Digital Geometry Processing (4)

Parametric (the PARAMETERIZATION)

　　Establishing a triangular mesh parameterization means finding a set of coordinates (U _I , V _I ) corresponding to each vertex, the following conditions should be met set of coordinates: after selfing not parameterized surface.

Several different parameters of the method:

　　Gravity map (Barycentric Mapping)

　　　　Focus mapping is more common triangular mesh parameterization method. Given a triangular mesh and the disk (Disk) homeomorphic if after the point of the boundary vertex parameter together into a convex polygon, the point after the interior vertex coordinates after it is parameterized 1- vertex parameter of the neighborhood convex combination, parameters such method is an effective method of parameterization (not selfing).

 

 

 

 

 　　Laplace operator

　　Laplacian function regularity measure, for example, a linear function; Laplacian is 0, thus minimizing u, v Laplace operator can obtain a smooth parametric coordinates, words, then, after the distortion minimizing parameterization. Geometric Laplace operator can be calculated by a discrete differential _{i, j}