Cutting for Arbitrary Genus Mesh Based on Poisson Scalar Field

Mesh cutting is widely used in graphics.We present a more efficient and simple method based on Poisson scalar field for cutting an arbitrary genus surface mesh into a disc-like mesh.Given a mesh,we first solve a Poisson equation to construct a scalar field and use it to generate some critical points.The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method.For meshes with nonzero-genus,we construct a Harmonic scalar field,and connect the saddle points with the boundaries based on the Morse theory.Our cutting cross a set of edges of the mesh including the boundaries if any,generating a single topological disc.We also reduce the distortion during mesh flattening.Our experiments show that the cutting path in this paper well approximate the shortest path given the critical points,and the proposed method is applicable to arbitrary genus meshes.