Harmonic Coordinates
نویسندگان
چکیده
Generalizations of barycentric coordinates in two and higher dimensions have been shown to have a number of applications in recent years, including finite element analysis, the definition of Spatches (n-sided generalizations of Bézier surfaces), free-form deformations, mesh parametrization, and interpolation. In this paper we present a new form of d dimensional generalized barycentric coordinates. The new coordinates are defined as solutions to Laplace’s equation subject to carefully chosen boundary conditions. Since solutions to Laplace’s equation are called harmonic functions, we call the new construction harmonic coordinates. We show that harmonic coordinates possess several properties that make them more attractive than mean value coordinates when used to define two and three dimensional deformations.
منابع مشابه
Fundamental Steady state Solution for the Transversely Isotropic Half Space
Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...
متن کاملBoundary Element Formulation of Harmonic Coordinates
We explain how Boundary Element Methods (BEM) can be used to speed up the computation and reduce the storage associated with Harmonic Coordinates. In addition, BEM formulation allows extending the harmonic coordinates to the exterior and makes possible to compare the transfinite harmonic coordinates with transfinite Shepard interpolation and Mean Value Coordinates. This comparison reveals that ...
متن کاملDiscrete Harmonic Functions from Local Coordinates
In this work we focus on approximations of continuous harmonic functions by discrete harmonic functions based on the discrete Laplacian in a triangulation of a point set. We show how the choice of edge weights based on generalized barycentric coordinates influences the approximation quality of discrete harmonic functions. Furthermore, we consider a varying point set to demonstrate that generali...
متن کاملOn the Uniqueness of Harmonic Coordinates * )
Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose across the material boundary, and on the conditions at infinity and at a suitable point inside the matter. This is illustrated in detail by simple fully solva...
متن کاملA unified, integral construction for coordinates over closed curves
We propose a simple generalization of Shephard’s interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A...
متن کامل