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16
ConstantTime Neighbor Finding in Hierarchical Tetrahedral Meshes
 IN PROCEEDINGS INTERNATIONAL CONFERENCE ON SHAPE MODELING
, 2001
"... Techniques are presented for moving between adjacent tetrahedra in a tetrahedral mesh. The tetrahedra result from a recursive decomposition of a cube into six initial congruent tetrahedra. A new technique is presented for labelingthe triangular faces. The labeling enables the implementation of a bin ..."
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Cited by 15 (12 self)
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Techniques are presented for moving between adjacent tetrahedra in a tetrahedral mesh. The tetrahedra result from a recursive decomposition of a cube into six initial congruent tetrahedra. A new technique is presented for labelingthe triangular faces. The labeling enables the implementation of a binarylike decomposition of each tetrahedron which is represented using a pointerless representation. Outlines of algorithms are given for traversing adjacent triangular faces of equal size in constant time.
Distance Oracles for Spatial Networks
"... Abstract — The popularity of locationbased services and the need to do realtime processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge is that these operations involve the computation o ..."
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Cited by 10 (4 self)
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Abstract — The popularity of locationbased services and the need to do realtime processing on them has led to an interest in performing queries on transportation networks, such as finding shortest paths and finding nearest neighbors. The challenge is that these operations involve the computation of distance along a spatial network rather than “as the crow flies. ” In many applications an estimate of the distance is sufficient, which can be achieved by use of an oracle. An approximate distance oracle is proposed for spatial networks that exploits the coherence between the spatial position of vertices and the network distance between them. Using this observation, a distance oracle is introduced that is able to obtain the εapproximate network distance between two vertices of the spatial network. The network distance between every pair of vertices in the spatial network is efficiently represented by adapting the wellseparated pair technique to spatial networks. Initially, use is made of an εapproximate distance oracle of size O ( n εd) that is capable of retrieving the approximate network distance in O(logn) time using a Btree. The retrieval time can be theoretically reduced to O(1) time by proposing another εapproximate distance oracle of size O ( nlogn εd) that uses a hash table. Experimental results indicate that the proposed technique is scalable and can be applied to sufficiently large road networks. A 10%approximate oracle (ε = 0.1) on a large network yielded an average error of 0.9 % with 90 % of the answers making an error of 2 % or less and an average retrieval time of 68µ seconds. Finally, a strategy for the integration of the distance oracle into any relational database system as well as using it to perform a variety of spatial queries such as region search, knearest neighbor search, and spatial joins on spatial networks is discussed. I.
ConstantTime Navigation in FourDimensional Nested Simplicial Meshes
, 2004
"... We consider a recursive decomposition of a fourdimensional hypercube into a hierarchy of nested 4dimensional simplexes, that we call pentatopes. The paper presents an algorithm for finding the neighbors of a pentatope along its five tetrahedral faces in constant time. To this aim, we develop a lab ..."
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Cited by 4 (4 self)
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We consider a recursive decomposition of a fourdimensional hypercube into a hierarchy of nested 4dimensional simplexes, that we call pentatopes. The paper presents an algorithm for finding the neighbors of a pentatope along its five tetrahedral faces in constant time. To this aim, we develop a labeling technique for nested pentatopes that enables their identification by using location codes. The constanttime behavior is achieved through bit manipulation operations, thus avoiding traversing the simplicial hierarchy via pointer following. We discuss an application of this representation to multiresolution representations of fourdimensional scalar fields. Extracting adaptive continuous approximations of the scalar field from such a model requires generating conforming meshes, i.e., meshes in which the pentatopes match along their tetrahedral faces. Our neighbor finding algorithm enables computing faceadjacent pentatopes efficiently.
Parallel Electronic Prototyping of Physical Objects
, 1993
"... The electronic prototyping of a physical object starts with the user completely specifying the problem on an assumed initial geometry, followed by the simulation of the physics and the satisfiability of some a priori defined design objectives. The process might be repeated several times until the op ..."
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Cited by 3 (2 self)
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The electronic prototyping of a physical object starts with the user completely specifying the problem on an assumed initial geometry, followed by the simulation of the physics and the satisfiability of some a priori defined design objectives. The process might be repeated several times until the optimal design is obtained. This paper addresses the various issues involved in the parallel implementation of the above design process. The methodology adopted is applied on the continuous and discrete geometric data associated with the physical object and the simulation of its physics respectively. In this paper we present the formulation of the parallel electronic prototyping process for some class of structural engineering problems and the parallel algorithms developed and implemented on the nCUBE II machine for the realization of adaptive mesh generation, mesh splitting and shape optimization together with their measured performance.
A Parallel Radiosity System for Large Data Sets
 In ACM International Conference on Computer Graphics, Pilzen
, 1995
"... this paper we will explore this definition and define a practical working system. Most radiosity methods use a discretisation approach, in which the environment is divided into a finite set of patches. This approach was initially used in thermal engineering and applied to diffuse reflection by Goral ..."
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Cited by 3 (0 self)
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this paper we will explore this definition and define a practical working system. Most radiosity methods use a discretisation approach, in which the environment is divided into a finite set of patches. This approach was initially used in thermal engineering and applied to diffuse reflection by Goral et al [6]. The radiance function of each surface is approximated by the set of patches attributed to that surface. More recent methods have used polynomials [15] and wavelet models [7] to represent the radiance functions over surfaces. The CARM system is patchbased, with each patch holding a mesh of sample points. Although discretised systems have a number of shortcomings (such as aliasing) they can accurately represent very abrupt changes in the radiance function. The input geometry to the system is triangulated; this allows all object primitives and also all complex objects to be represented by meshes. The input triangles are then automatically tested for D0 discontinuities (i.e. tests for intersecting or abutting triangles) and also for excessive size, and automatically subdivided if required. The triangles left after such subdivision correspond to a traditional handcrafted radiosity patches. Radiance values (or flux values) are stored at sample points, which are located at patch vertices, and also within the patch. These sample points are stored in a mesh, which can be triangulated and then interpolated to reconstruct the radiance function. By adaptive subdivision of the mesh the system allows sample points to be added as the solution progresses, When new sample points are added the mesh is retriangulated; these triangles are analogous to traditional elements. Subdivision is controlled by examining the gradient and difference between neighbouring sample points; if e...
