Abstract
An algorithm is presented for approximating a rational multi-sided M-patch by a C2 spline surface. The motivation is that the multi-sided patch can be assumed to have good shape but is in nonstandard representation or of too high a degree. The algorithm generates a finite approximation of the M-patch, by a sequence of patches of bidegree (5,5) capped off by patches of bidegree (11,11) surrounding the extraordinary point.
The philosophy of the approach is (i) that intricate reparametrizations are permissible if they improve the surface parametrization since they can be precomputed and thereby do not reduce the time efficiency at runtime: and (ii) that high patch degree is acceptable if the shape is controlled by a guiding patch.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
de Boor, C.: B-Form Basics. In Gerald Farin, editor, Geometric Modeling: Algorithms and New Trends, pages 131–148, Philadelphia, 1987. SIAM.
Catmull, E., Clark, J: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design 10, 350–355. (1978).
Farin, G.: 1997. Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, 4th Edition. Academic Press, New York, NY, USA.
Gregory, J., Zhou, J.: Irregular C2 surface construction using bi-polynomial rectangular patches. Computer Aided Geometric Design 16 (1999) 424–435
Karčiauskas, K.: Rational M-patches and tensor-border patches. Contemporary mathematics 334 (2003) 101–128
Karčiauskas, K., Peters, J., Reif, U.: Shape characterization of subdivision surfaces — Case studies. to appear in CAGD
Peters, J.: C2 free-form surfaces of degree (3,5). Computer Aided Geometric Design 19 (2002) 113–126
Peters, J., Reif, U.: Analysis of generalized B-spline subdivision algorithms. SIAM Journal on Numerical Analysis 35 (1998) 728–748
Peters, J., Reif, U.: Shape characterization of subdivision surfaces — Basic principles. to appear in CAGD
Peters, J.: Smoothness, Fairness and the need for better multi-sided patches. Contemporary mathematics 334 (2003) 55–64.
Prautzsch, H.: Freeform splines. Comput. Aided Geom. Design, 14(3):201–206, 1997.
Prautzsch H., Boehm, W., Paluszny, M.: Bézier and B-spline techniques. Springer Verlag, Berlin, Heidelberg. (2002)
Reif, U.: TURBS-topologically unrestricted rational B-splines. Constr. Approx., 14(1):57–77, 1998.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Karčciauskas, K., Peters, J. (2005). Polynomial C2 Spline Surfaces Guided by Rational Multisided Patches. In: Computational Methods for Algebraic Spline Surfaces. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27157-0_9
Download citation
DOI: https://doi.org/10.1007/3-540-27157-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23274-2
Online ISBN: 978-3-540-27157-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)