22 research outputs found
Acute Triangulations of the Cuboctahedral Surface
In this paper we prove that the surface of the cuboctahedron can be
triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore,
we show that both bounds are the best possible.Comment: 16 pages, 8 figures, presented on CGGA201
JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere
An algorithm for the generation of non-uniform, locally-orthogonal staggered
unstructured spheroidal grids is described. This technique is designed to
generate very high-quality staggered Voronoi/Delaunay meshes appropriate for
general circulation modelling on the sphere, including applications to
atmospheric simulation, ocean-modelling and numerical weather prediction. Using
a recently developed Frontal-Delaunay refinement technique, a method for the
construction of high-quality unstructured spheroidal Delaunay triangulations is
introduced. A locally-orthogonal polygonal grid, derived from the associated
Voronoi diagram, is computed as the staggered dual. It is shown that use of the
Frontal-Delaunay refinement technique allows for the generation of very
high-quality unstructured triangulations, satisfying a-priori bounds on element
size and shape. Grid-quality is further improved through the application of
hill-climbing type optimisation techniques. Overall, the algorithm is shown to
produce grids with very high element quality and smooth grading
characteristics, while imposing relatively low computational expense. A
selection of uniform and non-uniform spheroidal grids appropriate for
high-resolution, multi-scale general circulation modelling are presented. These
grids are shown to satisfy the geometric constraints associated with
contemporary unstructured C-grid type finite-volume models, including the Model
for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing
functions to generate smoothly graded, non-uniform grids for multi-resolution
type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally
orthogonal staggered unstructured grid generation for general circulation
modelling on the sphere, Geosci. Model Dev., 10, 2117-2140,
https://doi.org/10.5194/gmd-10-2117-2017, 201
Survey of two-dimensional acute triangulations
AbstractWe give a brief introduction to the topic of two-dimensional acute triangulations, mention results on related areas, survey existing achievements–with emphasis on recent activity–and list related open problems, both concrete and conceptual
On a proper acute triangulation of a polyhedral surface
AbstractLet Σ be a polyhedral surface in R3 with n edges. Let L be the length of the longest edge in Σ, δ be the minimum value of the geodesic distance from a vertex to an edge that is not incident to the vertex, and θ be the measure of the smallest face angle in Σ. We prove that Σ can be triangulated into at most CLn/(δθ) planar and rectilinear acute triangles, where C is an absolute constant
A Dihedral Acute Triangulation of the Cube
It is shown that there exists a dihedral acute triangulation of the
three-dimensional cube. The method of constructing the acute triangulation is
described, and symmetries of the triangulation are discussed.Comment: Minor edits for journal version. Added some material to the
introductio
無限グラフの熱核,グリーン核の大域解析
平成13年度-平成15年度科学研究費補助金(基盤研究(B)(2))研究成果報告書,課題番号.1344005