Higher Order Barycentric Coordinates

Abstract

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 coordinates and demonstrate, using higher order mean value coordinates, that our method, although conceptually simple and easy to implement, can be used to give easy and intuitive control at interactive frame rates over local space deformations such as rotations.