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Issue No.09 - September (1985 vol.5)
pp: 46-58
Brian Barsky , University of California, Berkeley
Tony DeRose , University of California, Berkeley
ABSTRACT
Simpler equations and computationally more efficient algorithms make the Beta2-spline technique easier to understand and useful to the designer.
INDEX TERMS
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CITATION
Brian Barsky, Tony DeRose, "The Beta2-spline: A Special Case of the Beta-spline Curve and Surface Representation", IEEE Computer Graphics and Applications, vol.5, no. 9, pp. 46-58, September 1985, doi:10.1109/MCG.1985.276524
REFERENCES
1. Brian A.Barsky, “The Beta-spline: A Local Representation Based on Shape Parameters and Fundamental Geometric Measures,” Dec. 1981
2. Brian A.Barsky, Computer Graphics and Geometric Modelling Using Beta-splines , Springer-Verlag 1985 to appear
3. Brian A.Barsky, “The Beta-spline: A Curve and Surface Representation for Computer Graphics and Computer Aided Geometric Design,” submitted for publication
4. Ivor D.Faux and Michael J.Pratt, Computational Geometry for Design and Manufacture , Ellis HorWood, Ltd. 1979
5. J. R.Manning, “Continuity Conditions for Spline Curves,” Computer J. Vol. 17, No. 2, pp. 181-186 May 1974
6. Brian A.Barsky and John C.Beatty, “Local Control of Bias and Tension in Beta-splines,” ACM Trans. Graphics Apr. 1983 Vol. 2, No. 2, pp. 109-134 Also published in Computer Graphics (Proc. SIGGRAPH 83), Vol. 17, No. 3, July 1983, pp. 193-218
7. Richard J.Fateman, “Addendum to the MACSYMA Reference Manual for the VAX,” , Computer Science Division, Univ. of California 1982 tech. report
8. Gregory M.Nielson, Robert E.Barnhill, and Richard F.Riesenfeld, Computer Aided Geometric Design , Academic Press 1974pp. 209-235
9. Richard H.Bartels and John C.Beatty, “Betasplines with a Difference,” , Department of Computer Science, Univ. of Waterloo May 1984
10. T.N.T.Goodman, “Properties of Beta-splines,” J. Approximation Theory accepted for publication
11. Edwin E.Catmull and James H.Clark, “Recursively Generated B-spline Surfaces on Arbitrary Topological Meshes,” Computer-Aided Design Vol. 10, No. 6, pp. 350-355 Nov. 1978
12. George M.Chaikin, Computer Graphics and Image Processing , 1974 Vol. 3, pp. 346-349
13. D. W. H.Doo and M. A.Sabin, “Behavior of Recursive Division Surfaces Near Extraordinary Points,” Computer-Aided Design Vol. 10, No. 6, pp. 356-360 Nov. 1978
14. Jeffrey M.Lane and Loren C.Carpenter, “A Generalized Scan Line Algorithm for the Computer Display of Parametrically Defined Surfaces,” Computer Graphics and Image Processing Vol. 11, No. 3, pp. 290-297 Nov. 1979
15. Jeffrey M.Lane and Richard F.Riesenfeld, “A Theoretical Development for the Computer Generation of Piecewise Polynomial Surfaces,” IEEE Trans. Pattern Analysis and Machine Intelligence Vol. PAMI-2, No. 1, pp. 35-46 Jan. 1980
16. Robert W.Nydegger, “A Data Minimization Algorithm of Analytical Models for Computer Graphics,” 1972
17. Edwin E.Catmull, “A Subdivision Algorithm for Computer Display of Curved Surfaces,” Dec. 1974 Also tech. report no. UTEC-CSc-74-133, Department of Computer Science, Univ. of Utah
18. Brian A.Barsky, “Arbitrary Subdivision of Bezier Curves,” submitted for publication
19. Ronald N.Goldman, “Using Degenerate Bézier Triangles and Tetrahedra to Subdivide Bézier Curves,” Computer-Aided Design Vol. 14, No. 6, pp. 307-311 Nov. 1982
20. Jeffrey M.Lane and Richard F.Riesenfeld, “Bounds on a Polynomial,” BIT Vol. 21, No. 1, pp. 112-117 1981
21. Ronald N.Goldman private communication
22. Brian A.Barsky, Tony D.DeRose, and Mark D.Dippe, “An Adaptive Subdivision Method with Crack Prevention for Rendering Beta-spline Objects,” submitted for publication
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