Patent ID: 8405659

Claim:
A method implemented in a computer system for parameterizing a 3D surface of genus g and arbitrary topology to the 2D plane comprising: receiving, at said computer system, an input 3D mesh of genus g, said 3D mesh representing a 3D arbitrary angle sized surface, said 3D arbitrary angle sized surface being a manifold 3D surface or non-manifold 3D surface; computing n discrete harmonic one-forms on the surface of the mesh to obtain n numbers for every edge in the graph represented by an input mesh, wherein 2g discrete harmonic one-forms are found in the 3D manifold surface, or less than 2g discrete harmonic one-forms or more than 2g discrete harmonic one-forms are found in the 3D non-manifold surface; selecting two compatible linearly independent discrete harmonic one-forms for parameterization; assigning an arbitrary vertex in the mesh as an origin, and then summing each of the two harmonic one-forms along the edges of the graph using a graph traversal strategy to form 2D coordinates for every other vertex of said mesh to form said 2D parameterization of said 3D surface; detecting all singularities in said 2D parameterization; and, removing and replacing the singularities, said removing comprising removing faces connected to the singularity, and said replacing comprising parameterizing the vertices of the removed faces using a 2D parameterization method and connecting these vertices using a 2D polygonalization algorithm, wherein a program using a processor unit executes one or more of said computing selecting, assigning, detecting, removing and replacing.