6,091 research outputs found
An exact general remeshing scheme applied to physically conservative voxelization
We present an exact general remeshing scheme to compute analytic integrals of
polynomial functions over the intersections between convex polyhedral cells of
old and new meshes. In physics applications this allows one to ensure global
mass, momentum, and energy conservation while applying higher-order polynomial
interpolation. We elaborate on applications of our algorithm arising in the
analysis of cosmological N-body data, computer graphics, and continuum
mechanics problems.
We focus on the particular case of remeshing tetrahedral cells onto a
Cartesian grid such that the volume integral of the polynomial density function
given on the input mesh is guaranteed to equal the corresponding integral over
the output mesh. We refer to this as "physically conservative voxelization".
At the core of our method is an algorithm for intersecting two convex
polyhedra by successively clipping one against the faces of the other. This
algorithm is an implementation of the ideas presented abstractly by Sugihara
(1994), who suggests using the planar graph representations of convex polyhedra
to ensure topological consistency of the output. This makes our implementation
robust to geometric degeneracy in the input. We employ a simplicial
decomposition to calculate moment integrals up to quadratic order over the
resulting intersection domain.
We also address practical issues arising in a software implementation,
including numerical stability in geometric calculations, management of
cancellation errors, and extension to two dimensions. In a comparison to recent
work, we show substantial performance gains. We provide a C implementation
intended to be a fast, accurate, and robust tool for geometric calculations on
polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3
A Parallel Rendering Algorithm for MIMD Architectures
Applications such as animation and scientific visualization demand high performance rendering of complex three dimensional scenes. To deliver the necessary rendering rates, highly parallel hardware architectures are required. The challenge is then to design algorithms and software which effectively use the hardware parallelism. A rendering algorithm targeted to distributed memory MIMD architectures is described. For maximum performance, the algorithm exploits both object-level and pixel-level parallelism. The behavior of the algorithm is examined both analytically and experimentally. Its performance for large numbers of processors is found to be limited primarily by communication overheads. An experimental implementation for the Intel iPSC/860 shows increasing performance from 1 to 128 processors across a wide range of scene complexities. It is shown that minimal modifications to the algorithm will adapt it for use on shared memory architectures as well
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