Fast mapping and morphing for genus-zero meshes with cross spherical parameterization

• A fast mesh mapping approach parameterizes complex genus-zero meshes.
• Our approach merges topological structures rather than mapping surface properties.
• A curvature reduction criterion and a distortion measurement metric are developed.
• A global optimization adjusts the vertex distribution on spherical representations.
• A novel two-step feature alignment procedure aligns user-specified feature points.

We introduce an efficient approach to establish surface correspondences between genus-zero triangle meshes and animate a morph between them. We employ the concept of mesh simplification and refinement to progressively parameterize meshes using a novel kernel sampling algorithm. Our two-step feature alignment method optimizes the distribution of vertices in a parametric domain. A new mesh is generated after merging mesh topologies, and it represents the shapes of all input meshes and their transitions in-between. Our approach merges topological structures rather than mapping surface properties. Complex meshes with tens of thousands of vertices can be parameterized and merged in a few minutes. The advantages of our approach are demonstrated through 3D morphing applications. Comparing to existing approaches, our solution advances in performance while maintaining high-quality parameterization and morphing.

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