Results 171 to 180 of about 188,550 (196)

The monotonicity of a family of barycentric coordinates for quadrilaterals

Computer Aided Geometric Design, 2017
Abstract Recently, Floater (2016) proved that four well-known kinds of generalized barycentric coordinates in convex polygons share a simple monotonicity property. In this note we proved that a family of barycentric coordinates for quadrilaterals ( Floater, 2015a ) are monotonic, too.
Chongyang Deng
exaly   +2 more sources

Transfinite Barycentric Coordinates

, 2017
In this chapter we study properties of transfinite barycentric interpolation schemes, which can be considered as continuous counterparts of generalized barycentric coordinates and are currently a subject of intensive research due to their fascinating ...
Alexander G. Belyaev, Pierre-Alain Fayolle   +1 more
openaire   +2 more sources

Hyperbolic barycentric coordinates and applications

Computer Aided Geometric Design, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alaa Eddine Bensad, Aziz Ikemakhen
openaire   +3 more sources

A general construction of barycentric coordinates over convex polygons

Advances in Computational Mathematics, 2006
Barycentric coordinates are unique for triangles, but there are many possible generalizations to convex polygons. In this paper we derive sharp upper and lower bounds on all barycentric coordinates over convex polygons and use them to show that all such ...
Kai Hormann, Géza Koß, Michael S Floater   +2 more
exaly   +1 more source

Special issue on “Generalized Barycentric Coordinates”

Computer Aided Geometric Design, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael S. Floater, Kai Hormann, N. Sukumar   +2 more
openaire   +1 more source

Generalized barycentric coordinates and approximations of convex functions on arbitrary convex polytopes

Computers and Mathematics With Applications, 2013
International audienceIn this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes.
Allal Guessab
exaly   +2 more sources

Generalized barycentric coordinates and applications

Acta Numerica, 2015
This paper surveys the construction, properties, and applications of generalized barycentric coordinates on polygons and polyhedra. Applications include: surface mesh parametrization in geometric modelling; image, curve, and surface deformation in computer graphics; and polygonal and polyhedral finite element methods.
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Barycentric coordinates for convex polytopes

Advances in Computational Mathematics, 1996
Continuing investigations of other authors referring to convex polygons and convex polytopes, the author generalizes the standard barycentric coordinate functions for simplices to those for arbitrary convex polytopes. In particular, a planar construction for polygons due to E.
openaire   +1 more source

Problem in Barycentric Coordinates

Journal of Applied Physics, 1965
When the phase coexistence pattern of a multicomponent system is known, it is theoretically a simple matter to decide which of the phase fields is represented by a given mixture of the p primary components. However, when p>3 the usual determinantal procedure is time consuming in practice and may even lead to an erroneous conclusion because of ...
openaire   +1 more source

Computing the Barycentric Coordinates of a Projected Point

Journal of Graphics Tools, 2005
An efficient algorithm is described for computing the barycentric coordinates of the projection of a point into the plane of a triangle. The method requires no square roots or conditionals, and only one floating point division, making it suitable for both CPU and GPU implementations.
openaire   +2 more sources