منابع مشابه
Mean value coordinates
We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its neighbouring vertices. The coordinates are motivated by the Mean Value Theorem for harmonic functions and can be used to simplify and improve methods for parameterization and morphing. 2003 Elsevier Science B.V. All rights reserved.
متن کاملMean value coordinates in 3D
Abstract: Trivariate barycentric coordinates can be used both to express a point inside a tetrahedron as a convex combination of the four vertices and to linearly interpolate data given at the vertices. In this paper we generalize these coordinates to convex polyhedra and the kernels of star-shaped polyhedra. These coordinates generalize in a natural way a recently constructed set of coordinate...
متن کاملGPU-assisted positive mean value coordinates for mesh deformations
In this paper we introduce positive mean value coordinates (PMVC) for mesh deformation. Following the observations of Joshi et al. [JMD∗07] we show the advantage of having positive coordinates. The control points of the deformation are the vertices of a "cage" enclosing the deformed mesh. To define positive mean value coordinates for a given vertex, the visible portion of the cage is integrated...
متن کاملMean Value Coordinates for Arbitrary Spherical Polygons and Polyhedra in
Since their introduction, mean value coordinates enjoy ever increasing popularity in computer graphics and computational mathematics because they exhibit a variety of good properties. Most importantly, they are defined in the whole plane which allows interpolation and extrapolation without restrictions. Recently, mean value coordinates were generalized to spheres and to 3. We show that these s...
متن کاملInterpolation error estimates for mean value coordinates over convex polygons
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter on...
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ژورنال
عنوان ژورنال: ACM Transactions on Graphics
سال: 2013
ISSN: 0730-0301,1557-7368
DOI: 10.1145/2461912.2461917