Results 11  20
of
10,672
On the Uniqueness of Barycentric Coordinates
, 2003
"... Given a convex polytope P, a set of coordinate... ..."
Interior Distance Using Barycentric Coordinates
"... This paper introduces a framework for defining a shapeaware distance measure between any two points in the interior of a surface mesh. Our framework is based on embedding the surface mesh into a highdimensional space in a way that best preserves boundary distances between vertices of the mesh, per ..."
Abstract
 Add to MetaCart
, performing a mapping of the mesh volume into this highdimensional space using barycentric coordinates, and defining the interior distance between any two points simply as their Euclidean distance in the embedding space. We investigate the theoretical properties of the interior distance in relation
Mass Point Geometry (Barycentric Coordinates)
, 2000
"... My original intention, when I mentioned this as possible topic was to just show a couple of examples of this technique along with my talk on Archimedes and the Arbelos (January 16, 2000). The words ”Mass Point Geometry ” were unfamiliar to Zvesda, so I mentioned ”Barycentric Coordinates ” to give he ..."
Abstract
 Add to MetaCart
My original intention, when I mentioned this as possible topic was to just show a couple of examples of this technique along with my talk on Archimedes and the Arbelos (January 16, 2000). The words ”Mass Point Geometry ” were unfamiliar to Zvesda, so I mentioned ”Barycentric Coordinates ” to give
Continuity of barycentric coordinates in Euclidean topological spaces
 Formalized Mathematics
"... Summary. In this paper we present selected properties of barycentric coordinates in the Euclidean topological space. We prove the topological correspondence between a subset of an affine closed space of En and the set of vectors created from barycentric coordinates of points of this subset. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Summary. In this paper we present selected properties of barycentric coordinates in the Euclidean topological space. We prove the topological correspondence between a subset of an affine closed space of En and the set of vectors created from barycentric coordinates of points of this subset.
Complex Barycentric Coordinates with Applications to Planar Shape Deformation
, 2009
"... Barycentric coordinates are heavily used in computer graphics applications to generalize a set of given data values. Traditionally, the coordinates are required to satisfy a number of key properties, the first being that they are real and positive. In this paper we relax this requirement, allowing t ..."
Abstract

Cited by 17 (4 self)
 Add to MetaCart
Barycentric coordinates are heavily used in computer graphics applications to generalize a set of given data values. Traditionally, the coordinates are required to satisfy a number of key properties, the first being that they are real and positive. In this paper we relax this requirement, allowing
Computing the barycentric coordinates of a projected point
 Journal of Graphics Tools v10
, 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. 1 ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
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. 1
Education Barycentric coordinates computation in homogeneous coordinates
, 2007
"... Homogeneous coordinates are often used in computer graphics and computer vision applications especially for the representation of geometric transformations. The homogeneous coordinates enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them pro ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
in computer graphics processing. Generally, triangles and tetrahedra are mostly represented by vertices. Several tests like ‘‘point insidey’ ’ or ‘‘intersection ofy’ ’ are very often used in applications. On the other hand, barycentric coordinates in E 2 or E 3 can be used to implement such tests, too
Robust Barycentric Coordinates Computation of the Closest Point to a Hyperplane in E n
"... Abstract—Barycentric coordinates are well known and used in many applications. They are used for a position computation inside of an (n+1)sided simplex in an ndimensional space, i.e. in a triangle in E2 or in a tetrahedron in E3. There are some cases when the given point is theoretically on the hy ..."
Abstract
 Add to MetaCart
Abstract—Barycentric coordinates are well known and used in many applications. They are used for a position computation inside of an (n+1)sided simplex in an ndimensional space, i.e. in a triangle in E2 or in a tetrahedron in E3. There are some cases when the given point is theoretically
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 coordinates have the same continuous extension ..."
Abstract

Cited by 63 (14 self)
 Add to MetaCart
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 coordinates have the same continuous
Results 11  20
of
10,672