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
A trivariate clough-tocher scheme for tetrahedral data
Computer Aided Geometric Design
Local Lagrange interpolation by quintic C1 splines on type-6 tetrahedral partitions
Journal of Computational and Applied Mathematics
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We consider a linear space of piecewise polynomials in three variables which are globally smooth, i.e. trivariate C^1-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-Bezier techniques, we analyze the structure of the spaces and establish formulae for the dimension of the smooth splines on such uniform type partitions.