561 research outputs found
Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
The typical goal of surface remeshing consists in finding a mesh that is (1)
geometrically faithful to the original geometry, (2) as coarse as possible to
obtain a low-complexity representation and (3) free of bad elements that would
hamper the desired application. In this paper, we design an algorithm to
address all three optimization goals simultaneously. The user specifies desired
bounds on approximation error {\delta}, minimal interior angle {\theta} and
maximum mesh complexity N (number of vertices). Since such a desired mesh might
not even exist, our optimization framework treats only the approximation error
bound {\delta} as a hard constraint and the other two criteria as optimization
goals. More specifically, we iteratively perform carefully prioritized local
operators, whenever they do not violate the approximation error bound and
improve the mesh otherwise. In this way our optimization framework greedily
searches for the coarsest mesh with minimal interior angle above {\theta} and
approximation error bounded by {\delta}. Fast runtime is enabled by a local
approximation error estimation, while implicit feature preservation is obtained
by specifically designed vertex relocation operators. Experiments show that our
approach delivers high-quality meshes with implicitly preserved features and
better balances between geometric fidelity, mesh complexity and element quality
than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization
and Computer Graphic
ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
Resolving numerically Vlasov-Poisson equations for initially cold systems can
be reduced to following the evolution of a three-dimensional sheet evolving in
six-dimensional phase-space. We describe a public parallel numerical algorithm
consisting in representing the phase-space sheet with a conforming,
self-adaptive simplicial tessellation of which the vertices follow the
Lagrangian equations of motion. The algorithm is implemented both in six- and
four-dimensional phase-space. Refinement of the tessellation mesh is performed
using the bisection method and a local representation of the phase-space sheet
at second order relying on additional tracers created when needed at runtime.
In order to preserve in the best way the Hamiltonian nature of the system,
refinement is anisotropic and constrained by measurements of local Poincar\'e
invariants. Resolution of Poisson equation is performed using the fast Fourier
method on a regular rectangular grid, similarly to particle in cells codes. To
compute the density projected onto this grid, the intersection of the
tessellation and the grid is calculated using the method of Franklin and
Kankanhalli (1993) generalised to linear order. As preliminary tests of the
code, we study in four dimensional phase-space the evolution of an initially
small patch in a chaotic potential and the cosmological collapse of a
fluctuation composed of two sinusoidal waves. We also perform a "warm" dark
matter simulation in six-dimensional phase-space that we use to check the
parallel scaling of the code.Comment: Code and illustration movies available at:
http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal
of Computational Physic
Hierarchical processing, editing and rendering of acquired geometry
La reprĂ©sentation des surfaces du monde rĂ©el dans la mĂ©moire dâune machine peut dĂ©sormais ĂȘtre obtenue automatiquement via divers pĂ©riphĂ©riques de capture tels que les scanners 3D. Ces nouvelles sources de donnĂ©es, prĂ©cises et rapides, amplifient de plusieurs ordres de grandeur la rĂ©solution des surfaces 3D, apportant un niveau de prĂ©cision Ă©levĂ© pour les applications nĂ©cessitant des modĂšles numĂ©riques de surfaces telles que la conception assistĂ©e par ordinateur, la simulation physique, la rĂ©alitĂ© virtuelle, lâimagerie mĂ©dicale, lâarchitecture, lâĂ©tude archĂ©ologique, les effets spĂ©ciaux, lâanimation ou bien encore les jeux video. Malheureusement, la richesse de la gĂ©omĂ©trie produite par ces mĂ©thodes induit une grande, voire gigantesque masse de donnĂ©es Ă traiter, nĂ©cessitant de nouvelles structures de donnĂ©es et de nouveaux algorithmes capables de passer Ă lâĂ©chelle dâobjets pouvant atteindre le milliard dâĂ©chantillons. Dans cette thĂšse, je propose des solutions performantes en temps et en espace aux problĂšmes de la modĂ©lisation, du traitement gĂ©omĂ©trique, de lâĂ©dition intĂ©ractive et de la visualisation de ces surfaces 3D complexes. La mĂ©thodologie adoptĂ©e pendant lâĂ©laboration transverse de ces nouveaux algorithmes est articulĂ©e autour de 4 Ă©lĂ©ments clĂ©s : une approche hiĂ©rarchique systĂ©matique, une rĂ©duction locale de la dimension des problĂšmes, un principe dâĂ©chantillonage-reconstruction et une indĂ©pendance Ă lâĂ©numĂ©ration explicite des relations topologiques aussi appelĂ©e approche basĂ©e-points. En pratique, ce manuscrit propose un certain nombre de contributions, parmi lesquelles : une nouvelle structure hiĂ©rarchique hybride de partitionnement, lâArbre Volume-Surface (VS-Tree) ainsi que de nouveaux algorithmes de simplification et de reconstruction ; un systĂšme dâĂ©dition intĂ©ractive de grands objets ; un noyau temps-rĂ©el de synthĂšse gĂ©omĂ©trique par raffinement et une structure multi-rĂ©solution offrant un rendu efficace de grands objets. Ces structures, algorithmes et systĂšmes forment une chaĂźne capable de traiter les objets en provenance du pipeline dâacquisition, quâils soient reprĂ©sentĂ©s par des nuages de points ou des maillages, possiblement