Multiresolution analysis for minimal energy Cr-surfaces on Powell-Sabin type meshes

Authors:
Miguel A. Fortes;Pedro González;Maria Moncayo;Miguel Pasadas
Affiliations:
Departamento de Matemática Aplicada, Universidad de Granada., Granada, Spain;Departamento de Matemática Aplicada, Universidad de Granada., Granada, Spain;Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena (UPCT), Cartagena, Spain;Departamento de Matemática Aplicada, Universidad de Granada., Granada, Spain
Venue:
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Year:
2008

Citing 10
Cited 0

Ten lectures on wavelets

Ten lectures on wavelets
Multiresolution representation of data: a general framework

SIAM Journal on Numerical Analysis
Approximation order of bivariate spline interpolation for arbitrary smoothness

Journal of Computational and Applied Mathematics
The lifting scheme: a construction of second generation wavelets

SIAM Journal on Mathematical Analysis
Piecewise Quadratic Approximations on Triangles

ACM Transactions on Mathematical Software (TOMS)
Uniform Powell--Sabin spline wavelets

Journal of Computational and Applied Mathematics
Surface compression using a space of C1 cubic splines with a hierarchical basis

Computing - Geometric modelling dagstuhl 2002
Local energy-optimizing subdivision algorithms

Computer Aided Geometric Design
Minimal energy Cr-surfaces on uniform Powell-Sabin type meshes

Mathematics and Computers in Simulation
Minimal energy Cr-surfaces on uniform Powell-Sabin-type meshes for noisy data

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is intended to provide a multiresolution analysis (MRA) scheme to obtain a sequence of Cr-spline surfaces over a Powell-Sabin triangulation of a polygonal domain approximating a Lagrangian data set and minimizing a certain “energy functional”. We define certain non separable scaling and wavelet functions in bidimensional domains, and we give the decomposition and reconstruction formulas in the framework of lifting schemes. Two important applications of the theory are given: In the first one we develop an algorithm for noise reduction of signals. The second one is related to the localization of the regions where the energy of a given function is mostly concentrated. Some numerical and graphical examples for different test functions and resolution levels are given.