shen, Computing μ-bases of rational curves and surfaces using polynomial matrix factorization, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.132-139, July 24-27, 2005, Beijing, China
	A. Marco , J. J. Martínez, Implicitization of rational surfaces by means of polynomial interpolation, Computer Aided Geometric Design, v.19 n.5, p.327-344, May 2002
	Bert Jüttler , Pavel Chalmovianský, Approximate parameterization by planar rational curves, Proceedings of the 20th spring conference on Computer graphics, April 22-24, 2004, Budmerice, Slovakia
	S. Petitjean, Algebraic Geometry and Computer Vision: Polynomial Systems, Real andComplex Roots, Journal of Mathematical Imaging and Vision, v.10 n.3, p.191-220, May 1999
	Zhaoying Lu , Claire Willis , Derek Paddon, Surface animation for flower growth, Mathematical Methods for Curves and Surfaces: Oslo 2000, Vanderbilt University, Nashville, TN, 2001
	Tie-ru Wu , Hong-lu Cheng, Basic lines, axes and geometric modeling on implicit algebraic surfaces, Journal of Computational and Applied Mathematics, v.195 n.1, p.212-219, 15 October 2006
	Rosario Rubio , J. Miguel Serradilla , M. Pilar Vélez, A note on implicitization and normal parametrization of rational curves, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	A. Galligo , M. Stillman, On the geometry of parametrized bicubic surfaces, Journal of Symbolic Computation, v.42 n.1-2, p.136-158, January, 2007
	Ning Song , Falai Chen , Ron Goldman, Axial moving lines and singularities of rational planar curves, Computer Aided Geometric Design, v.24 n.4, p.200-209, May, 2007
	Quoc-Nam Tran, A new class of term orders for elimination, Journal of Symbolic Computation, v.42 n.5, p.533-548, May, 2007
	Mohamed Elkadi , Alain Yger, Residue calculus and applications, Publications of the Research Institute for Mathematical Sciences, v.43 n.1, p.55-73, March 2007
	Falai Chen , Wenping Wang , Yang Liu, Computing singular points of plane rational curves, Journal of Symbolic Computation, v.43 n.2, p.92-117, February, 2008
	Eng-Wee Chionh, 0/0 Simplifies implicitization, Journal of Symbolic Computation, v.43 n.6-7, p.475-489, June, 2008
	Bohumír Bastl , Bert Jüttler , Jiří Kosinka , Miroslav Lávička, Computing exact rational offsets of quadratic triangular Bézier surface patches, Computer-Aided Design, v.40 n.2, p.197-209, February, 2008
	Sonia Pérez-Díaz , J. Rafael Sendra, A univariate resultant-based implicitization algorithm for surfaces, Journal of Symbolic Computation, v.43 n.2, p.118-139, February, 2008
	David A. Cox, The moving curve ideal and the Rees algebra, Theoretical Computer Science, v.392 n.1-3, p.23-36, February, 2008
	Mario Fioravanti , Laureano Gonzalez-Vega , Andreas Seidl, Real implicitization of curves and geometric extraneous components, Proceedings of the 2007 international workshop on Symbolic-numeric computation, July 25-27, 2007, London, Ontario, Canada
	Laurent Busé , Marc Dohm, Implicitization of bihomogeneous parametrizations of algebraic surfaces via linear syzygies, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Laurent Busé , Ron Goldman, Division algorithms for Bernstein polynomials, Computer Aided Geometric Design, v.25 n.9, p.850-865, December, 2008
	Xuhui Wang , Falai Chen , Jiansong Deng, Implicitization and parametrization of quadratic surfaces with one simple base point, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, July 20-23, 2008, Linz/Hagenberg, Austria
	Haohao Wang , Xiaohong Jia , Ron Goldman, Axial moving planes and singularities of rational space curves, Computer Aided Geometric Design, v.26 n.3, p.300-316, March, 2009
	Ning Song , Ron Goldman, μ-bases for polynomial systems in one variable, Computer Aided Geometric Design, v.26 n.2, p.217-230, February, 2009
	Eng-Wee Chionh, Shifting planes always implicitize a surface of revolution, Computer Aided Geometric Design, v.26 n.4, p.369-377, May, 2009
	Luu Ba Thang , Laurent Busé , Bernard Mourrain, Curve/surface intersection problem by means of matrix representations, Proceedings of the 2009 conference on Symbolic numeric computation, August 03-05, 2009, Kyoto, Japan