Mean value coordinates in 3D

By Michael S. Floater, Géza Kós, Martin Reimers. Computer Aided Geometric Design, 2005

296 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/1f6a6f4f2726dab005813a64d6c5474ded10b3da

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

A scaled boundary polygon formulation for elasto-plastic analyses (2014, methodology): “The shape functions of the polygon elements reported in [1, 2, 3, 4, 11, 12] are rational polynomials and require special integration techniques e.”
New perspectives on polygonal and polyhedral finite element methods (2014, methodology): “mean value coordinates to higher-dimensional polytopes have been realized [30, 80, 81], and they have been used in finite element computations [43, 44].”
Mean value coordinates for closed triangular meshes (2005, background): “(In independent contemporaneous work, [Floater et al. 2005] have proposed an extension of mean value coordinates from 2D polygons to 3D triangular meshes identical to section 3.”
Subspace gradient domain mesh deformation (2006, methodology): “We then project the deformation energy and the hard constraints onto the control mesh vertices using mean value interpolation [Ju et al. 2005; Floater et al. 2005], and perform the energy minimization in the subspace formed by control mesh vertices.”
Extended finite element method on polygonal and quadtree meshes (2008, methodology): “As an alternative to the above approach, conforming approximations can be constructed on quadtree meshes using mean value coordinates [14,15], which is a potentially preferred choice in three dimensions.”
Scaled boundary polygons with application to fracture analysis of functionally graded materials (2014, background): “[11] introduced the concept of mean value coordinates and generalized them to arbitrary-shaped polygons.”
Harmonic coordinates for character articulation (2007, unknown): “[2005] used generalized barycentric coordinates, specifically, mean value coordinates (see also Floater et al.[2005]) to define deformations controlled by a surface mesh rather than a three dimensional lattice.”
Topology optimization using polytopes (2013, methodology): “In the past, special interpolants have been proposed for arbitrary shaped elements such as Wachspress [4,5], Sibson coordinates [6,7], non-Sibson coordinates or Laplace shape functions [8–10,7,11], mean value coordinates [12,13], metric coordinate method [14], and maximum entropy shape function [15–”