908 research outputs found
Coding and Compression of Three Dimensional Meshes by Planes
The present paper suggests a new approach for geometric representation of 3D
spatial models and provides a new compression algorithm for 3D meshes, which is
based on mathematical theory of convex geometry. In our approach we represent a
3D convex polyhedron by means of planes, containing only its faces. This allows
not to consider topological aspects of the problem (connectivity information
among vertices and edges) since by means of the planes we construct the
polyhedron uniquely. Due to the fact that the topological data is ignored this
representation provides high degree of compression. Also planes based
representation provides a compression of geometrical data because most of the
faces of the polyhedron are not triangles but polygons with more than three
vertices.Comment: 10 pages, 7 figure
Discrete curvature approximations and segmentation of polyhedral surfaces
The segmentation of digitized data to divide a free form surface into patches is one of the key steps required to perform a reverse engineering process of an object. To this end, discrete curvature approximations are introduced as the basis of a segmentation process that lead to a decomposition of digitized data into areas that will help the construction of parametric surface patches. The approach proposed relies on the use of a polyhedral representation of the object built from the digitized data input. Then, it is shown how noise reduction, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases to provide a geometry that highlights useful characteristics for the segmentation process. The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedron produced during the preparation phases. The segmentation process proposed involves two phases: the identification of characteristic polygonal lines and the identification of polyhedral areas useful for a patch construction process. Discrete curvature criteria are adapted to each phase and the concept of invariant evaluation of curvatures is introduced to generate criteria that are constant over equivalent meshes. A description of the segmentation procedure is provided together with examples of results for free form object surfaces
Identifying and remeshing contact interfaces in a polyhedral assembly for digital mock-up applications
Polyhedral models are widely used for applications such as manufacturing, digital simulation or visualization. They are discrete models; easy to store, to manipulate, allowing levels of resolution for visualization. They can be easily exchanged between CAD systems without loss of data. Previous works (Comput Aided Des 29(4):287â298, 1997, Comput Graphics 22(5):565â585, 1998) have focused on simplification process applied to polyhedral part models. The goal of the proposed approach is to extend these processes to polyhedral assembly models, describing the digital mock-up of a future manufacturing product. To apply simplification techniques or other processes on polyhedral assemblies, contact surfaces between interacting objects have to be identified and specific constraints must be applied for processing. The approach proposed allows checking and maintaining a global consistency of the assembly model to ensure the reliability of the future processes. Thus, contacts between objects are detected using an approach that works for a static configuration of the assembly. Finally, a precise detection of the faces involved in each contact area is made and the resulting input domains identified are processed using a local Frontal Delaunay re-meshing technique to produce an identical tessellation on both objects involved in the processed contact. The quality of the triangulation produced is also checked
Optimal Dual Schemes for Adaptive Grid Based Hexmeshing
Hexahedral meshes are an ubiquitous domain for the numerical resolution of
partial differential equations. Computing a pure hexahedral mesh from an
adaptively refined grid is a prominent approach to automatic hexmeshing, and
requires the ability to restore the all hex property around the hanging nodes
that arise at the interface between cells having different size. The most
advanced tools to accomplish this task are based on mesh dualization. These
approaches use topological schemes to regularize the valence of inner vertices
and edges, such that dualizing the grid yields a pure hexahedral mesh. In this
paper we study in detail the dual approach, and propose four main contributions
to it: (i) we enumerate all the possible transitions that dual methods must be
able to handle, showing that prior schemes do not natively cover all of them;
(ii) we show that schemes are internally asymmetric, therefore not only their
implementation is ambiguous, but different implementation choices lead to
hexahedral meshes with different singular structure; (iii) we explore the
combinatorial space of dual schemes, selecting the minimum set that covers all
the possible configurations and also yields the simplest singular structure in
the output hexmesh; (iv) we enlarge the class of adaptive grids that can be
transformed into pure hexahedral meshes, relaxing one of the tight requirements
imposed by previous approaches, and ultimately permitting to obtain much
coarser meshes for same geometric accuracy. Last but not least, for the first
time we make grid-based hexmeshing truly reproducible, releasing our code and
also revealing a conspicuous amount of technical details that were always
overlooked in previous literature, creating an entry barrier that was hard to
overcome for practitioners in the field
Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh
This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC
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