An accurate algorithm for rasterizing algebraic curves

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An accurate algorithm for rasterizing algebraic curves

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ACM Symposium on Solid and Physical Modeling archive
Proceedings on the second ACM symposium on Solid modeling and applications table of contents

Montreal, Quebec, Canada

Pages: 221 - 230

Year of Publication: 1993

ISBN:0-89791-584-4

Author

Gabriel Taubin

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): 8, Downloads (12 Months): 30, Citation Count: 5

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REFERENCES

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	1	S. S. Abhyankar , C. Bajaj, Automatic parameterization of rational curves and surfaces 1: conics and conicoids, Computer-Aided Design, v.19 n.1, p.11-14, Jan./Feb. 1987 [doi>10.1016/0010-4485(87)90147-3]
	2	S. S. Abhyanker , C. Bajaj, Automatic parametrization of rational curves and surfaces II: cubics and cubicoids, Computer-Aided Design, v.19 n.9, p.499-502, Nov. 1987 [doi>10.1016/0010-4485(87)90235-1]
	3	S.S. Abhyankar and C. Bajaj. Automatic parameterization of rational curves and surfaces III: algebraic plane curves. Technical Report CSD-TR-619, Purdue University, Computer Sciences Department, West Lafayette, Indiana, February 1987.
	4	S.S. Abhyankar and C. Bajaj. Automatic parameterization of rational curves and surfaces W: algebraic space curves. Technical Report CSD-TR-703, Purdue University, Computer Sciences Department, West Lafayette, Indiana, February 1988.
	5	E. Allgower and K. Georg. Simplicial and continuation methods for approximating fixed points and solutions to systems of equations. SIAM Rev/ew, 22(1):28-85, january 1980.
	6	E. L. Allgower , S. Gnutzmann, Simplicial pivoting for mesh generation of implicitly defined surfaces, Computer Aided Geometric Design, v.8 n.4, p.305-325, Oct. 1991 [doi>10.1016/0167-8396(91)90018-7]
	7	E.L. Allgower and P.H. Schmidt. An algorithm for piecewise-linear approximation of an implicitly defined manifold. SIAM Journal of Numerical Analysis, 22(2):322- 346, April 1985.
	8	Dennis S. Arnon, Topologically reliable display of algebraic curves, ACM SIGGRAPH Computer Graphics, v.17 n.3, p.219-227, July 1983
	9	C.L. Bajaj, C.M. Hoffmann, J.E. Hopcroft, and R.E. Lynch. Tracing surface intersections. Technical Report CSD-TR-728, Department of Computer Science, Purdue University, West Lafayette, Indiana, December 1987.
	10	H. Baker. Building surfaces of evolution: The weaving wall. international Journal of Computer Vision, 3:51-71, 1989.
	11	J. Bloomenthal, Polygonization of implicit surfaces, Computer Aided Geometric Design, v.5 n.4, p.341-355, Nov. 1988 [doi>10.1016/0167-8396(88)90013-1]
	12	A. Borodin and I. Munro. The Computational Complexity of Algebraic and Numeric Problems. American Elsevier, New York, 1975.
	13	Y. De Mountaudouin. Resolution of p(z. ll)= 0. Computer Aided Design, 23(9):653-4x54, November 1991.
	14	David P. Dobkin , Allan R. Wilks , Silvio V. F. Levy , William P. Thurston, Contour tracing by piecewise linear approximations, ACM Transactions on Graphics (TOG), v.9 n.4, p.389-423, Oct. 1990 [doi>10.1145/88560.88575]
	15	Michael L. Dowling, A fast parallel Horner algorithm, SIAM Journal on Computing, v.19 n.1, p.133-142, Feb. 1990 [doi>10.1137/0219008]
	16	R.T. Farouki, and V.T. Rajan. On the numerical condition of Berstein polynomials. IBM Research Division Technical Report RC-12626, March 1987.
	17	R.T. Farouki, and V.T. Rajan. On the numerical condition of algebraic curves and surfaces. IBM Research Division Technical Report RC-13263, November 1987.
	18	Mark Hall , Joe Warren, Adaptive Polygonalization of Implicitly Defined Surfaces, IEEE Computer Graphics and Applications, v.10 n.6, p.33-42, November 1990 [doi>10.1109/38.62694]
	19	John D. Hobby, Rasterization of nonparametric curves, ACM Transactions on Graphics (TOG), v.9 n.3, p.262-277, July 1990 [doi>10.1145/78964.78966]
	20	B.W. Jordan Jr., w.J. Lennon, and B.D. Holm. An improved algorithm for the generation of nonparametric curves. IEEE Transactions on Computers, C-22(12):1052- 1060, December 1973.
	21	Alan David Kalvin, Segmentation and surface-based modeling of objects in three-dimensional biomedical images, New York University, New York, NY, 1992
	22	William E. Lorensen , Harvey E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, v.21 n.4, p.163-169, July 1987
	23	P.H. Milne. Symbolic and Numerical Computation for Artificial Intelligence, chapter On the Solution of a Set of Polynomial Equations, pages 89-101. Academic Press Ltd., London, UK, 1992.
	24	D. Moore and J. Warren. Adaptive mesh generation ii: Packing solids. Technical Report Rice COMP TR90- 139, Department of Computer Science, Rice University, Houston, TX, March 1991.
	25	R. Morris, A New Method for Drawing Algebraic Surfaces, Proceedings of the 5th IMA Conference on the Mathematics of Surfaces, p.31-47, September 14-16, 1992
	26	Paul Christian Pedersen , Bud Mishra, Counting real zeros, 1991
	27	T.W. Sederberg, D.C. Anderson, and R.N. Goldman. Implicit representation of parametric curves and surfaces. Computer Vision, Graphics, and Image Processing, 28:72- 84,1984.
	28	T.W. Sederberg, D.C. Anderson, and R.N. Goldman. Implicitization, inversion, and intersection of planar rational cubic curves. Computer Vision, Graphics, and Image Processing, 31 (1):89-102, July 1985.
	29	G. Taubin. Rasterizing implicit curves by space subdivision. IBM Research Division Technical Report RC17913, apn11992.
	30	Jerry Van Aken , Mark Novak, Curve-drawing algorithms for Raster displays, ACM Transactions on Graphics (TOG), v.4 n.2, p.147-169, April 1985 [doi>10.1145/282918.282943]
	31	R. Walker. Algebraic Curves. Princeton University Press, 1950.

CITED BY 5

	M. O. Benouamer , D. Michelucci, Bridging the gap between CSG and Brep via a triple ray representation, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.68-79, May 14-16, 1997, Atlanta, Georgia, United States
	Jeff Tupper, Reliable two-dimensional graphing methods for mathematical formulae with two free variables, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.77-86, August 2001
	Gabriel Taubin, Distance approximations for rasterizing implicit curves, ACM Transactions on Graphics (TOG), v.13 n.1, p.3-42, Jan. 1994
	G. Taubin , F. Cukierman , S. Sullivan , J. Ponce , D. J. Kriegman, Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting, IEEE Transactions on Pattern Analysis and Machine Intelligence, v.16 n.3, p.287-303, March 1994
	Wen Y. Su , John C. Hart, A programmable particle system framework for shape modeling, ACM SIGGRAPH 2005 Courses, July 31-August 04, 2005, Los Angeles, California