Hierarchical Parameterization of Triangular Mesh with a Boundary Polygon Triangulation

Parameterizing a 3D triangular mesh is the process of finding an isomorphic planar mesh. It is widely used in graphics, as it is required, for instance, for surface fitting, texture mapping and re-meshing. In this paper, we present a new 3D approach to triangular mesh parameterization, which includes three steps: (1) construct a boundary polygon triangulation by mesh simplification; (2) parameterize the boundary polygon triangulation by first smoothing and then flattening it; (3) parameterize the interior vertices by parameterizing the vertex-split-cells one by one while refining the boundary polygon triangulation to the original one. The fact that all calculations are local makes it a fast approach, and the fact that a series of meshes in a multiresolution representation model could be well parameterized makes it appropriate for hierarchical surface fitting. Experiments show that the approach presented can result in a low distortion parameterization.

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