Relaxation of spherical parameterization meshes

For closed two-manifold genus-0 meshes, the sphere is the most natural parameterization domain. Like planar parameterization, spherical parameterization without foldover and with low distortion consitutes two basic challenges. However, in order to prevent foldovers, many current studies cannot validly reduce distortion, especially area distortion. In this paper, we present a two-stage relaxation method to reduce the distortion of spherical meshes parameterized by traditional methods. The first stage is an authalic (area-preserving) relaxation algorithm that iteratively relaxes the mesh surface by growing patches around seed triangles. The second one is a relaxation procedure based on SCDM (spherical-domain compositive distortion metric).

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