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16
SingleStrip Triangulation of Manifolds with Arbitrary Topology
, 2004
"... Triangle strips have been widely used for efficient rendering. It is NPcomplete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few long strips. In this paper, we present a new algorithm for cre ..."
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Cited by 17 (5 self)
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Triangle strips have been widely used for efficient rendering. It is NPcomplete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few long strips. In this paper, we present a new algorithm for creating a single triangle loop or strip from a triangulated model. Our method applies a dual graph matching algorithm to partition the mesh into cycles, and then merges pairs of cycles by splitting adjacent triangles when necessary. New vertices are introduced at midpoints of edges and the new triangles thus formed are coplanar with their parent triangles, hence the visual fidelity of the geometry is not changed. We prove that the increase in the number of triangles due to this splitting is 50 % in the worst case, however for all models we tested the increase was less than 2%. We also prove tight bounds on the number of triangles needed for a singlestrip representation of a model with holes on its boundary. Our strips can be used not only for efficient rendering, but also for other applications including the generation of space filling curves on a manifold of any arbitrary topology.
On the Quality of Partitions based on SpaceFilling Curves
, 2002
"... This paper presents bounds on the quality of partitions induced by spacefilling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times ..."
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Cited by 8 (1 self)
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This paper presents bounds on the quality of partitions induced by spacefilling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 3 times larger than the optimal in average case.
Blockstructured adaptive grids on the sphere: advection experiments
, 2006
"... A spherical 2D adaptive mesh refinement (AMR) technique is applied to the socalled Lin–Rood advection algorithm, which is built upon a conservative and oscillationfree finitevolume discretization in flux form. The AMR design is based on two modules: a blockstructured data layout and a spherical ..."
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Cited by 8 (3 self)
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A spherical 2D adaptive mesh refinement (AMR) technique is applied to the socalled Lin–Rood advection algorithm, which is built upon a conservative and oscillationfree finitevolume discretization in flux form. The AMR design is based on two modules: a blockstructured data layout and a spherical AMR grid library for parallel computer architectures. The latter defines and manages the adaptive blocks in spherical geometry, provides user interfaces for interpolation routines, and supports the communication and loadbalancing aspects for parallel applications. The adaptive grid simulations are guided by userdefined adaptation criteria. Both statically and dynamically adaptive setups that start from a regular blockstructured latitude–longitude grid are supported. All blocks are logically rectangular, selfsimilar, and independent data units that are split into four in the event of refinement requests, thereby doubling the horizontal resolution. Grid coarsenings reverse this refinement principle. Refinement and coarsening levels are constrained so that there is a uniform 2:1 mesh ratio at all fine–coarsegrid interfaces. The adaptive advection model is tested using three standard advection tests with increasing complexity. These include the transport of a cosine bell around the sphere, the advection of a slotted cylinder, and a smooth deformational flow that describes the rollup of two vortices. The latter two examples exhibit very sharp edges and gradients that
Inverse Spacefilling Curve Partitioning of a Global Ocean Model
 IEEE International Parallel & Distributed Processing Symposium, 2630 March 2007, pp 110 350 Oakmead Pkwy, Sunnyvale, CA 94085 Tel: 4089703400 • Fax: 4089703403 www.hpcadvisorycouncil.com © Copyright 2010. HPC Advisory Council. All rights reserved
"... In this paper, we describe how inverse spacefilling curve partitioning is used to increase the simulation rate of a global ocean model. Spacefilling curve partitioning allows for the elimination of load imbalance in the computational grid due to land points. Improved load balance combined with cod ..."
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Cited by 3 (1 self)
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In this paper, we describe how inverse spacefilling curve partitioning is used to increase the simulation rate of a global ocean model. Spacefilling curve partitioning allows for the elimination of load imbalance in the computational grid due to land points. Improved load balance combined with code modifications within the conjugate gradient solver significantly increase the simulation rate of the Parallel Ocean Program at high resolution. The simulation rate for a high resolution model nearly doubled from 4.0 to 7.9 simulated years per day on 28,972 IBM Blue Gene/L processors. We also demonstrate that our techniques increase the simulation rate on 7545 Cray XT3 processors from 6.3 to 8.1 simulated years per day. Our results demonstrate how minor code modifications can have significant impact on resulting performance for very large processor counts. 1
Average Case Quality of Partitions Induced by the Lebesgue Indexing
, 2001
"... This paper presents the quality of partitions induced by the Lebesgue curve in average case. The surface that surrounds an arbitrary index range is compared with the optimal partition in the grid, i. e. the square. The upper bound on the surface is asymptotically 3 times the optimal size. ..."
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Cited by 2 (2 self)
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This paper presents the quality of partitions induced by the Lebesgue curve in average case. The surface that surrounds an arbitrary index range is compared with the optimal partition in the grid, i. e. the square. The upper bound on the surface is asymptotically 3 times the optimal size.
On the use of space filling curves for parallel anisotropic mesh adaptation, in "18th International Meshing Roundtable
"... Summary. Efficiently parallelizing a whole set of meshing tools, as required by an automated mesh adaptation loop, relies strongly on data localization to avoid memory access contention. In this regard, renumbering mesh items through a space filling curve (SFC), like Hilbert or Peano, is of great he ..."
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Summary. Efficiently parallelizing a whole set of meshing tools, as required by an automated mesh adaptation loop, relies strongly on data localization to avoid memory access contention. In this regard, renumbering mesh items through a space filling curve (SFC), like Hilbert or Peano, is of great help and proved to be quite versatile. This paper briefly introduces the Hilbert SFC renumbering technique and illustrates its use with two different approaches to parallelization: an outofcore method and a sharedmemory multithreaded algorithm. Key words: Space filling curves, sharedmemory multithreaded parallelization, outofcore parallelization, anisotropic mesh adaptation, mesh partition.
Definition of a New Circular SpaceFilling Curve  βΩIndexing
"... This technical report presents the definition of a circular Hilbertlike spacefilling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert, Lebesgue, and HInde ..."
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This technical report presents the definition of a circular Hilbertlike spacefilling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert, Lebesgue, and HIndexing. We evaluated partitions induced by the indexing schemes and uses the diameter and the surface as measures. For both we present worst case and average case results.
Multilevel optimization by spacefilling curves in adaptive atmospheric modeling
"... Adaptive atmospheric modeling is a relatively young discipline in the wide area of atmospheric sciences. Many obstacles – mainly of technological character – hindered the introduction of adaptive modeling techniques into atmospheric simulation software. In recent years, however, a number of approa ..."
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Adaptive atmospheric modeling is a relatively young discipline in the wide area of atmospheric sciences. Many obstacles – mainly of technological character – hindered the introduction of adaptive modeling techniques into atmospheric simulation software. In recent years, however, a number of approaches has shown up. One of the main reasons for the recent success is the introduction of sophisticated optimization on all levels. In this work spacefilling curves are used on several levels of algorithmic abstraction in order to optimize an atmospheric modeling tool. For dynamic load balancing or irregular meshes which rapidly change during the computation, spacefilling curve based partitioning proves to be beneficial. Furthermore, spacefilling curve induced indexing can help to reorder the unknowns such that data locality is maintained. Finally, the reordering leads to better behavior of ILU based preconditioned system solvers. These techniques have been used in PLASMA, a parallel adaptive atmospheric model for global studies of climate variability. PLASMA utilizes the grid generation and management tool amatos with built in spacefilling curve support. 1