On the number of face-connected components of morton-type space-filling curves
The Morton-or z-curve is one example for a space-filling curve: Given a level of refinement L
∈ N _0 L∈ N 0, it maps the interval 0, 2^ dL) ∩ Z 0, 2 dL)∩ Z one-to-one to a set of d …
∈ N _0 L∈ N 0, it maps the interval 0, 2^ dL) ∩ Z 0, 2 dL)∩ Z one-to-one to a set of d …
Kinetic compressed quadtrees in the black-box model with applications to collision detection for low-density scenes
M De Berg, M Roeloffzen, B Speckmann - Algorithms–ESA 2012: 20th …, 2012 - Springer
We present an efficient method for maintaining a compressed quadtree for a set of moving
points in ℝ d. Our method works in the black-box KDS model, where we receive the …
points in ℝ d. Our method works in the black-box KDS model, where we receive the …
Down the rabbit hole: Robust proximity search and density estimation in sublinear space
S Har-Peled, N Kumar - SIAM Journal on Computing, 2014 - SIAM
For a set of n points in R^d, and parameters k and ε, we present a data structure that
answers (1+ε,k) approximate nearest neighbor queries in logarithmic time. Surprisingly, the …
answers (1+ε,k) approximate nearest neighbor queries in logarithmic time. Surprisingly, the …
[PDF][PDF] Morton curve segments produce no more than two distinct face-connected subdomains
C Burstedde, T Isaac - CoRR, abs/1505.05055 v2, 2015 - researchgate.net
The Morton-or z-curve is one example for a space filling curve: Given a level of refinement
L∈ N0, it maps the interval [0, 2dL)∩ Z one-to-one to a set of d-dimensional cubes of edge …
L∈ N0, it maps the interval [0, 2dL)∩ Z one-to-one to a set of d-dimensional cubes of edge …
[PDF][PDF] Enhancing Quad tree for spatial index using space filling curves
AA Hussain, RF Hassan - Engineering and Technology Journal, 2020 - iasj.net
Engineering and Technology Journal Enhancing Quad Tree for Spatial Index Using Space
Filling Curves Page 1 Engineering and Technology Journal Vol. 38, Part B (2020), No. 01 …
Filling Curves Page 1 Engineering and Technology Journal Vol. 38, Part B (2020), No. 01 …
Bounds on the number of discontinuities of Morton-type space-filling curves
The Morton-or z-curve is one example for a space filling curve: Given a level of refinement L,
it maps the interval [0, 2** dL) one-to-one to a set of d-dimensional cubes of edge length 2 …
it maps the interval [0, 2** dL) one-to-one to a set of d-dimensional cubes of edge length 2 …
Weiterführende Ergebnisse
R Klein, A Driemel, H Haverkort - Algorithmische Geometrie: Grundlagen …, 2022 - Springer
Weiterführende Ergebnisse Page 1 7 Weiterführende Ergebnisse In diesem Kapitel möchten
wir ein paar Ergebnisse der algorithmischen und diskreten Geometrie vorstellen, die ein wenig …
wir ein paar Ergebnisse der algorithmischen und diskreten Geometrie vorstellen, die ein wenig …
[PDF][PDF] Spatial Indexing of large-scale geo-referenced point data on GPGPUs using parallel primitives
J Zhang, L Gruenwald - Department of Computer Science, The City …, 2012 - academia.edu
Modern positioning and locating technologies, eg, GPS, have generated huge amounts of
geo-referenced point data that are crucial to understand environmental and social-economic …
geo-referenced point data that are crucial to understand environmental and social-economic …
An edge quadtree for external memory
H Haverkort, M McGranaghan, L Toma - International Symposium on …, 2013 - Springer
We consider the problem of building a quadtree subdivision for a set E of n non-intersecting
edges in the plane. Our approach is to first build a quadtree on the vertices corresponding to …
edges in the plane. Our approach is to first build a quadtree on the vertices corresponding to …
Robust proximity search for balls using sublinear space
S Har-Peled, N Kumar - Algorithmica, 2018 - Springer
Given a set of n disjoint balls b_1,\dots, b_n b 1,⋯, bn in I\! R^ d IR d, we provide a data
structure of near linear size that can answer (1 ± ε)(1±ε)-approximate k th-nearest neighbor …
structure of near linear size that can answer (1 ± ε)(1±ε)-approximate k th-nearest neighbor …