Barycentric interpolation and mappings on smooth convex domains

In a recent paper, Warren, Schaefer, Hirani, and Desbrun proposed a simple method of interpolating a function defined on the boundary of a smooth convex domain, using an integral kernel with properties similar to those of barycentric coordinates on simplexes. When applied to vector-valued data, the interpolation can map one convex region into another, with various potential applications in computer graphics, such as curve and image deformation. In this paper we establish some basic mathematical properties of barycentric kernels in general, including the interpolation property and a formula for the Jacobian of the mappings they generate. We then use this formula to prove the injectivity of the mapping of Warren et al. Categories and Subject Descriptors

• Type: Conference
• Year: 2010
• Where: SMA
• Authors: Michael S. Floater, Jirí Kosinka
• Keywords: Basic Mathematical Properties, SMA 2010, Smooth Convex Domain, Solid Modeling, Various Potential Applications