Abstract
Triangular B-splines are a new tool for the modeling of complex objects with non-rectangular topology. The new B-spline scheme is based on blending functions and control points and allows modeling piecewise polynomial surfaces of degree n that are C n-1-continuous throughout [4, 15, 17]. An implementation of the new scheme at the University of Waterloo has succeeded in demonstrating the practical feasibility of the fundamental algorithms underlying the new scheme [6, 7].
This is a preview of subscription content, log in via an institution to check access.
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
S. Auerbach, R.H.J. Gmelig Meyling, M. Neamtu, H. Schachen. Approximation and geometric modeling with simplex B-splines associated with irregulär triangles. Computer-Aided Geom. Design, 8: 67–87, 1991.
W. Dahmen, C.A. Miechelli. On the linear independence of multivariate B-splines I. Triangulations of simploids. SIAM J. Numer. Anal., 19: 993–1012, 1982.
W. Dahmen, C.A. Micchelli. Recent progress in multivariate splines. In Approximation Theory IV, pages 27–121. Academic Press, 1983.
W. Dahmen, C.A. Micchelli, H.-P. Seidel. Blossoming begets B-splines built better by B-patehes. Math. Comp., 59: 97–115, 1992.
P. de Casteljau. Formes à Pôles. Hermes, Paris, 1985.
P. Fong. Shape control for B-splines over arbitrary triangulations. Master’s thesis, University of Waterloo, Waterloo, Canada, 1992.
Ph. Fong, H.-P. Seidel. An implementation of multivariate B-spline surfaces over arbitrary triangulations. In Proc. Graphics Interface’92, pages 1–10. Morgan Kaufmann Publishers, 1992.
R.H.J. Gmelig Meyling. Polynomial spline approximation in two variables. PhD thesis, University of Amsterdam, 1986.
T.A. Grandine. The stable evaluation of multivariate simplex splines. Math. Comp., 50: 197–205, 1988.
K. Höllig. Multivariate splines. SIAM J. Numer. Anal., 19: 1013–1031, 1982.
C.A. Miechelli. On a numerically efficient method for Computing with multivariate B-splines. In W. Schempp, K. Zeller, editors, Multivariate Approximation Theory, pages 211–248, Basel, 1979. Birkhäuser.
M. Neamtu. A Contribution to the Theory and Practice of Multivariate Splines. PhD thesis, University of Twente, Ensehede, 1991.
L. Ramshaw. Blossoming: A connect-the-dots approach to splines. Technical report, Digital Systems Research Center, Palo Alto, 1987.
L. Ramshaw. Blossoms are polar forms. Computer-Aided Geom. Design, 6: 323–358, 1989.
H.-P. Seidel. Polar forms and triangular B-Spline surfaces. In Blossoming: The New Polar-Form Approach to Spline Curves and Surfaces, SIGGRAPH’91 Course Notes #26, pages 8.1–8.52. ACM SIGGRAPH, 1991.
H.-P. Seidel. Symmetrie recursive algorithms for surfaces: B-patches and the de Boor algorithm for polynomials over triangles. Constr. Approx., 7: 257–279, 1991.
H.-P. Seidel. Representing pieeewise polynomials as linear combinations of multivariate B-splines. In T. Lyche, L. L. Schumaker, editors, Curves and Surfaces, pages 559–566. Academic Press, 1992.
C.R. Traas. Practice of bivariate quadratic simplicial splines. In W. Dahmen, M. Gasca, C.A. Micchelli, editors, Computation of Curves and Surfaces, pages 383–422, Dordrecht, 1990. NATO ASI Series, Kluwer Academic Publishers.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seidel, HP. (1995). Triangular B-Splines. In: Straßer, W., Wahl, F. (eds) Graphics and Robotics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79210-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-79210-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58358-5
Online ISBN: 978-3-642-79210-6
eBook Packages: Springer Book Archive