Breaking the Fog: Defining and Orienting Surfaces in Complex Point Cloud Datasets
"... Abstract — We present a vertex clustering algorithm for the purposes of surface determination and normal estimation that can help provide detailed visualizations of complex point cloud datasets. The proposed method combines a novel bucket and layer spatial partitioning scheme, along with an iterativ ..."
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Cited by 2 (0 self)
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Abstract — We present a vertex clustering algorithm for the purposes of surface determination and normal estimation that can help provide detailed visualizations of complex point cloud datasets. The proposed method combines a novel bucket and layer spatial partitioning scheme, along with an iterative process for surface subdivision based on the optimization of qualityoffit statistics. Our approach can efficiently decompose and approximate a dataset through the local classification and fitting of surface regions. The algorithm uses a standard least squares approach combined with Delaunaybased triangulation for developing these approximated surfaces. To demonstrate the effectiveness of our approach, we execute the algorithm on several realworld datasets scanned from complex environments. We perform an analysis of the various techniques presented and provide a comparison of our approach with the standard knearest neighbors method commonly used for solving this problem. Through this performance analysis we show that as the complexity of the datasets increase, the performance and accuracy of our proposed approach continues to function at an effective level. Index Terms—Vertex clustering, surface determination, normal estimation, layered surfaces, uncertain environments. 1
Automatic Assembly Feature Recognition and Disassembly Sequence Generation
, 2001
"... This thesis is concerned not with geometric features on a single component but rather with those that arise from the spatial adjacency of two, or more, components in an assembly. From a review of the literature on the nature and use of assembly features, it is concluded that the majority of assembly ..."
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Cited by 1 (0 self)
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This thesis is concerned not with geometric features on a single component but rather with those that arise from the spatial adjacency of two, or more, components in an assembly. From a review of the literature on the nature and use of assembly features, it is concluded that the majority of assembly features involve sets of spatially adjacent faces. Three principle types of adjacency relationships proposed in CHAPTER 3.1 are identified and an algorithm is presented for identifying assembly features which arise from "external spatial", "internal spatial" and "contact" face adjacency relationships (known as esadjacency , isadjacency and cadjacency respectively).
A Sorting Approach to Indexing Spatial Data
, 2008
"... Spatial data is distinguished from conventional data by having extent. Therefore, spatial queries involve both the objects and the space that they occupy. The handling of queries that involve spatial data is facilitated by building an index on the data. The traditional role of the index is to sort t ..."
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Cited by 1 (1 self)
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Spatial data is distinguished from conventional data by having extent. Therefore, spatial queries involve both the objects and the space that they occupy. The handling of queries that involve spatial data is facilitated by building an index on the data. The traditional role of the index is to sort the data, which means that it orders the data. However, since generally no ordering exists in dimensions greater than 1 without a transformation of the data to one dimension, the role of the sort process is one of differentiating between the data and what is usually done is to sort the spatial objects with respect to the space that they occupy. The resulting ordering is usually implicit rather than explicit so that the data need not be resorted (i.e., the index need not be rebuilt) when the queries change (e.g., the query reference objects). The index is said to order the space and the characteristics of such indexes are explored further.
Octree Based Recognition of Assembly Features
 CDROM Proceedings of the ASME 2000 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 1013 September, ASME
, 2000
"... This paper reviews the nature and use of assembly features. One of the conclusions drawn from this survey is that the majority of assembly features involve sets of spatially adjacent faces. Two principle types of adjacency relationships are identified and an algorithm is presented for identifying as ..."
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Cited by 1 (0 self)
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This paper reviews the nature and use of assembly features. One of the conclusions drawn from this survey is that the majority of assembly features involve sets of spatially adjacent faces. Two principle types of adjacency relationships are identified and an algorithm is presented for identifying assembly features, these are features which arise from these spatial and contact face adjacency relationships (known as s and cadjacency respectively). The algorithm uses an octree representation of a Brep model to support the geometric reasoning required to locate assembly features on disjoint bodies. Once all the adjacent faces which form features have been located, they are used to partition the original faces of the assembly into adjacent and nonadjacent portions. The resulting system can locate and partition spatially adjacent faces in a wide range of situations and at different resolutions. By way of illustration, the algorithm is applied to a trial component. Keywords: Octree representation, Assembly features, Feature recognition, Geometric modelling, Assembly planning. 1
Walking the Data Cube: An Immersed Virtual Environment for Visualising Data Mining Results
"... In an attempt to stay competitive, organisations are looking to use data obtained through customer transactions to make strategic business decisions. Visualisation tools are an excellent aid for these types of applications. Due to the visual nature of humans, visual abstractions are usually easier t ..."
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In an attempt to stay competitive, organisations are looking to use data obtained through customer transactions to make strategic business decisions. Visualisation tools are an excellent aid for these types of applications. Due to the visual nature of humans, visual abstractions are usually easier to understand than charts and numbers. Most visualisation tools are limited in use due to the 2D nature of I/O devices. A system was developed for visualising data mining results in an immersed virtual reality environment in an attempt to overcome some of these limitations. This system will allow users to navigate through an abstraction of data in a virtual environment and perform various operations to inspect this data.