Structure Preserving Mesh Parameterization

The traditional parameterization methods focused on preserving the local geometry properties by minimizing the distortions of angle and stretch. In this paper, we present a mesh parameterization method to preserve some global geometry properties, such as symmetry structure, of the input mesh. Given an input triangular mesh, the symmetry regions can be automatically detected using shape analysis method or manually specified by the users. For each vertex in the symmetry regions, we can identify the symmetric point and represent it as a triangle index and the corresponding bary centric coordinates. We extend the harmonic map to parameterize the input mesh by adding new error metric to measure how the symmetry property of the point pairs are preserved. Since the new error metric is non-linear, we develop an iterative update method to solve the parameterization problem. At last, we show some structure preservation parameterization results, and compare them with the results of the traditional harmonic map.