A family of tangent continuous cubic algebraic splines

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A family of tangent continuous cubic algebraic splines

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ACM Transactions on Graphics (TOG) archive
Volume 12 , Issue 3 (July 1993) table of contents

Pages: 209 - 232

Year of Publication: 1993

ISSN:0730-0301

Authors

Marco Paluszny	Univ. Central de Venezuela, Caracas, Venezuela
Richard R. Patterson	Purdue Univ., Indianapolis, IN

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 21, Citation Count: 5

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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.

	1	Chandrajit L. Bajaj, Surface fitting using implicit algebraic surface patches, Topics in surface modeling, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
	2	C. L. Bajaj , C. M. Hoffman , R. E. Lynch , J. E. H. Hopcroft, Tracing surface intersections, Computer Aided Geometric Design, v.5 n.4, p.285-307, Nov. 1988 [doi>10.1016/0167-8396(88)90010-6]
	3	BAaAJ, C. L., ANI) XtT, G. Piecewise rational approximation of real algebraic curves. Comput. Sci. Tech. Rep. CAPO 91-19, Purdue Univ., 1991.
	4	Richard E. Chandler, A Tracking Algorithm for Implicitly Defined Curves, IEEE Computer Graphics and Applications, v.8 n.2, p.83-89, March 1988 [doi>10.1109/38.506]
	5	Wolfgang Dahmen, Smooth piecewise quadric surfaces, Mathematical methods in computer aided geometric design, Academic Press Professional, Inc., San Diego, CA, 1989
	6	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]
	7	Gerald Farin, Curves and surfaces for computer aided geometric design: a practical guide, Academic Press Professional, Inc., San Diego, CA, 1988
	8	Joe Warren , Thomas Garrity, Geometric continuity, Computer Aided Geometric Design, v.8 n.1, p.51-65, Feb. 1991 [doi>10.1016/0167-8396(91)90049-H]
	9	HOFFMANN, C. M., ANO HOPCROrr, J. E. Automatic surface generation in computer aided design. Visual Comput. 1 (1985), 95-100.
	10	HOFFMANN, C. M., AND HOPCROFT, J. E. The potential method for blending surfaces and curves. Geometric Modeling: Algorithms and New Trends, G. Farin, Ed., SIAM, Philadelphia, 1987.
	11	Josef Hoschek , Erich Hartmann, Functional splines for interpolation, approximation, and blending of curves, surfaces, and solids, Topics in surface modeling, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
	12	J. Li , J. Hoschek , E. Hartmann, Gn-1-functional splines for interpolation and approximation of curves, surfaces and solids, Computer Aided Geometric Design, v.7 n.1-4, p.209-220, Jun. 1990 [doi>10.1016/0167-8396(90)90032-M]
	13	LoDtiA, S., AND WARREN, J. BSzier representation for cubic surface patches. Comput. Aided Des. To appear.
	14	S. Lodha , J. Warren, Be´zier representation for quadric surface patches, Computer-Aided Design, v.22 n.9, p.574-579, Nov. 1990 [doi>10.1016/0010-4485(90)90042-B]
	15	Richard R. Patterson, Parametric cubics as algebraic curves, Computer Aided Geometric Design, v.5 n.2, p.139-160, July 1988 [doi>10.1016/0167-8396(88)90028-3]
	16	R. R. Patterson, Parametrizing and graphing nonsingular cubic curves, Computer-Aided Design, v.20 n.10, p.615-623, December 1988 [doi>10.1016/0010-4485(88)90208-4]
	17	Michael A. Penna , Richarad R. Patterson, Projective geometry and its applications to computer graphics, Prentice-Hall, Inc., Upper Saddle River, NJ, 1986
	18	SALMON, G. Higher Plane Curves. Hodges, Foster and Figgis, Dublin, 1879.
	19	SEDERBERG, T.W. Algebraic geometry for surfaces and solid modeling. Geometric Modeling: Algorithms and New Trends, G. Farin, Ed., SIAM, Philadelphia, 1987.
	20	T. W. Sederberg, Algorithm for algebraic curve intersection, Computer-Aided Design, v.21 n.9, p.547-554, Nov. 1989 [doi>10.1016/0010-4485(89)90015-8]
	21	SEOERBERO, T. W. Piecewise algebraic surface patches. Comput. Aided Geom. Des. 2 (1985), 53-59.
	22	SEDERBERO, T.W. Planar piecewise algebraic curves. Comput. Aided Geom. Des. I (1984), 241-255.
	23	J. Warren, Blending algebraic surfaces, ACM Transactions on Graphics (TOG), v.8 n.4, p.263-278, Oct. 1989 [doi>10.1145/77269.77270]
	24	Joe Warren, Free-form blending: a technique for creating piecewise implicit surfaces, Topics in surface modeling, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
	25	WARREN, J. Several notions of geometric continuity for implicit plane curves. Monograflas de la Academia de Ciencias de Zaragoza, Comunicaciones presentadas en el Instituto de Estudios Avanzados de la OTAN sobre "Computaci6n de Curvas y Superficies", Puerto de la Cruz (Tenerife, Espafia, 1989) 2 (1990).

CITED BY 5

	M. Paluszny , R. Patterson , F. Tovar, The singular point of an algebraic cubic, Applied Numerical Mathematics, v.40 n.1-2, p.23-31, January 2002
	Chandrajit L. Bajaj , Guoliang Xu, Error bounded regular algebraic spline curves, Proceedings of the fifteenth annual symposium on Computational geometry, p.332-340, June 13-16, 1999, Miami Beach, Florida, United States
	IEEE Computer Graphics and Applications Staff, Quartic Discriminants and Tensor Invariants, IEEE Computer Graphics and Applications, v.22 n.2, p.86-91, March 2002
	J. Daza , T. Goncalves , F. Tovar, Path splines with circle envelopes, Computer Aided Geometric Design, v.24 n.3, p.151-160, April, 2007
	Chun-Gang Zhu , Ren-Hong Wang , Xiquan Shi , Fengshan Liu, Functional splines with different degrees of smoothness and their applications, Computer-Aided Design, v.40 n.5, p.616-624, May, 2008

INDEX TERMS

Primary Classification:
I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling
Subjects: Splines

General Terms:
Algorithms, Design

Keywords:
cubic ovals, cubic splines, implicit curves, interpolation, piecewise algebraic curves

REVIEW

"Vadim Shapiro : Reviewer"

The algebraic splines studied in this paper are a subclass of piecewise cubic planar curves where each curve segment is a subset of some cubic curve fx,y=0 , constr more...

Collaborative Colleagues:

Marco Paluszny: colleagues

Richard R. Patterson: colleagues

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