Generalized barycentric coordinates
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چکیده
منابع مشابه
Generalized Barycentric Coordinates on Irregular Polygons
In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex n-sided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to ray-tracing. Our new equations preserve many of the familiar properties of the triangular barycentric coordinates with an equally simple calculat...
متن کاملOn Generalized Barycentric Coordinates and Their Applications in Geometric Modeling
Generalized barycentric coordinate systems allow us to express the position of a point in space with respect to a given polygon or higher dimensional polytope. In such a system, a coordinate exists for each vertex of the polytope such that its vertices are represented by unit vectors ei (where the coordinate associated with the respective vertex is 1, and all other coordinates are 0). Coordinat...
متن کاملBijective Mappings with Generalized Barycentric Coordinates: A Counterexample
Many recent works attempt to generalize barycentric coordinates to arbitrary polygons. I construct a counterexample proving that no such generalization will produce purely bijective mappings in the plane provided the coordinates meet the Lagrange, reproduction, and partition of unity properties. The proof concerns generalized barycentric coordinates in a square, but trivially generalizes to arb...
متن کاملHigher Order Barycentric Coordinates
In recent years, a wide range of generalized barycentric coordinates has been suggested. However, all of them lack control over derivatives. We show how the notion of barycentric coordinates can be extended to specify derivatives at control points. This is also known as Hermite interpolation. We introduce a method to modify existing barycentric coordinates to higher order barycentric coordinate...
متن کاملVolume-preserving deformation using generalized barycentric coordinates
The cage-based deformation of a 3D object through generalized barycentric coordinates is a simple, e cient, e ective and hence widely used shape manipulation scheme. Editing vertices of the polyhedral cage induces a smooth space deformation of its interior; the vertices thus become control handles of the nal deformation. However, in some application elds, as medicine, constrained volumepreservi...
متن کاملBlended barycentric coordinates
Generalized barycentric coordinates are widely used to represent a point inside a polygon as an affine combination of the polygon’s vertices, and it is desirable to have coordinates that are non-negative, smooth, and locally supported. Unfortunately, the existing coordinate functions that satisfy all these properties do not have a simple analytic expression, making them expensive to evaluate an...
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تاریخ انتشار 2009