Local barycentric coordinates

Barycentric Coordinates on Surfaces

This paper introduces a method for defining and efficiently computing barycentric coordinates with respect to polygons on general surfaces. Our construction is geared towards injective polygons (polygons that can be enclosed in a metric ball of an appropriate size) and is based on replacing the linear precision property of planar coordinates by a requirement in terms of center of mass, and gene...

Blended 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...

Circles in barycentric coordinates

Let ABC be a fundamental triangle with the area . For a circle K the powers of vertices A, B, C with regard to K divided by 2 are said to be the barycentric coordinates of K with respect to triangle ABC. This paper gives some theory and applications of these coordinates.

Generalized barycentric coordinates

Barycentric Coordinates as Interpolants

The points P0, P1 and P2 are the vertices of the triangle. P is a point at which interpolation will be performed. For purposes of this document, point P0 has cartesian coordinates (x0,y0,w0), color coordinates (r0,g0,b0) and texture coordinates (u0,v0). Points P1 and P2 are similarly defined. The cartesian coordinates are defined in perspective space, i.e., they have been multiplied by a perspe...