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11
BoxTrees and Rtrees with NearOptimal Query Time
, 2001
"... A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. The query complexity of a boxtree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing boxtrees with ..."
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Cited by 31 (6 self)
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A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. The query complexity of a boxtree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing boxtrees with small worstcase query complexity with respect to queries with axisparallel boxes and with points. We also prove lower bounds on the worstcase query complexity for boxtrees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert boxtrees to Rtrees, resulting in Rtrees with (almost) optimal query complexity. 1
Minimal Hierarchical Collision Detection
 IN PROC. VRST 2002
, 2002
"... We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axisaligned bounding box trees. In additio ..."
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Cited by 31 (6 self)
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We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axisaligned bounding box trees. In addition to being very memory efficient, it can be constructed efficiently and very fast. We also propose
Fast Final Gathering via Reverse Photon Mapping
, 2005
"... We present a new algorithm for computing indirect illumination based on density estimation similarly to photon mapping. We accelerate the search for final gathering by reorganizing the computation in the reverse order. We use two trees that organize spatially not only the position of photons but a ..."
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Cited by 10 (2 self)
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We present a new algorithm for computing indirect illumination based on density estimation similarly to photon mapping. We accelerate the search for final gathering by reorganizing the computation in the reverse order. We use two trees that organize spatially not only the position of photons but also the position of final gather rays. The achieved
BoxTrees for Collision Checking in Industrial Installations
, 2002
"... A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. We describe a new algorithm to construct a boxtree for objects in a 3D scene, and we analyze its worstcase query time for approximate range queries. If the input scene has certain characteristics that we ..."
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Cited by 10 (4 self)
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A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. We describe a new algorithm to construct a boxtree for objects in a 3D scene, and we analyze its worstcase query time for approximate range queries. If the input scene has certain characteristics that we derived from our applicationcollision detection in industrial installationsthen the query times are polylogarithmic, not only for searching with boxes but also for range searching with other constantcomplexity ranges.
An Improved Algorithm for Computing the Volume of the Union of Cubes
, 2010
"... Let C be a set of n axisaligned cubes in R³, and let U(C) denote the union of C. We present an algorithm that computes the volume of U(C) in time O(n polylog(n)). The previously best known algorithm takes O(n 4/3 log² n) time. ..."
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Cited by 5 (0 self)
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Let C be a set of n axisaligned cubes in R³, and let U(C) denote the union of C. We present an algorithm that computes the volume of U(C) in time O(n polylog(n)). The previously best known algorithm takes O(n 4/3 log² n) time.
Master’s �esis Data Structures for Interpolation of Illumination with Radiance and Irradiance Caching
"... I would like to thank Vlastimil Havran for supervising and correcting this thesis, and for his helpful ideas, cjx��� � for the chess pieces model, Jiří “Biolit ” Friml for providing the Diffuse interior model, and Ludvík “Rawalanche ” Koutný for making the Glossy interior model and testing the irrad ..."
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I would like to thank Vlastimil Havran for supervising and correcting this thesis, and for his helpful ideas, cjx��� � for the chess pieces model, Jiří “Biolit ” Friml for providing the Diffuse interior model, and Ludvík “Rawalanche ” Koutný for making the Glossy interior model and testing the irradiance caching algorithm. Finally, I would like to thank my family and friends for their support. v Declaration I hereby declare that I have completed this thesis independently and that I have listed all the literature and publications used. I have no objection to usage of this work in compliance with the act §60 Zákon č. 121/2000Sb. (copyright law), and with the rights connected with the copyright act including the changes in the act. Irradiance and radiance caching are important algorithms for solving the light transport problem in realistic image synthesis. �ey both require geometric search data structures for efficient rendering. Our goal was to improve the caching algorithms by improving these data structures. We have implemented 6 different data structures for irradiance caching, 2 previously used and 4 newly adapted to the problem. Our testing showed that multiplereference data structures offer the best traversal
Abstract Minimal Hierarchical Collision Detection ∗
"... We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axisaligned bounding box trees. In additio ..."
