Application of Barycentric Coordinates in Space Vector PWM Computations

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.

Barycentric coordinates computation in homogeneous coordinates

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 properly. Today’s graphics hardware based on GPU offers a very high computational power using pixel ...

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...

Generalized barycentric coordinates