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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 30 (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 28 (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 9 (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