Efficient algorithm for general polygon clipping

International audienceWe present an efficient algorithm to determine the intersection of two planar general polygons. A new method based on rotation angle is proposed to obtain the classification of an edge with respect to a polygon. The edge candidates can be determined efficiently by a 1-dimensional range searching approach based on an AVL tree (a balanced binary search tree). The simplicial chain is used to represent the general polygons, and to determine the classification of polygon edges. Examples are given to illustrate the algorithm

OPTIMIZATION APPROACHES TO MPI AND AREA MERGING-BASED PARALLEL BUFFER ALGORITHM

On buffer zone construction, the rasterization-based dilation method inevitablyintroduces errors, and the double-sided parallel line method involves a series ofcomplex operations. In this paper, we proposed a parallel buffer algorithm based onarea merging and MPI (Message Passing Interface) to improve the performances ofbuffer analyses on processing large datasets. Experimental results reveal that thereare three major performance bottlenecks which significantly impact the serial andparallel buffer construction efficiencies, including the area merging strategy, thetask load balance method and the MPI inter-process results merging strategy.Corresponding optimization approaches involving tree-like area merging strategy, the vertex number oriented parallel task partition method and the inter-processresults merging strategy were suggested to overcome these bottlenecks. Experimentswere carried out to examine the performance efficiency of the optimized parallelalgorithm. The estimation results suggested that the optimization approaches couldprovide high performance and processing ability for buffer construction in a clusterparallel environment. Our method could provide insights into the parallelization ofspatial analysis algorithm

Simultaneous Generation of Stereoscopic Views

Currently almost all computer graphic stereoscopic images are generated by doubling the work required to create a single image. In this paper we derive and analyze algorithms for simultaneous generation of the two views necessary for a stereoscopic image. We begin with a discussion of the similarities of the two perspective views of a stereo pair. Following this, several graphics algorithms that have been optimized from known single-view methods are described and performance results obtained from testing the new stereo algorithms against the originals are presented

Analysis of General Polygon Boolean Operation Algorithms

Tato diplomová práce se zabývá algoritmy pro booleovské operace nad obecnými polygony. Mezi booleovské operace se řadí např. průnik, sjednocení nebo rozdíl. Obecný polygon může být např. sebeprotínající s otvorem. Pravděpodobně nejznámější booleovskou operací je oříznutí polygonu obdélníkovým oknem. Na začátku práce jsou vysvětleny základní pojmy. V další části je popsán princip vybrané množiny algoritmů, které provádějí booleovské operace nad polygony. V závěrečné části je provedeno komplexní srovnání implementací algoritmů jak z hlediska rychlosti výpočtu, tak z hlediska schopnosti zpracovat různě složité typy vstupních dat. Výstupem práce je souhrnné zhodnocení všech algoritmů a dynamická knihovna, která obsahuje implementace všech algoritmů.This thesis deals with general polygon boolean operation algorithms. Boolean operations are e.g. intersection, union or difference. A general polygon can be e.g. a selfinterecting polygon with inner hole. Clipping of polygons against a rectangular window is probably the most familiar boolean operation on polygons. At first, basic definitions are listed. Then the principles of a selected set of boolean operation algorithms are reviewed. Finally, a complex comparison of the algorithms is undertaken. Performance as well as the ability to handle degenerate cases are tested. The output of this thesis is an overall evaluation of algorithm properties and a dynamic library that contains the implementation of all of the tested algorithms.

Efficient Parallel and Distributed Algorithms for GIS Polygon Overlay Processing

Polygon clipping is one of the complex operations in computational geometry. It is used in Geographic Information Systems (GIS), Computer Graphics, and VLSI CAD. For two polygons with n and m vertices, the number of intersections can be O(nm). In this dissertation, we present the first output-sensitive CREW PRAM algorithm, which can perform polygon clipping in O(log n) time using O(n + k + k\u27) processors, where n is the number of vertices, k is the number of intersections, and k\u27 is the additional temporary vertices introduced due to the partitioning of polygons. The current best algorithm by Karinthi, Srinivas, and Almasi does not handle self-intersecting polygons, is not output-sensitive and must employ O(n^2) processors to achieve O(log n) time. The second parallel algorithm is an output-sensitive PRAM algorithm based on Greiner-Hormann algorithm with O(log n) time complexity using O(n + k) processors. This is cost-optimal when compared to the time complexity of the best-known sequential plane-sweep based algorithm for polygon clipping. For self-intersecting polygons, the time complexity is O(((n + k) log n log log n)/p) using p In addition to these parallel algorithms, the other main contributions in this dissertation are 1) multi-core and many-core implementation for clipping a pair of polygons and 2) MPI-GIS and Hadoop Topology Suite for distributed polygon overlay using a cluster of nodes. Nvidia GPU and CUDA are used for the many-core implementation. The MPI based system achieves 44X speedup while processing about 600K polygons in two real-world GIS shapefiles 1) USA Detailed Water Bodies and 2) USA Block Group Boundaries) within 20 seconds on a 32-node (8 cores each) IBM iDataPlex cluster interconnected by InfiniBand technology