Work

Transfinite barycentric coordinates for arbitrary planar domains

Year: 2025

Type: article

Abstract: Generalized barycentric coordinates provide a simple way of interpolating data given at the vertices of a polygon or polyhedron, with widespread applications in computer graphics, geometry processing, and other fields. Transfinite barycentric coordinates, also known as barycentric kernels, extend this idea to curved domains and can be used to interpolate continuous data given on the boundary of such domains. We present a novel framework for defining non-negative barycentric kernels over arbitrary bounded planar domains. This framework is inspired by the construction of a transfinite version of maximum likelihood coordinates and can be used to define a variety of barycentric kernels, including a simple pseudo-harmonic kernel and a non-negative variant of the mean value kernel. Moreover, we propose a novel barycentric kernel which yields transfinite interpolants that are similar to harmonic interpolants. We tested our new kernel for domains and boundary data described by closed uniform quadratic splines and in particular for image deformation. The results indicate that our method has several advantages over alternative approaches.

Source: Computer Aided Geometric Design

DOI: 10.1016/j.cagd.2025.102433

Authors: Qingjun Chang, Kai Hormann

Institution: Università della Svizzera italiana

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,930

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung