Isosurface stuffing

Abstract

0 160 180 140 20 40 60 80 100 120 158.2 15.2 Figure 1: A 134,400-tetrahedron mesh produced by isosurface stuffing, with cutaway views. At the lower right is a histogram of tetrahedron dihedral angles in 2 • intervals; multiply the heights of the red bars by 20. (Angles of 45 • , 60 • , and 90 • occur with high frequency.) The extreme dihedral angles are 15.2 • and 158.2 • . This mesh took 55 seconds to generate on a Mac Pro with a 2.66 GHz Intel Xeon processor, but the mesh generation time was only 642 milliseconds; nearly all the time was spent in the isosurface evaluation code. AbstractThe isosurface stuffing algorithm fills an isosurface with a uniformly sized tetrahedral mesh whose dihedral angles are bounded between 10.7 • and 164.8 • , or (with a change in parameters) between 8.9 • and 158.8 • . The algorithm is whip fast, numerically robust, and easy to implement because, like Marching Cubes, it generates tetrahedra from a small set of precomputed stencils. A variant of the algorithm creates a mesh with internal grading: on the boundary, where high resolution is generally desired, the elements are fine and uniformly sized, and in the interior they may be coarser and vary in size. This combination of features makes isosurface stuffing a powerful tool for dynamic fluid simulation, large-deformation mechanics, and applications that require interactive remeshing or use objects defined by smooth implicit surfaces. It is the first algorithm that rigorously guarantees the suitability of tetrahedra for finite element methods in domains whose shapes are substantially more challenging than boxes. Our angle bounds are guaranteed by a computer-assisted proof. If the isosurface is a smooth 2-manifold with bounded curvature, and the tetrahedra are sufficiently small, then the boundary of the mesh is guaranteed to be a geometrically and topologically accurate approximation of the isosurface.

Ultraliser: a framework for creating multiscale, high-fidelity and geometrically realistic 3D models for in silico neuroscience

“…U ltraliser has native support to import and export polygonal surface meshes with multiple file formats including those that are commonly used for visual analytics with Blender 86 (blender.org) or MeshLab 87 (meshlab.net), such as OBJ and PLY, and also those required for 3D printing, molecular simulations and conversion into tetrahedral meshes by tetrahedralization applications 38,39 such as STL and OFF file formats. The meshes downloaded from the MICrONS program 48 are stored in H5 files based on the HDF5 88 library.…”

“…S1b, S2 ). For instance, the generation of a volumetric mesh from a surface input —using TetGen 38 , QuarTet 39 , GMsh 40 or CGAL 41 — requires the surface mesh to be watertight. TetWild can tetrahedralize non-watertight meshes, but it has limited performance 29 and fails to handle complex biological models with realistic geometries 42 .…”

Metaball skinning of synthetic astroglial morphologies into realistic mesh models for in silico simulations and visual analytics

“…Implementing a tetrahedral mesh generator is beyond the scope of this work, and therefore we have relied on a convenient solution to synthesize tetrahedral astrocytic models to complement our pipeline. Various open source implementations and Application Programming Interfaces (APIs) are already available, for example Tet Gen ( Si and TetGen, 2006 ), CGAL ( Boissonnat et al , 2000 ) and Quartet ( Labelle and Shewchuk, 2007 ). For convenience, we have extended the Quartet implementation and integrated it into our pipeline to create tetrahedral meshes that are stored in the G Mesh file format ( Geuzaine and Remacle, 2009 ).…”

Tetrahedral meshing in the wild

“…Grid Methods. An alternative approach is the use of a background grid [Baker et al 1988;Bern et al 1994;Bridson and Doran 2014;Bronson et al 2013;Doran et al 2013;Labelle and Shewchuk 2007;Molino et al 2003;Yerry and Shephard 1983]: these algorithms start by filling the entire bounding box of the input with a regular lattice or with a hierarchical space partitioning, optionally intersect the background mesh with the input surface, and then discard the elements outside of the input. These methods are simpler and more robust than Delaunay methods, but still struggle with imperfect input geometry, and create high-quality elements only in the interior of the mesh, where the background mesh is preserved exactly.…”