non 2-variĂ©tĂ©s. Les solutions obtenues ont Ă©tĂ© appliquĂ©es avec succĂšs aux donnĂ©es issues des divers domaines dâapplication prĂ©citĂ©s.Digital representations of real-world surfaces can now be obtained automatically using various acquisition devices such as 3D scanners and stereo camera systems. These new fast and accurate data sources increase 3D surface resolution by several orders of magnitude, borrowing higher precision to applications which require digital surfaces. All major computer graphics applications can take benefit of this automatic modeling process, including: computer-aided design, physical simulation, virtual reality, medical imaging, architecture, archaeological study, special effects, computer animation and video games. Unfortunately, the richness of the geometry produced by these media comes at the price of a large, possibility gigantic, amount of data which requires new efficient data structures and algorithms offering scalability for processing such objects. This thesis proposes time and space efficient solutions for modeling, editing and rendering such complex surfaces, solving these problems with new algorithms sharing 4 fundamental elements: a systematic hierarchical approach, a local dimension reduction, a sampling-reconstruction paradigm and a pointbased basis. Basically, this manuscript proposes several contributions, including: a new hierarchical space subdivision structure, the Volume-Surface Tree, for geometry processing such as simplification and reconstruction; a streaming system featuring new algorithms for interactive editing of large objects, an appearancepreserving multiresolution structure for efficient rendering of large point-based surfaces, and a generic kernel for real-time geometry synthesis by refinement. These elements form a pipeline able to process acquired geometry, either represented by point clouds or non-manifold meshes. Effective results have been successfully obtained with data coming from the various applications mentioned
Simple quad domains for field aligned mesh parametrization
We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axis-aligned rectangular patches, which form an abstract base complex without T-junctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing
Geospatial phrase grounding and disambiguation
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 101-107).GeoCoder is a spatial reasoning system that converts natural language inputs into a set of precise spatial coordinates to display on a map. GeoCoder's spatial knowledge is represented in a set of ontologies. GeoCoder parses input phrases and adds location reference individuals to its ontology model. Relationships between location references are recognized based on mid-level structural patterns in the parsed phrase. GeoCoder grounds (or finds possible geometries for) location references in an iterative process, in which locations are grounded based on their relationships to previously grounded locations. GeoCoder improves upon previous systems by grounding and disambiguating at the phrase level, interpreting parses with rules that match mid level structure patterns, expressing disambiguation heuristics in ontologies, and improving scalability by separating grounding from reasoning about relationships.by Amy Michelle Slagle.M.Eng
Geometric, topological and semantic analysis of multi-building floor plan data
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2006.Includes bibliographical references (leaves 65-67).Generating a comprehensive model of a university campus or other large urban space is a challenging undertaking due to the size, geometric complexity, and levels of rich semantic information contained in inhabited environments. This thesis presents a practical approach to constructing topological models of large environments from labeled floor plan geometry. An exhaustive classification of adjacency types is provided for a university infrastructure including roads, walkways, green-space, and the detailed interior spaces of campus buildings. The system models geospatial features for over 160 buildings within the MIT campus, consisting of more than 800 individual floors, and approximately 36,000 spaces spanning indoor and outdoor terrain. The main motivation is to develop an intuitive, human-centered approach to navigation systems. An application is presented for generating efficient routes between locations on MIT's campus with coverage of both interior and exterior environments. A second application, the MIT WikiMap, aims to generate a more expressive record of the environment by drawing from the knowledge of its inhabitants. The WikiMap provides an interface for collaborative tagging of geographical locations on the MIT campus, designed for interfacing with users to collect semantic data.by Emily J Whiting.S.M
Lp Centroidal Voronoi Tesselation and its applications
International audienceThis paper introduces Lp -Centroidal Voronoi Tessellation (Lp -CVT), a generalization of CVT that minimizes a higher-order moment of the coordinates on the Voronoi cells. This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy). Lp -CVT is computed by a quasi-Newton optimization framework, based on closed-form derivations of the objective function and its gradient. The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field). Applications to anisotropic, quad-dominant surface remeshing and to hex-dominant volume meshing are presented. Unlike previous work, Lp -CVT captures sharp features and intersections without requiring any pre-tagging
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