Patent ID: 7239313

Claim:
A method for distributing curvature from the boundary vertices of a received mesh to its interior vertices, comprising: receiving a mesh, where each boundary vertex B of the mesh has a prescribed normal n B ; computing and saving for each interior vertex V a set of weights w i of an associated umbrella operator; computing a curvature k B of each boundary vertex B using the formula k B =c B n B ·Umbrella(B), where k B is a scalar, Umbrella(B) is a positional umbrella operator at B, and c B = ∑ ( cot ⁢ ⁢ α i + cot ⁢ ⁢ β i ) 4 ⁢ Area is computed from local angle and area information; finding a target curvature k V for each interior vertex V by solving simultaneous equations Umbrella(k)=0 for all V; repositioning each vertex V to a new position b V +cn V , where c is chosen such that a curvature of V at the new position is the target curvature k V , and neighbors V i of V and the saved weights w i are used to find a base position b v = ∑ w i ⁢ V i ∑ w i and a normal n v = ∑ V i × V i + 1 ∑  V i × V i + 1  ; and displaying the mesh.