Statistical optimization of octree searches

Castro, Rener; Lewiner, Thomas; Lopes, Hélio; Tavares, Geovan; Bordignon, Alex

doi:10.1111/j.1467-8659.2007.01104.x

Cited by 19 publications

(12 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bounding volume hierarchies construct a tree by subdividing the model into small pieces, which should be tighter for lower levels; for more details see (Bradshaw, 2002). Finally, spatial subdivision divides the space into cells; every object falls into a cell; for more details, see (Castro et al, 2008).…”

Section: Collision Detectionmentioning

confidence: 99%

Revisión de literatura de jerarquía volúmenes acotantes enfocados en detección de colisiones

Dinas

Bañón

2015

IyC

View full text Add to dashboard Cite

A bounding volume is a common method to simplify object representation by using the composition of geometrical shapes that enclose the object; it encapsulates complex objects by means of simple volumes and it is widely useful in collision detection applications and ray tracing for rendering algorithms. They are popular in computer graphics and computational geometry. Most popular bounding volumes are spheres, Oriented-Bounding Boxes (OBB's), Axis-Aligned Bounding Boxes (AABB's); moreover, the literature review includes ellipsoids, cylinders, sphere packing, sphere shells, k-DOP's, convex hulls, cloud of points, and minimal bounding boxes, among others. A Bounding Volume Hierarchy is usually a tree in which the complete object is represented tighter fitting every level of the hierarchy. Additionally, each bounding volume has a cost associated to construction, update, and interference tests. For instance, spheres are invariant to rotation and translations, then they do not require being updated; their constructions and interference tests are more straightforward then OBB's; however, their tightness is lower than other bounding volumes. Finally, three comparisons between two polyhedra; seven different algorithms were used, of which five are public libraries for collision detection. Keywords: Axis-aligned bounding box (AABB), bounding volumes hierarchies, convex objects, oriented bounding box (OBB), spheres. ResumenUn volumen acotante es un método común para simplificar la representación de los objetos por medio de composición de formas geométricas que encierran el objeto; estos encapsulan objetos complejos por medio de volúmenes simples y son ampliamente usados en aplicaciones de detección de colisiones y trazador de rayos para algoritmos de renderización. Los volúmenes acotantes son populares en computación gráfica y en geometría computacional; los más populares son las esferas, las cajas acotantes orientadas (OBB's) y las cajas acotantes alineadas a los ejes (AABB's); no obstante, la literatura incluye elipses, cilindros empaquetamiento de esferas, conchas de esferas, k-DOP's, convex hulls, nubes de puntos y cajas acotantes mínimas, entre otras. Una jerarquía de volúmenes acotantes es usualmente un árbol, en el cual la representación de los objetos es más ajustada en cada uno de los niveles de la jerarquía. Adicionalmente, cada volumen acotante tiene asociado costos de construcción, actualización, pruebas de interferencia. Por ejemplo, las esferas so invariantes a rotación y translación, por lo tanto no requieren ser actualizadas en comparación con los AABB no son invariantes a la rotación. Por otro lado la construcción y las pruebas de solapamiento de las esferas son más simples que los OBB's; sin embargo, el ajuste de las esferas es menor que otros volúmenes acotantes. Finalmente, se comparan dos poliedros con siete algoritmos diferentes de los cuales cinco son librerías públicas para detección de colisiones. Palabras Clave: Cajas acotantes orientadas (CAO), cajas acotantes alineadas a los ejes (CAAE), ...

show abstract

Section: Collision Detectionmentioning

confidence: 99%

Revisión de literatura de jerarquía volúmenes acotantes enfocados en detección de colisiones

Dinas

Bañón

2015

IyC

View full text Add to dashboard Cite

show abstract

“…In efficient schemes, the key cumulates both significations (see Figure 3). This allows at the same time to identify the children of a node by the octant orientation for traversal algorithms, and to access a node directly from its position, for search procedures [CLL*08].…”

