Adaptive and Unstructured Mesh Cleaving.

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoids this conflict by extracting the boundary conforming constraint into a secondary step. We first build a background mesh having a desired set of tetrahedral properties, and then use a generalized stenciling method to divide, or "cleave", these elements to get a set of conforming tetrahedra, while limiting the impacts cleaving has on element quality. In developing this new framework, we make several technical contributions including a new method for building graded tetrahedral meshes as well as a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes.

Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality.

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

Particle systems for adaptive, isotropic meshing of CAD models.

We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain.