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Author Kobbelt, Leif
Source CiteSeerX
Content type Text
Publisher University Press
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Non-linear Geometric Functionals ♦ Local Parameterizations ♦ Introduction Fairing Scheme ♦ Triangular Mesh ♦ Hand Efficient ♦ Finite Difference Method ♦ Optimization Problem ♦ Minimum Bending Energy ♦ Efficient Multi-grid Solver ♦ High Quality ♦ Flexible Scheme ♦ Refined Mesh ♦ Finite Difference Technique ♦ Specific Parameterization ♦ Generate Surface ♦ Piecewise Polynomial Representation ♦ Sparse Linear System ♦ Major Difficulty ♦ General Dependent
Description . We propose an efficient and flexible scheme to fairly interpolate or approximate the vertices of a given triangular mesh. Instead of generating a piecewise polynomial representation, our output will be a refined mesh with vertices lying densely on a surface with minimum bending energy. To obtain those, we generalize the finite differences technique to parametric meshes. The use of local parameterizations (charts) makes it possible to cast the minimization of non-linear geometric functionals into solving a sparse linear system. Efficient multi-grid solvers can be applied which leads to fast algorithms that generate surfaces of high quality. x1. Introduction Fairing schemes which construct a surface by solving a constrained optimization problem, are traditionally based on piecewise polynomial representations [2,9,16,18]. The major difficulty in this approach is that on one hand efficient (linear) schemes are in general dependent on the specific parameterization and hence fail to be pr...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1998-01-01
Publisher Institution Schumaker: Mathematical Methods for Curves and Surfaces II, Vanderbilt