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Bijective and Coarse High-Order Tetrahedral Meshes

Coarse yet accurate geometry with high order elements. We introduce a robust and automatic approach to convert triangle meshes to coarse high-order tetmeshes. We bound geometric error, ensure valid elements, and preserve features precisely. We can also transfer attributes and solutions between input and output boundary.

Bijective Projection in a Shell

Adjusting the common used orthogonal projection between discrete surfaces a reliable tool, by constructing a shell to restrict the domain. The bijective association between meshes in the shell provide a robust way to construct high quality computational proxy.

A Low-Parametric Rhombic Microstructure Family for Irregular Lattices

Microstructure family defined on rhombic meshes, with better approximation on (planar) irregular geometric domains. A smoother material-to-geometry map and fabricated results.

Progressive Embedding

A numerically stable, and provably correct replacement for Tutte's embedding. Avoid exponential area change and serve as a robust building block for locally injective maps with hard constraints, in quad meshing.

Simplicial Complex Augmentation Framework for Bijective Maps

A robust and efficient way optimize the distortion of bijective maps. Applicable to 2D (bijective surface parameterization) as well as 3D (intersection free deformation) problems.