Mesh segmentation driven by Gaussian curvature

Mesh parameterization is a fundamental problem in computer graphics as it allows for texture mapping and facilitates many mesh processing tasks. Although there exists a variety of good parameterization methods for meshes that are topologically equivalent to a disk, the segmentation into nicely parameterizable charts of higher genus meshes has been studied less. In this paper we propose a new segmentation method for the generation of charts that can be flattened efficiently. The integrated Gaussian curvature is used to measure the developability of a chart, and a robust and simple scheme is proposed to integrate the Gaussian curvature. The segmentation approach evenly distributes Gaussian curvature over the charts and automatically ensures a disklike topology of each chart. For numerical stability, we use an area on the Gauss map to represent Gaussian curvature. The resulting parameterization shows that charts generated in this way have less distortion compared to charts generated by other methods.