Locally controllable conic splines with curvature continuity

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Locally controllable conic splines with curvature continuity

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ACM Transactions on Graphics (TOG) archive
Volume 10 , Issue 4 (October 1991) table of contents

Pages: 366 - 377

Year of Publication: 1991

ISSN:0730-0301

Author

Helmut Pottman

Purdue Univ., West Lafayette, IN

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 9, Downloads (12 Months): 24, Citation Count: 5

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references cited by index terms review

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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	BERGER, M., PANSU, P., BERRY, J. P., AND SAINT-RAYMOND, X. Problems in Geometry. Springer-Verlag, New York, 1984.
	2	Wolfgang Boehm, Rational geometric splines, Computer Aided Geometric Design, v.4 n.1-2, p.67-77, July 1987 [doi>10.1016/0167-8396(87)90025-2]
	3	BOL, G, Projektive Differentialgeometrie I. Vandenhoeck & Ruprecht, Goettingen, 1950.
	4	BOUTON, C. Some examples of differential invariants. Bull. Am. Math. Soc. 4 (1898), 313-322.
	5	De BOOR, C., H()LLIG, K., ^No S^BI~, M. High accuracy geometric Hermite interpolation. Comput. Aided Geom. Des. 4 (1987), 269-278.
	6	G. Farin, Curvature continuity and offsets for piecewise conics, ACM Transactions on Graphics (TOG), v.8 n.2, p.89-99, April 1989 [doi>10.1145/62054.62056]
	7	G. Farin, Rational curves and surfaces, Mathematical methods in computer aided geometric design, Academic Press Professional, Inc., San Diego, CA, 1989
	8	LEE, E. The rational B~zier representation for conics. In Geometric Modeling, G. Farin, Ed., SIAM, Philadelphia, 1987, pp. 3-19.
	9	N1ELSON, G.M. Private communication, 1989.
	10	Theodosios Pavlidis, Curve Fitting with Conic Splines, ACM Transactions on Graphics (TOG), v.2 n.1, p.1-31, Jan. 1983 [doi>10.1145/357314.357315]
	11	Michael A. Penna , Richarad R. Patterson, Projective geometry and its applications to computer graphics, Prentice-Hall, Inc., Upper Saddle River, NJ, 1986
	12	Vaughan Pratt, Techniques for conic splines, Proceedings of the 12th annual conference on Computer graphics and interactive techniques, p.151-160, July 1985
	13	WALKER, R.J. Algebraic Curves. Springer, New York, 1978.

CITED BY 5

	D. S. Meek, Coaxing a planar curve to comply, Journal of Computational and Applied Mathematics, v.140 n.1-2, p.599-618, 1 March 2002
	Gerald Farin, From Conics to NURBS: A Tutorial and Survey, IEEE Computer Graphics and Applications, v.12 n.5, p.78-86, September 1992
	Xiao-Shan Gao , Ming Li, Rational quadratic approximation to real algebraic curves, Computer Aided Geometric Design, v.21 n.8, p.805-828, October 2004
	D. S. Meek , D. J. Walton, Planar G² Hermite interpolation with some fair, C-shaped curves, Journal of Computational and Applied Mathematics, v.139 n.1, p.141-161, 1 February 2002
	Seok Hur , Tae-wan Kim, Finding the best conic approximation to the convolution curve of two compatible conics based on Hausdorff distance, Computer-Aided Design, v.41 n.7, p.513-524, July, 2009

INDEX TERMS

Primary Classification:
I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling
Subjects: Curve, surface, solid, and object representations

General Terms:
Algorithms, Design

REVIEW

"Claudio Delrieux : Reviewer"

Research on the construction of locally convex conic splines with curvature continuity is the subject of this paper. The construction requires two curvature elements, (p0, T< more...

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