Mean value coordinates

By Michael S. Floater. Computer Aided Geometric Design, 2003

1,192 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c16f03480935ca2eb4cb55df1a06b071f32959f8

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 novel virtual node method for polygonal elements (2009, methodology): “Therefore, the polygonal finite element method (PFEM) is potentially useful in many areas, such as serving as transitional elements in adaptive computations [2-3] .I n 2003, Floater [ 4 ] proposed the mean value method and extended the PFEM to arbitrary polygonal elements.”
Interior Distance Using Barycentric Coordinates (2009, methodology): “Unless otherwise speciﬁed, we use the diffusion distance [CLL ∗ 05,GGV08] as the boundary distance and mean value coordinates [Flo03,JSW05] as the barycentric coordinates.”
Some basic formulations of the virtual element method (VEM) for finite deformations (2017, methodology): “The Mean Value coordinates are used to construct the displacement spaces [46] and the gradient correction scheme [23] is also adopted to ensure the polynomial consistency of the finite element approximations.”
PolyCube-Maps (2004, background): “The first one is based on the mean value coordinates [Floater 2003] and has the advantage of leading to a linear local optimization problem.”
Harmonic coordinates for character articulation (2007, neutral): “The problem of generalizing barycentric coordinates is rich and has received considerable attention in recent years ([Wachpress 1975], [R.Sibson 1981], [Loop and DeRose 1989], [Warren 1996], [Meyer et al. 2002], [Floater 2003]).”
A Local/Global Approach to Mesh Parameterization (2008, background): “The most celebrated weight recipes are the so-called cotangent weights [PP93], and the so-called mean-value weights [Flo03], which are both related to harmonic mappings.”
Inter-surface mapping (2004, methodology): “We use the mean-value parametrization scheme of Floater [2003] to relax the 2D locations inside Ν of the vertices of M ˆ ( ) v 1”
New perspectives on polygonal and polyhedral finite element methods (2014, methodology): “The advent of Floater’s mean value coordinate [7] was the turning point in graphics, and now the notion of generalized barycentric coordinates [8, 9, 10] is well-established.”
Mesh Manifold Based Riemannian Motion Planning for Omnidirectional Micro Aerial Vehicles (2021, methodology): “One important property needed for this planner is a surface flattening method that provides a bijective one-to-one mapping H. Algorithms such as Tutte Barycentric Mapping [22], Discrete Authalic Parametrization [23] and Floater Mean Value Coordinates [24] provide such a mapping.”
Extended finite element method on polygonal and quadtree meshes (2008, methodology): “Hormann and Floater [15] have presented the important properties of mean value coordinates along with an implementation for planar polygons.”
Conforming polygonal finite elements (2004, methodology): “We focus on two recent and important results that are germane to our explorations on polygonal finite elements: a generalized barycentric co-ordinate for n-gons [42] and mean value co-ordinates [43], which is particularly striking.”
ABF++: fast and robust angle based flattening (2005, background): “…each triangle): — Planarity (for each interior vertex): where V int is the set of interior vertices, and v ∗ is the set of angles incident on vertex v ; — Reconstruction (for each interior vertex)—this constraint ensures that edges shared by pairs of triangles have the same length (Figure 2):…”