Dimension of C1-splines on type-6 tetrahedral partitions

Authors:
Thomas Hangelbroek;Günther Nürnberger;Christian Rössl;Hans-Peter Seidel;Frank Zeilfelder
Affiliations:
Max Planck Institut für Informatik, AG 4, Computergrafik, D-66 123 Saarbrücken, Germany;Institut für Mathematik, Lehrstuhl IV, Universität Mannheim, D-68 131 Mannaheim, Germany;Max Planck Institut für Informatik, AG 4, Computergrafik, D-66 123 Saarbrücken, Germany;Max Planck Institut für Informatik, AG 4, Computergrafik, D-66 123 Saarbrücken, Germany;Institut für Mathematik, Lehrstuhl IV, Universität Mannheim, D-68 131 Mannaheim, Germany
Venue:
Journal of Approximation Theory
Year:
2004

Citing 12
Cited 6

Triangular Berstein-Be´zier patches

Computer Aided Geometric Design
An explicit basis for C1 quartic by various bivariate splines

SIAM Journal on Numerical Analysis
Dual bases for spline spaces on cells

Computer Aided Geometric Design
The generic dimension of the space of C1 splines of degree d≥8 on tetrahedral decompositions

SIAM Journal on Numerical Analysis
On dimension and existence of local bases for multivariate spline spaces

Journal of Approximation Theory
Automatic reconstruction of surfaces and scalar fields from 3D scans

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Developments in bivariate spline interpolation

Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Bezier and B-Spline Techniques

Bezier and B-Spline Techniques
Simplicial subdivisions and sampling artifacts

Proceedings of the conference on Visualization '01
Smooth approximation and rendering of large scattered data sets

Proceedings of the conference on Visualization '01
Quasi-interpolation by quadratic piecewise polynomials in three variables

Computer Aided Geometric Design
Reconstruction of volume data with quadratic super splines

IEEE Transactions on Visualization and Computer Graphics

Quasi-interpolation by quadratic piecewise polynomials in three variables

Computer Aided Geometric Design
Spline approximation of general volumetric data

SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
An octahedral C2 macro-element

Computer Aided Geometric Design
Quasi-interpolation by quadratic C1-splines on truncated octahedral partitions

Computer Aided Geometric Design
Quasi-interpolation by quadratic piecewise polynomials in three variables

Computer Aided Geometric Design
An octahedral C2 macro-element

Computer Aided Geometric Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a linear space of piecewise polynomials in three variables which are globally smooth, i,e. trivariate C1-splines of arbitrary polynomial degree. The splines are defined on type-6 tetrahedral partitions, which are natural generalizations of the four-directional mesh. By using Bernstein-Bézier techniques, we analyze the structure of the spaces and establish formulae for the dimension of the smooth splines on such uniform type partitions.