DWSI: AN APPROACH TO SOLVING THE POLYGON INTERSECTION-SPREADING PROBLEM WITH A PARALLEL UNION ALGORITHM AT THE FEATURE LAYER LEVEL

A dual-way seeds indexing (DWSI) method based on R-tree and the OpenGeospatial Consortium (OGC) simple feature model was proposed to solve the polygon intersection-spreading problem. The parallel polygon union algorithm based on the improved DWSI and the OpenMP parallel programming model was developed to validate the usability of the data partition method. The experimental results reveal that the improved DWSI method can implement a robust parallel task partition by overcoming the polygon intersection-spreading problem. The parallel union algorithm applied DWSI not only scaled up the data processing but alsospeeded up the computation compared with the serial proposal, and it showed ahigher computational efficiency with higher speedup benchmarks in the treatment of larger-scale dataset. Therefore, the improved DWSI can be a potential approach to parallelizing the vector data overlay algorithms based on the OGC simple data model at the feature layer level

DWSI: AN APPROACH TO SOLVING THE POLYGON INTERSECTION-SPREADING PROBLEM WITH A PARALLEL UNION ALGORITHM AT THE FEATURE LAYER LEVEL

A dual-way seeds indexing (DWSI) method based on R-tree and the OpenGeospatial Consortium (OGC) simple feature model was proposed to solve the polygon intersection-spreading problem. The parallel polygon union algorithm based on the improved DWSI and the OpenMP parallel programming model was developed to validate the usability of the data partition method. The experimental results reveal that the improved DWSI method can implement a robust parallel task partition by overcoming the polygon intersection-spreading problem. The parallel union algorithm applied DWSI not only scaled up the data processing but alsospeeded up the computation compared with the serial proposal, and it showed ahigher computational efficiency with higher speedup benchmarks in the treatment of larger-scale dataset. Therefore, the improved DWSI can be a potential approach to parallelizing the vector data overlay algorithms based on the OGC simple data model at the feature layer level

Collision free region determination by modified polygonal\ud Boolean operations

Cutting and packing problems are found in numerous industries such as garment, wood and shipbuilding. The collision free region concept is presented, as it represents all the translations possible for an item to be inserted into a container with already placed items. The often adopted nofit polygon concept and its analogous concept inner fit polygon are used to determine the collision free region. Boolean operations involving nofit polygons and inner fit polygons are used to determine the collision free region. New robust non-regularized Boolean operations algorithm is proposed to determine the collision free region. The algorithm is capable of dealing with degenerated boundaries. This capability is important because degenerated boundaries often represent local optimal placements. A parallelized version of the algorithm is also proposed and tests are performed in order to determine the execution times of both the serial and parallel versions of the algorithm.CNPqFAPES

Acceleration of Computational Geometry Algorithms for High Performance Computing Based Geo-Spatial Big Data Analysis

Geo-Spatial computing and data analysis is the branch of computer science that deals with real world location-based data. Computational geometry algorithms are algorithms that process geometry/shapes and is one of the pillars of geo-spatial computing. Real world map and location-based data can be huge in size and the data structures used to process them extremely big leading to huge computational costs. Furthermore, Geo-Spatial datasets are growing on all V’s (Volume, Variety, Value, etc.) and are becoming larger and more complex to process in-turn demanding more computational resources. High Performance Computing is a way to breakdown the problem in ways that it can run in parallel on big computers with massive processing power and hence reduce the computing time delivering the same results but much faster.This dissertation explores different techniques to accelerate the processing of computational geometry algorithms and geo-spatial computing like using Many-core Graphics Processing Units (GPU), Multi-core Central Processing Units (CPU), Multi-node setup with Message Passing Interface (MPI), Cache optimizations, Memory and Communication optimizations, load balancing, Algorithmic Modifications, Directive based parallelization with OpenMP or OpenACC and Vectorization with compiler intrinsic (AVX). This dissertation has applied at least one of the mentioned techniques to the following problems. Novel method to parallelize plane sweep based geometric intersection for GPU with directives is presented. Parallelization of plane sweep based Voronoi construction, parallelization of Segment tree construction, Segment tree queries and Segment tree-based operations has been presented. Spatial autocorrelation, computation of getis-ord hotspots are also presented. Acceleration performance and speedup results are presented in each corresponding chapter

Comparing Boolean Operation Methods on 3D Solids

Geometric engines are developed to give answers on geometrical queries, such as, what is the volume of a shape? Developing, testing and maintaining a geometric engine which can be used generically to answer arbitrary geometric queries is a tedious and time consuming task. Thousands of work hours are being spent towards this purpose. A very important element of such geometric engines is the Boolean operations on 3D objects. Boolean operations can be used to develop powerful tools for CAD/CAM applications, by which, end users can save thousands of work hours during modeling. While robust Boolean operations on 3D objects are difficult to implement, once available, many geometric queries can be reduced to a collection of Boolean operations. This reduction would save thousands of hours for the developers of such CAD/CAM applications. The goal of this thesis is to compare the Boolean implementation of Tekla Structures with the Boolean implementation of CGAL and a recently introduced method, EMBER. Using the results of this thesis, Tekla Structures’ currently unidentified vulnerabilities in its Boolean implementation can be identified and thus, improved. Quantitative results showed that Tekla Structures’ Boolean implementation, while being fast, suffered in terms of robustness during the union and difference operations with respect to CGAL and EMBER while doing remarkably well in the intersection operations

Fast and Accurate Visibility Preprocessing

Visibility culling is a means of accelerating the graphical rendering of geometric models. Invisible objects are efficiently culled to prevent their submission to the standard graphics pipeline. It is advantageous to preprocess scenes in order to determine invisible objects from all possible camera views. This information is typically saved to disk and may then be reused until the model geometry changes. Such preprocessing algorithms are therefore used for scenes that are primarily static. Currently, the standard approach to visibility preprocessing algorithms is to use a form of approximate solution, known as conservative culling. Such algorithms over-estimate the set of visible polygons. This compromise has been considered necessary in order to perform visibility preprocessing quickly. These algorithms attempt to satisfy the goals of both rapid preprocessing and rapid run-time rendering. We observe, however, that there is a need for algorithms with superior performance in preprocessing, as well as for algorithms that are more accurate. For most applications these features are not required simultaneously. In this thesis we present two novel visibility preprocessing algorithms, each of which is strongly biased toward one of these requirements. The first algorithm has the advantage of performance. It executes quickly by exploiting graphics hardware. The algorithm also has the features of output sensitivity (to what is visible), and a logarithmic dependency in the size of the camera space partition. These advantages come at the cost of image error. We present a heuristic guided adaptive sampling methodology that minimises this error. We further show how this algorithm may be parallelised and also present a natural extension of the algorithm to five dimensions for accelerating generalised ray shooting. The second algorithm has the advantage of accuracy. No over-estimation is performed, nor are any sacrifices made in terms of image quality. The cost is primarily that of time. Despite the relatively long computation, the algorithm is still tractable and on average scales slightly superlinearly with the input size. This algorithm also has the advantage of output sensitivity. This is the first known tractable exact solution to the general 3D from-region visibility problem. In order to solve the exact from-region visibility problem, we had to first solve a more general form of the standard stabbing problem. An efficient solution to this problem is presented independently