The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.01 - January/February (1993 vol.13)
pp: 38-46
ABSTRACT
<p>Polar forms, which simplify the construction of polynomial and piecewise-polynomial curves and surfaces and lead to new surface representations and algorithms, are reviewed. The polar forms of polynomial curves, Bezier curves, and B-spline are discussed. Tensor product surfaces, the most popular surfaces in computer-aided geometric design, true surfaces, Bezier triangles, B-patches, and a triangular B-spline scheme that combines B-patches and simplex splines are also discussed.</p>
CITATION
Hans-Peter Seidel, "An Introduction to Polar Forms", IEEE Computer Graphics and Applications, vol.13, no. 1, pp. 38-46, January/February 1993, doi:10.1109/38.180116
REFERENCES
1. P. de Casteljau, "Outillages Methodes Calculations," tech. report, Andre Citroen, Paris, 1959.
2. P. de Casteljau,FormesàPôles, Hermes, Paris, 1985.
3. L. Ramshaw, "Blossoming: A Connect-the-Dots Approach to Splines," tech. report, Digital Systems Research Center, Palo Alto, Calif., 1987.
4. L. Ramshaw, "Bezier and B-splines as Multiaffine Maps,"Theoretical Foundations of Computer Graphics and CAD, R. Earnshaw, ed., 1988, pp. 757-776.
5. L. Ramshaw, "Blossoms are Polar Forms,"Computer Aided Geometric Design, Vol. 6, 1989, pp. 323-358.
6. P. de Casteljau,Le Lissage, Hermes, Paris, 1990.
7. H.P. Seidel, "A New Multiaffine Approach to B-splines,"Computer Aided Geometric Design, Vol. 6, 1989, pp. 23-32.
8. P.J. Barry and R.N. Goldman, "Algorithms for Progressive Curves: Extending B-spline and Blossoming Techniques to the Monomial, Power, and Newton Dual Bases," inKnot Insertion and Deletion Algorithms for B-Spline Modeling, R.N. Goldman and T. Lyche, eds., SIAM, Bellingham, Wash., 1992.
9. R.N. Goldman, "Blossoming and Knot Insertion Algorithms for B-spline Curves,"Computer Aided Geomtric Design, Vol. 7, 1990, pp. 69-81.
10. E.T.Y. Lee, "A Note on Blossoming,"Computer-Aided Geometric Design, Vol. 6, 1989, pp. 359-362.
11. K. Strom,Splines, Polynomials, and Polar Forms, Phd thesis, University, of Oslo, Oslo, Norway, 1992.
12. H.P. Seidel, "Polar Forms and Triangular B-Spline Surfaces," inEuclidean Geometry and Computers, A. Du and F. Hwang, eds., World Scientific Publishing, River Edge, N.J., 1992.
13. G. Schmeltz,Variation Diminishing Curve Representations and Curvature Criteria for Bezier Surfaces, PhD thesis, Technical University of Darmstadt, Germany, 1992.
14. T. DeRose, R.N. Goldman, and M. Lounsberry, "A Tutorial Introduction to Blossoming," inGeometric Modelling, Methods and Applications, H. Hagen and D. Roller, eds., Springer Verlag, New York, 1991, pp. 267-286.
15. H.P. Seidel, "Symmetric Recursive Algorithms for Surfaces: B-patches and the de Boor Algorithm for Polynomials over Triangles,"Constructive Approximations, Vol. 7, 1991, pp. 257-279.
16. W. Dahmen, C.A. Micchelli, and H.P. Seidel, "Blossoming Begets B-splines Built Better by B-patches,"Mathematics of Computation, Vol. 59, No. 199, July 1992, pp. 97-115.
17. P. Fong,Shape Control for B-splines over Arbitrary Triangulations, master's thesis, University of Waterloo, Waterloo, Canada, 1992.
18. P.J. Barry et al.,Blossoming: The New Polar-Form Approach to Spline Curves and Surfaces, Siggraph 91 Course Notes, No. 26, Siggraph, Chicago, 1991.
30 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool