5,119 research outputs found
Geometric Rounding and Feature Separation in Meshes
Geometric rounding of a mesh is the task of approximating its vertex
coordinates by floating point numbers while preserving mesh structure.
Geometric rounding allows algorithms of computational geometry to interface
with numerical algorithms. We present a practical geometric rounding algorithm
for 3D triangle meshes that preserves the topology of the mesh. The basis of
the algorithm is a novel strategy: 1) modify the mesh to achieve a feature
separation that prevents topology changes when the coordinates change by the
rounding unit; and 2) round each vertex coordinate to the closest floating
point number. Feature separation is also useful on its own, for example for
satisfying minimum separation rules in CAD models. We demonstrate a robust,
accurate implementation
Rounding meshes in 3D
International audienceLet be a set of polygons in , each of constant complexity and with pairwise disjoint interiors. We propose a rounding algorithm that maps to a simplicial complex whose vertices have integer coordinates. Every face of is mapped to a set of faces (or edges or vertices) of and the mapping from to can be done through a continuous motion of the faces such that (i) the Hausdorff distance between a face and its image during the motion is at most 3/2 and (ii) if two points become equal during the motion, they remain equal through the rest of the motion. In the worst case the size of is and the time complexity of the algorithm is but, under reasonable assumptions, these complexities decrease to and . Furthermore, these complexities are likely not tight and we expect, in practice on non-pathological data, space and time complexities
Partial Differential Equations for 3D Data Compression and Reconstruction
This paper describes a PDE-based method for 3D reconstruction of surface patches. The PDE method is exploited using data obtained from standard 3D scanners. First the original surface data are intersected by a number of cutting planes whose intersection points on the mesh are represented by Fourier transforms in each plane. Information on the number of vertices and scale of the surface are defined and, together, these efficiently define the compressed data. The PDE method is then applied at the reconstruction stage by defining PDE surface patches between the cutting planes
Molecular dynamics in arbitrary geometries : parallel evaluation of pair forces
A new algorithm for calculating intermolecular pair forces in molecular dynamics (MD) simulations on a distributed parallel computer is presented. The arbitrary interacting cells algorithm (AICA) is designed to operate on geometrical domains defined by an unstructured, arbitrary polyhedral mesh that has been spatially decomposed into irregular portions for parallelisation. It is intended for nano scale fluid mechanics simulation by MD in complex geometries, and to provide the MD component of a hybrid MD/continuum simulation. The spatial relationship of the cells of the mesh is calculated at the start of the simulation and only the molecules contained in cells that have part of their surface closer than the cut-off radius of the intermolecular pair potential are required to interact. AICA has been implemented in the open source C++ code OpenFOAM, and its accuracy has been indirectly verified against a published MD code. The same system simulated in serial and in parallel on 12 and 32 processors gives the same results. Performance tests show that there is an optimal number of cells in a mesh for maximum speed of calculating intermolecular forces, and that having a large number of empty cells in the mesh does not add a significant computational overhead
Quality Measurements on Quantised Meshes
In computer graphics, triangle mesh has emerged as the ubiquitous shape rep- resentation for 3D modelling and visualisation applications. Triangle meshes, often undergo compression by specialised algorithms for the purposes of storage and trans- mission. During the compression processes, the coordinates of the vertices of the triangle meshes are quantised using fixed-point arithmetic. Potentially, that can alter the visual quality of the 3D model. Indeed, if the number of bits per vertex coordinate is too low, the mesh will be deemed by the user as visually too coarse as quantisation artifacts will become perceptible. Therefore, there is the need for the development of quality metrics that will enable us to predict the visual appearance of a triangle mesh at a given level of vertex coordinate quantisation
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