Finding neighbors of equal size in linear quadtrees and octrees in constant time

Schrack, Günther F.

doi:10.1016/1049-9660(92)90022-u

Cited by 59 publications

(38 citation statements)

References 23 publications

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“…Schrack shows how to effect efficient cartesian indexing from row i and column j indices into Morton-order matrices [14]. The trick is to represent i and j as dilated integers, with information stored only in every other bit.…”

Section: Dilated Integersmentioning

confidence: 99%

“…Often (normalized dilated integers [14]) addition will be used instead of disjunction to associate at compile time with an adjacent addition. Addition and subtraction of dilated integers can be performed with a couple of minor instructions.…”

Section: Theorem 6 [14] If " " Is Read As Semantic Equivalence and "mentioning

confidence: 99%

“…b ; { + ; n = ( ; { + ; ! b + ; n )^ ; b [14] ; The index computations of ; ! k and ; k in the innermost loop above reduce to three RISC instructions, plus two to sum the matrix-element addresses.…”

Section: Theorem 8 Subtraction Addition Constant Addition and Shimentioning

confidence: 99%

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Ahnentafel Indexing into Morton-Ordered Arrays, or Matrix Locality for Free

Wise

2000

Euro-Par 2000 Parallel Processing

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Abstract. Definitions for the uniform representation of d-dimensional matrices serially in Morton-order (or Z-order) support both their use with cartesian indices, and their divide-and-conquer manipulation as quaternary trees. In the latter case, d-dimensional arrays are accessed as 2 d -ary trees. This data structure is important because, at once, it relaxes serious problems of locality and latency, and the tree helps schedule multiprocessing. It enables algorithms that avoid cache misses and page faults at all levels in hierarchical memory, independently of a specific runtime environment.This paper gathers the properties of Morton order and its mappings to other indexings, and outlines for compiler support of it. Statistics elsewhere show that the new ordering and block algorithms achieve high flop rates and, indirectly, parallelism without any low-level tuning.

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Section: Dilated Integersmentioning

confidence: 99%

Section: Theorem 6 [14] If " " Is Read As Semantic Equivalence and "mentioning

confidence: 99%

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Ahnentafel Indexing into Morton-Ordered Arrays, or Matrix Locality for Free

Wise

2000

Euro-Par 2000 Parallel Processing

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“…The resulting code was an interleaved coordinate where the bits successively denoted the y and x coordinates. In a pair of bits, the first one indicated the northern child (0) or the southern child (1). Similarly, the second bit denoted the western child (0) or the eastern child (1).…”

Section: Fig 1: a Space Decomposition And Its Quadtree Representatiomentioning

confidence: 99%

“…Gunter Schrack's solution [1] was able to compute the location code of equal size neighbors in constant-time without guaranteeing their existence. The structure proposed by Aizawa [3][2][3]was able to determine the existence of equal or greater size neighbors and compute their location in constant time, to which the access-time complexity should be added.…”

Section: Introductionmentioning

confidence: 99%

Cardinal Neighbor Quadtree: a New Quadtree-based Structure for Constant-Time Neighbor Finding

Qasem¹,

Touir²

2015

IJCA

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This paper presents a new quadtree structure: Cardinal Neighbor Quadtrees (CN-Quadtree), that allows finding neighbor quadrants in constant time regardless of their sizes. Gunter Schrack's solution [1] was able to compute the location code of equal size neighbors in constant-time without guaranteeing their existence. The structure proposed by Aizawa [3][2][3]was able to determine the existence of equal or greater size neighbors and compute their location in constant time, to which the access-time complexity should be added. The proposed structure, the Cardinal Neighbor Quadtree, a pointer based data structure, can determine the existence, and access a smaller, equal or greater size neighbor in constant-time O(1). The time complexity reduction is obtained through the addition of only four pointers per leaf node in the quadtree.

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Time‐critical animation of deformable solids

Dequidt¹,

Marchal²,

Grisoni³

2005

Computer Animation & Virtual

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This article presents a model for handling multi-resolution animation of complex deformable models. An octree-based animation and algorithmic tools are introduced to provide real-time interaction on complex objects. Some efficient collision detection scheme is also described for deformable models. A method is also presented for time-guaranteed mechanical simulation: It allows an automatic tuning of the octree resolution to match some external performance constraints, such as a pre-defined CPU consumption limit.

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Finding neighbors of equal size in linear quadtrees and octrees in constant time

Cited by 59 publications

References 23 publications

Ahnentafel Indexing into Morton-Ordered Arrays, or Matrix Locality for Free

Ahnentafel Indexing into Morton-Ordered Arrays, or Matrix Locality for Free

Cardinal Neighbor Quadtree: a New Quadtree-based Structure for Constant-Time Neighbor Finding

Time‐critical animation of deformable solids

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