Amortized analysis of smooth quadtrees in all dimensions

Quadtrees are a well-known data structure for representing geometric data in the plane, and naturally generalize to higher dimensions. A basic operation is to expand the tree by splitting a given leaf. A quadtree is smooth if adjacent leaf boxes differ by at most one in height.

[1]  Boris Aronov,et al.  Cost prediction for ray shooting in octrees , 2006, Comput. Geom..

[2]  Cong Wang,et al.  On soft predicates in subdivision motion planning , 2013, SoCG '13.

[3]  D. Moore.  Simplicial Mesh Generation with Applications , 1992 .

[4]  Ronald L. Rivest,et al.  Introduction to Algorithms, third edition , 2009 .

[5]  Chee-Keng Yap,et al.  Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams , 2016, Comput. Graph. Forum.

[6]  Hanan Samet,et al.  Hierarchical Spatial Data Structures , 1989, SSD.

[7]  Jim Ruppert,et al.  A new and simple algorithm for quality 2-dimensional mesh generation , 1993, SODA '93.

[8]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[9]  Jan van Leeuwen,et al.  Dynamic multi-dimensional data structures based on quad- and k—d trees , 1982, Acta Informatica.

[10]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[11]  Don Sheehy,et al.  New Bounds on the Size of Optimal Meshes , 2012, Comput. Graph. Forum.

[12]  Maarten Löffler,et al.  Dynamic Planar Point Location with Sub-logarithmic Local Updates , 2012, WADS.

[13]  David M. Mount,et al.  A Self-adjusting Data Structure for Multidimensional Point Sets , 2012, ESA.

[14]  Bettina Speckmann,et al.  Kinetic Compressed Quadtrees in the Black-Box Model with Applications to Collision Detection for Low-Density Scenes , 2012, ESA.

[15]  Chee-Keng Yap,et al.  Amortized analysis of smooth quadtrees in all dimensions , 2014, Comput. Geom..

[16]  David Eppstein,et al.  Provably Good Mesh Generation , 1994, J. Comput. Syst. Sci..

[17]  Jon Louis Bentley,et al.  Quad trees a data structure for retrieval on composite keys , 1974, Acta Informatica.

[18]  Hanan Samet,et al.  Applications of spatial data structures - computer graphics, image processing, and GIS , 1990 .

[19]  Doug Moore.  The cost of balancing generalized quadtrees , 1995, SMA '95.

[20]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .