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