Spatial Point Location and Its Applications

This paper considers the problem of locating a point in a polyhedral subdivision of the space defined by planar polygonal faces. A persistent form of binary-binary search tree is presented so that the point location problem can be solved in O(log N) query time and O(N+K) space, where N is the total number of edges and K the edge intersections in the image plane. The persistent structure also gives new better solutions for many other geometric problems.

[1]  Derick Wood,et al.  An Optimal Worst Case Algorithm for Reporting Intersections of Rectangles , 1980, IEEE Transactions on Computers.

[2]  Otto Nurmi.  On translating a set of objects in 2- and 3-dimensional space , 1986, Comput. Vis. Graph. Image Process..

[3]  Franco P. Preparata,et al.  Plane-sweep algorithms for intersecting geometric figures , 1982, CACM.

[4]  Kenneth L. Clarkson,et al.  New applications of random sampling in computational geometry , 1987, Discret. Comput. Geom..

[5]  Wolfgang Leister,et al.  Ray Tracing Algorithms — Theory and Practice , 1988 .

[6]  Michael McKenna.  Worst-case optimal hidden-surface removal , 1987, TOGS.

[7]  Robert E. Tarjan,et al.  Making data structures persistent , 1986, STOC '86.

[8]  Otto Nurmi.  A fast line-sweep algorithm for hidden line elimination , 1985, BIT Comput. Sci. Sect..

[9]  Leonidas J. Guibas,et al.  A dichromatic framework for balanced trees , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[10]  Richard J. Lipton,et al.  Multidimensional Searching Problems , 1976, SIAM J. Comput..

[11]  Robert E. Tarjan,et al.  Planar point location using persistent search trees , 1986, CACM.

[12]  Roberto Tamassia,et al.  Fully dynamic techniques for point location and transitive closure in planar structures , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[13]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[14]  David G. Kirkpatrick,et al.  Polygonal Intersection Searching , 1982, Inf. Process. Lett..

[15]  W ShorPeter,et al.  Applications of random sampling in computational geometry, II , 1989 .

[16]  Raimund Seidel,et al.  Some methods of computational geometry applied to computer graphics , 1984, Comput. Vis. Graph. Image Process..

[17]  Roberto Tamassia,et al.  Fully Dynamic Point Location in a Monotone Subdivision , 1989, SIAM J. Comput..

[18]  Richard Cole,et al.  Searching and Storing Similar Lists , 2018, J. Algorithms.

[19]  Paul F. Dietz,et al.  Two algorithms for maintaining order in a list , 1987, STOC.

[20]  Bernard Chazelle,et al.  How to Search in History , 1983, Inf. Control..

[21]  Bernard Chazelle,et al.  A deterministic view of random sampling and its use in geometry , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[22]  Roberto Tamassia,et al.  Efficient Spatial Point Location (Extended Abstract) , 1989, WADS.