Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
An explicit basis for C1 quartic by various bivariate splines
SIAM Journal on Numerical Analysis
A sharp upper bound on the approximation order of smooth bivariate PP functions
Journal of Approximation Theory
Construction of local C1 quartic spline elements for optimal-order approximation
Mathematics of Computation
Swapping Edges of Arbitrary Triangulations to Achieve the Optimal Order of Approximation
SIAM Journal on Numerical Analysis
Optimal triangulation and quadric-based surface simplification
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Interpolation by spline spaces on classes of triangulations
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
Developments in bivariate spline interpolation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Interpolation by C1 splines of degree q≥4 on triangulations
Journal of Computational and Applied Mathematics
Local Lagrange interpolation by bivariate C1 cubic splines
Mathematical Methods for Curves and Surfaces
Stable Approximation and Interpolation with C1 Quartic Bivariate Splines
SIAM Journal on Numerical Analysis
An explicit quasi-interpolation scheme based on C 1 quartic splines on type-1 triangulations
Computer Aided Geometric Design
Adaptive quasi-interpolating quartic splines
Computing - Geometric Modelling, Dagstuhl 2008
Optimal bivariate C1 cubic quasi-interpolation on a type-2 triangulation
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
We develop a local Lagrange interpolation scheme for quartic C^1 splines on triangulations. Given an arbitrary triangulation @D, we decompose @D into pairs of neighboring triangles and add ''diagonals'' to some of these pairs. Only in exceptional cases, a few triangles are split. Based on this simple refinement of @D, we describe an algorithm for constructing Lagrange interpolation points such that the interpolation method is local, stable and has optimal approximation order. The complexity for computing the interpolating splines is linear in the number of triangles. For the local Lagrange interpolation methods known in the literature, about half of the triangles have to be split.