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We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axisaligned bounding box trees. In addition to being very memory efficient, it can be constructed efficiently and very fast. We also propose a criterion to be used during the construction of the BV hierarchies is more formally established than previous heuristics. The idea of the argument is general and can be applied to other bounding volume hierarchies as well. Furthermore, we describe a general optimization technique that can be applied to most hierarchical collision detection algorithms. Finally, we describe several box overlap tests that exploit the special features of our new BV hierarchy. These are compared experimentally among each other and with the DOP tree using a benchmark suite of realworld CAD data. Keywords: Interference detection, virtual prototyping, hierarchical partitioning, hierarchical data structure, shape approximation, physicallybased modeling, Rtrees. 1
Balanced Aspect Ratio Trees Revisited
"... Spatial databases support a variety of geometric queries on point data such as range searches, nearest neighbor searches, etc. Balanced Aspect Ratio (BAR) trees are hierarchical space decomposition structures that are generalpurpose and spaceefficient, and, in addition, enjoy a worst case perfor ..."
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Spatial databases support a variety of geometric queries on point data such as range searches, nearest neighbor searches, etc. Balanced Aspect Ratio (BAR) trees are hierarchical space decomposition structures that are generalpurpose and spaceefficient, and, in addition, enjoy a worst case performance polylogarithmic in the number of points for approximate queries. They maintain limits on their depth, as well as on the aspect ratio (intuitively, how skinny the regions can be). BAR trees were initially developed for 2 dimensional spaces and a fixed set of partitioning planes, and then extended to d dimensional spaces and more general partitioning planes. Here we revisit 2 dimensional spaces and show that, for any given set of 3 partitioning planes, it is not only possible to construct such trees, it is also possible to derive a simple closedform upper bound on the aspect ratio. This bound, and the resulting algorithm, are much simpler than what is known for general BAR trees. We call the resulting BAR trees Parameterized BAR trees and empirically evaluate them for different partitioning planes. Our experiments show that our theoretical bound converges to the empirically obtained values in the lower ranges, and also make a case for using evenly oriented partitioning planes.
ABSTRACT Minimal Hierarchical Collision Detection
"... We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axisaligned bounding box trees. In additio ..."
Abstract
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We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axisaligned bounding box trees. In addition to being very memory efficient, it can be constructed efficiently and very fast. We also propose a criterion to be used during the construction of the BV hierarchies is more formally established than previous heuristics. The idea of the argument is general and can be applied to other bounding volume hierarchies as well. Furthermore, we describe a general optimization technique that can be applied to most hierarchical collision detection algorithms. Finally, we describe several box overlap tests that exploit the special features of our new BV hierarchy. These are compared experimentally among each other and with the DOP tree using a benchmark suite of CAD data.
Parameterized Balanced Aspect Ratio Trees
"... Spatial databases support a variety of geometric queries on point data such as range searches, nearest neighbor searches, etc. Hierarchical space decomposition structures like kd trees and quad trees are useful since they are generalpurpose and spaceefficient. But they have bad worst case tim ..."
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Spatial databases support a variety of geometric queries on point data such as range searches, nearest neighbor searches, etc. Hierarchical space decomposition structures like kd trees and quad trees are useful since they are generalpurpose and spaceefficient. But they have bad worst case time performance for both exact and approximate versions of the queries. We present a new general purpose data structure for 2 dimensional spaces, the Parameterized Balanced Aspect Ratio (PBAR) tree, that has a worst case performance polylogarithmic in the number of points for approximate queries. These trees are an improvement on regular Balanced Aspect Ratio (BAR) trees that have the same asymptotic performance. Both PBAR and BAR trees maintain strict limits on their depth, as well as on the aspect ratio (intuitively, how skinny the regions can be). PBAR trees have been specialized for two dimensional spaces; they allow for complete freedom in the choice of partitioning planes, have tighter bounds on the aspect ratio of regions, and are faster in empirical tests.