3,847 research outputs found
Spherical Sampling by Archimedes\u27 Theorem
In this paper we present a simple and efficient algorithm for generating uniformaly distributed samples on the unit sphere based on an Archimedes\u27 theorem. The implementation is straightforward and may be easily extended to include stratified sampling for variance reduction. Applications in image synthesis include solid angle measurement, irradiance computation, and rendering equation solution for geometrically complex environments
Area-preserving parameterizations for spherical ellipses
We present new methods for uniformly sampling the solid angle subtended by a
disk. To achieve this, we devise two novel area-preserving mappings from the
unit square to a spherical ellipse (i.e. the projection of the disk
onto the unit sphere). These mappings allow for low-variance stratified
sampling of direct illumination from disk-shaped light sources. We discuss how
to efficiently incorporate our methods into a production renderer and
demonstrate the quality of our maps, showing significantly lower variance than
previous work
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
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