Section: Octrees and Their Representationsmentioning

confidence: 99%

“…This is particularly inefficient, but can be avoided if using pointerless representations [Gar82, Sam90]. Such representations associate to each node of the octree a unique key [Mor66,SS09], and the traversal operations resume to key manipulations that can be performed in local memory [Sch92,GDB03,CLL*08]. This work proposes to generate the dual of an octree using such key manipulations, enjoying the reduced memory footprint of pointerless representations and improving the execution time by several factors.…”

Section: Introductionmentioning

confidence: 99%

“…Pointerless representations of octrees [Gar82] have become popular for sparing memory [CJC*09] and for their ability to work on parallel [WS93] and GPU architectures [BC08]. The use of Morton codes [Mor66, SS09] for indexing the octree (see Section 2) is widely used, since they allow for efficient manipulation as dilated integers [Sch92,SS95] and optimized search [GDB03,CLL*08].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fast Generation of Pointerless Octree Duals

Lewiner

Mello

Peixoto

et al. 2010

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

Abstract. Geometry processing applications frequently rely on octree structures, since they provide simple and efficient hierarchies for discrete data. However, octrees do not guarantee direct continuous interpolation of this data inside its nodes. This motivates the use of the octree's dual structure, which is one of the simplest continuous hierarchical structures. With the emergence of pointerless representations, with their ability to reduce memory footprint and adapt to parallel architectures, the generation of duals of pointerless octrees becomes a natural challenge. This work proposes strategies for dual generation of static or dynamic pointerless octrees. Experimentally, those methods enjoy the memory reduction of pointerless representations and speed up the execution by several factors compared to the usual recursive generation.

show abstract

“…As GPUs are widely used in both industry and academics, research into parallel data structures on many-core architectures has become urgent and promising. A number of treebased data structures, such as R-tree [1], KD-tree [2][3][4], Octree [5][6][7][8][9][10][11], decision tree [12], [13], and bounding volume hierarchy [14] have been ported to GPGPUs. Besides the treebased data structures, hash tables on GPGPUs have also been discussed in [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

GPU-based Parallel R-tree Construction and Querying

Prasad

McDermott

et al. 2015

2015 IEEE International Parallel and Distributed Processing Symposium Workshop

View full text Add to dashboard Cite

An R-tree is a data structure for organizing and querying multi-dimensional non-uniform and overlapping data. Efficient parallelization of R-tree is an important problem due to societal applications such as geographic information systems (GIS), spatial database management systems, and VLSI layout which employ R-trees for spatial analysis tasks such as mapoverlay. As graphics processing units (GPUs) have emerged as powerful computing platforms, these R-tree related applications demand efficient R-tree construction and search algorithms on GPUs. This problem is hard both due to (i) non-linear tree topology of the data structure itself and (ii) the unconventional single-instruction multiple-thread (SIMT) architecture of modern GPUs requiring careful engineering of a host of issues. Therefore, the current best parallelizations of R-tree on GPU has limited speedup of only about 20-fold. We present a space-efficient data structure design and a non-trivial bottom-up construction algorithm for R-tree on GPUs. This has yielded the first demonstrated 226-fold speedup in parallel construction of an R-tree on a GPU compared to one-core execution on a CPU. We also present innovative R-tree search algorithms that are designed to overcome GPU's architectural and resource limitations. The best of these algorithms gives a speed up of 91-fold to 180-fold on an R-tree with 16384 base objects for query sizes ranging from 2k to 16k. 1

show abstract

Statistical optimization of octree searches

Cited by 19 publications

References 10 publications

Revisión de literatura de jerarquía volúmenes acotantes enfocados en detección de colisiones

Revisión de literatura de jerarquía volúmenes acotantes enfocados en detección de colisiones

Fast Generation of Pointerless Octree Duals

GPU-based Parallel R-tree Construction and Querying

Contact Info

Product

Resources

About