Setting the Boundary Free: A Composite Approach to Surface Parameterization

Figure 1: Boundary-free parameterization of a human model (66K△). From left: surface mesh with cut highlighed, initial discrete conformal map, boundary-free conformal map, and boundary-free quasi-harmonic map. In the last decade, surface mesh parameterization has emerged as a standard technique in computer graphics. The ever increasing need for processing large and highly detailed data sets fosters the development of efficient parameterization techniques that can capture the geometry of the input meshes and produce low distortion planar maps. We present a set of novel techniques allowing for low distortion parameterization. In particular, we address one of the major shortcomings of linear methods by allowing the parametric representation to evolve freely on the plane without any fixed boundary vertices. Our method consists of several simple steps, each solving a linear problem. Our results exhibit a fair balance between high-quality and computational efficiency. 1