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Selfimproving algorithms
 in SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
"... We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an al ..."
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Cited by 24 (4 self)
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We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1
Geometric Data Structures for Computer Graphics
, 2003
"... pefully make them curious about further powerful treasures to be discovered in the area of computational geometry. In order to achieve these goals in an engaging yet sound manner, the general concept throughout the course is to present each geometric data structure in the following way: first, th ..."
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Cited by 17 (3 self)
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pefully make them curious about further powerful treasures to be discovered in the area of computational geometry. In order to achieve these goals in an engaging yet sound manner, the general concept throughout the course is to present each geometric data structure in the following way: first, the data strucure will be defined and described in detail; then, some of its fundamental properties will be highlighted; after that, one or more computational geometry algorithms based on the data structure will be presented; and finally, a number of recent, representative and practically relevant algorithms from computer graphics will be described in detail, showing the utilization of the data structure in a creative and enlightening way. We have arranged the topics in roughly increasing degree of difficulty. The hierarchical data structures are ordered by increasing flexibility, while the nonhierarchical topics build on each other. Finally, the last topic presents a generic technique for
ADBTrees: Controlling the Error of TimeCritical Collision Detection
 IN 8TH INTERNATIONAL FALL WORKSHOP VISION, MODELING, AND VISUALIZATION (VMV
, 2003
"... We present a novel framework for hierarchical collision detection that can be applied to virtually all bounding volume (BV) hierarchies. It allows an application to trade quality for speed. Our algorithm yields an estimation of the quality, so that applications can specify the desired quality. In a ..."
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Cited by 12 (4 self)
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We present a novel framework for hierarchical collision detection that can be applied to virtually all bounding volume (BV) hierarchies. It allows an application to trade quality for speed. Our algorithm yields an estimation of the quality, so that applications can specify the desired quality. In a timecritical system, applications can specify the maximum time budget instead, and quantitatively assess the quality of the results returned by the collision detection afterwards. Our framework
TimeCritical Collision Detection Using an AverageCase Approach
 IN PROC. ACM SYMPOSIUM ON VIRTUAL REALITY SOFTWARE AND TECHNOLOGY (VRST 2003) (OSAKA
, 2003
"... We present a novel, generic framework and algorithm for hierarchical collision detection, which allows an application to balance speed and quality of the collision detection. We pursue ..."
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Cited by 6 (2 self)
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We present a novel, generic framework and algorithm for hierarchical collision detection, which allows an application to balance speed and quality of the collision detection. We pursue
Vissort: Fast visibility ordering of 3d geometric primitives
, 2004
"... Abstract: We present a novel sorting algorithm, VisSort, to sort 1D and 3D geometric elements. Given a set of acyclic and nonintersecting 3D geometric primitives, VisSort computes the visibility ordering from a viewpoint. The running time of our algorithm is dependent upon the degree of sortednes ..."
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Cited by 2 (1 self)
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Abstract: We present a novel sorting algorithm, VisSort, to sort 1D and 3D geometric elements. Given a set of acyclic and nonintersecting 3D geometric primitives, VisSort computes the visibility ordering from a viewpoint. The running time of our algorithm is dependent upon the degree of sortedness in the 3D sequence and is bounded by O(�Y �n), where n is the number of primitives and �Y � is the Knuth’s measure of disorder. The Knuth’s measure of disorder computes the minimum number of elements that need to be removed from the sequence for the remaining sequence to be sorted [35]. VisSort exploits the spatial and temporal coherence between successive instances in a dynamic environment and performs incremental computations. Our algorithm requires no preprocessing and is applicable to all kind of models, including polygon soups and deformable models. We have used our algorithm for orderindependent transparency computations in highdepth complexity environments and performing Nbody collision culling in dynamic environments. We have implemented our algorithm and tested the system on a PC with a 3.4 GHz Pentium IV CPU with an NVIDIA GeForce FX 6800 Ultra GPU and applied it to complex environments with tens or hundreds of thousands of polygons. Our algorithm can compute a visibility ordering among the objects and triangles at interactive frame rates.
Binary Plane Partitions for Disjoint Line Segments
"... A binary space partition (BSP) for a set of disjoint objects in Euclidean space is a recursive decomposition, where each step partitions the space (and some of the objects) along a hyperplane and recurses on the objects clipped in each of the two open halfspaces. The size of a BSP is defined as the ..."
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Cited by 1 (1 self)
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A binary space partition (BSP) for a set of disjoint objects in Euclidean space is a recursive decomposition, where each step partitions the space (and some of the objects) along a hyperplane and recurses on the objects clipped in each of the two open halfspaces. The size of a BSP is defined as the number of resulting fragments of the input objects. It is shown that every set of n disjoint line segments in the plane admits a BSP of size O(n log n / log log n). This bound is best possible apart from the constant factor. 1
Binary Space Partitions  Recent Developments
, 2004
"... A binary space partition tree is a data structure for the representation of a set of objectsin space. It found an increasing number of applications over the last decades. In recent years, intensifying research focused on its combinatorial properties, which affect directly the efficiency of applica ..."
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Cited by 1 (0 self)
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A binary space partition tree is a data structure for the representation of a set of objectsin space. It found an increasing number of applications over the last decades. In recent years, intensifying research focused on its combinatorial properties, which affect directly the efficiency of applications. Important advances were made on binary space partitions for disjoint line segments in the plane and for axisaligned objects in higher dimensions. New research directions were also initiated on some realistic polygonal scenes and on kinetic binary space partitions. This paper attempts to give an overview of these results and reiterates some of the most pressing open problems.
Prerequisites
, 2003
"... In recent years, methods from computational geometry have been widely adopted by the computer graphics community yielding elegant and efficient algorithms. This course aims at familiarizing practitioners in the computer graphics field with a wide range of data structures from computational geometry. ..."
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In recent years, methods from computational geometry have been widely adopted by the computer graphics community yielding elegant and efficient algorithms. This course aims at familiarizing practitioners in the computer graphics field with a wide range of data structures from computational geometry. It will enable attendees to recognize geometrical problems and select the most suitable data structure when developing computer graphics algorithms. The course will focus on algorithms and data structures that have proven to be versatile, efficient, fundamental and easy to implement. Thus practitioners and researchers will benefit immediately from this course for their everyday work.