Fast as-isometric-as-possible shape interpolation

• We propose a 3D as-isometric-as-possible shape interpolation method.
• We efficiently address the AIAP optimization using a block-coordinate descent scheme.
• A propagation-based initialization method is proposed via connection maps.
• Our initialization can easily be transplanted to other shape interpolation methods.
• Our method outperforms state-of-the-art interpolation methods in efficiency or quality.

Shape interpolation, as a bridge communicating static geometries and dynamic shape sequences, is a fundamental operation in digital geometry processing and computer animation. We propose a fast as-isometric-as-possible (AIAP) 3D mesh interpolation approach which casts the shape interpolation problem to finding an AIAP motion trajectory from the start shape to the end shape. This leads to a nonlinear optimization problem with all intermediate shapes as unknowns. The block-coordinate descent method is then employed to iteratively solve the optimization. In each iteration, we need to solve two linear equations whose dimensionality can further be reduced based on a decoupling strategy. Connection maps between orthogonal frames of adjacent edges are further introduced for producing an initial shape sequence in order to address the large-scale deformation problem. A propagation–optimization strategy is then presented to quickly reconstruct the orthogonal frames of all edges from connection maps as well as the orthogonal frame of a specified edge. Refinement of edge quality is available in our method due to the AIAP iterative procedure. In the end, a shape manipulation framework is established for shape sequence transfer and shape sequence editing.

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