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35
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 334 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
BOTTOMUP CONSTRUCTION AND 2:1 BALANCE REFINEMENT OF LINEAR OCTREES IN PARALLEL ∗
"... Abstract. In this article, we propose new parallel algorithms for the construction and 2:1 balance refinement of large linear octrees on distributed memory machines. Such octrees are used in many problems in computational science and engineering, e.g., object representation, image analysis, unstruct ..."
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Cited by 34 (10 self)
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Abstract. In this article, we propose new parallel algorithms for the construction and 2:1 balance refinement of large linear octrees on distributed memory machines. Such octrees are used in many problems in computational science and engineering, e.g., object representation, image analysis, unstructured meshing, finite elements, adaptive mesh refinement and Nbody simulations. Fixedsize scalability and isogranular analysis of the algorithms, using an MPIbased parallel implementation, was performed on a variety of input data and demonstrated good scalability for different processor counts (1 to 1024 processors) at the Pittsburgh Supercomputing Center’s TCS1 AlphaServer. The results are consistent for different data distributions. Octrees with over a billion octants were constructed and balanced in less than a minute on 1024 processors. Like other existing algorithms for constructing and balancing octrees, our algorithms have O(n log n) work and O(n) storage complexity. Under reasonable assumptions on the distribution of octants and the work per octant, the parallel time complexity is O(n/np log(n/np) + np log np), were n is the final number of leaves and np is the number of processors. Key words. Linear octrees, Balance refinement, Morton encoding, large scale parallel computing, space filling curves AMS subject classifications. 65N50, 65Y05, 68W10, 68W15 1. Introduction. Spatial
Implementing ray tracing with octrees and neighbor finding
 Computers And Graphics
, 1989
"... AbstractA ray tracing implementation is described that is based on an octree representation of a scene. Rays are traced through the scene by calculating the blocks through which they pass. This calculation is performed in a bottomup manner through the use of neighbor finding. The octrees are assu ..."
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Cited by 28 (4 self)
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AbstractA ray tracing implementation is described that is based on an octree representation of a scene. Rays are traced through the scene by calculating the blocks through which they pass. This calculation is performed in a bottomup manner through the use of neighbor finding. The octrees are assumed to be implemented by a pointer representation. The most basic operation in computer graphics is the conversion of an internal model of a threedimensional scene into a twodimensional scene that lies on the viewplane. The purpose is to generate an image of the
Efficient Algorithms for TwoPhase Collision Detection
, 1997
"... This article describes practical collision detection algorithms for robot motion planning. Attention is restricted to algorithms that handle rigid, polyhedral geometries. ..."
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Cited by 24 (0 self)
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This article describes practical collision detection algorithms for robot motion planning. Attention is restricted to algorithms that handle rigid, polyhedral geometries.
An Overview of Quadtrees, Octrees, and Related Hierarchical Data Structures
 NATO ASI Series
, 1988
"... An overview of hierarchical data structures for representing images, such as the quadtree and octree, is presented. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in computer graphics, computeraided design, robotics, co ..."
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Cited by 21 (2 self)
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An overview of hierarchical data structures for representing images, such as the quadtree and octree, is presented. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in computer graphics, computeraided design, robotics, computer vision, and cartography. There is a greater emphasis on region data (i.e., 2dimensional shapes) and to a lesser extent on point, lin.e, and 3dimensional data.
Exact and robust (self)intersections for polygonal meshes
, 2010
"... We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and selfintersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for me ..."
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Cited by 16 (1 self)
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We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and selfintersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate meshbased front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness ( = correctness) and robustness ( = completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a planebased BSPrepresentation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency.
An Improved ZBuffer CSG Rendering Algorithm
 In HWWS ’98: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
, 1998
"... We present an improved zbuffer based CSG rendering algorithm, based on previous techniques using zbuffer parity based surface clipping. We show that while this type of algorithm has been reported as requiring O(n^2)), (where n is the number of primitives), an O(kn) (where k is depth complexity) a ..."
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Cited by 15 (0 self)
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We present an improved zbuffer based CSG rendering algorithm, based on previous techniques using zbuffer parity based surface clipping. We show that while this type of algorithm has been reported as requiring O(n^2)), (where n is the number of primitives), an O(kn) (where k is depth complexity) algorithm may be substituted. For cases where k is less than n this translates into a significant performance gain.
Rigid Body Contact: Collision Detection to Force Computation
 MITSUBISHI ELECTRIC RESEARCH LABORATORIES
, 1998
"... The most difficult aspect of rigidbody simulation is contact modeling. Two major subproblems of contact modeling are detecting contacts and computing contact forces. Although typically studied in isolation, these problems are tightly intertwined in simulation. This paper describes a method for fitt ..."
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Cited by 15 (0 self)
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The most difficult aspect of rigidbody simulation is contact modeling. Two major subproblems of contact modeling are detecting contacts and computing contact forces. Although typically studied in isolation, these problems are tightly intertwined in simulation. This paper describes a method for fitting the pieces together. It gives an overview of the VClip collision detection algorithm, which can rapidly and robustly locate pairs of closest features between polyhedral models. Using the results from multiple invocations of VClip, persistent, one and twodimensional contact regions can be modeled. The paper briefly describes several methods for computing contact forces that act between bodies. It also presents a new, easy to implement method, based on the singular value decomposition of the contact matrix.
Mobile Robot Navigation Exploration Algorithm
, 1992
"... This paper will present an algorithm for path planning to a goal with a mobile robot in an unknown environment. The robot maps the environment only to the extent that is necessary to achieve the goal. Mapping is achieved using tactile sensing while the robot is executing a path to the specified goal ..."
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Cited by 10 (0 self)
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This paper will present an algorithm for path planning to a goal with a mobile robot in an unknown environment. The robot maps the environment only to the extent that is necessary to achieve the goal. Mapping is achieved using tactile sensing while the robot is executing a path to the specified goal. Paths are generated by treating unknown regions in the environment as free space. As obstacles are encountered en route to a goal, the model of the environment is updated and a new path to the goal is planned and executed. Initially the paths to the goal generated by this algorithm will be negotiable paths. However as the robot acquires more knowledge about the environment, the length of the planned paths will be optimised. The optimisation criteria can be modified to favour or avoid unexplored regions in the environment. The algorithm presented in this paper makes use of the quadtree data structure to model the environment and uses the distance transform methodology to generate paths for ...