Summary Point in Polygon Calculation Using Vector Geometry arxiv.org
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One Line
The article compares different algorithms for determining whether a point lies within a polygon using vector geometry and finds that the numba implementation with parallelization is the fastest, with tables and figures showing execution times and accuracy.
Key Points
- Various resources related to point-in-polygon calculations using vector geometry are discussed, including books, research papers, and software packages such as scikit-image, geopandas, and Shapely.
- An algorithm for point-in-polygon calculation using vector geometry is presented and tested on different computers with different numbers of points, showing linear execution time and scalability.
- The article compares the performance of different algorithms for calculating point in polygon calculations using vector geometry, with the numba implementation with parallelization consistently performing the fastest.
- The proposed algorithm for point-in-polygon calculations using vector geometry is more efficient than other methods and can take advantage of processor parallelization, and it outperforms other methods used by the shapely and OpenCV libraries.
- The point in polygon problem is commonly used in computer graphics, painting simulation, robotics, geosciences, remote sensing, and geographic information systems.
Summaries
308 word summary
The article presents an algorithm for determining whether a point lies within a polygon using vector geometry, which is faster and more efficient than other methods, including those used by the shapely and OpenCV libraries. The algorithm involves casting a ray from the point and testing for edge crossings, with time complexity ranging from O(n) to O(n^2). The article includes a method section, implementation section with python code, and simulation section to test the algorithm on real-world data. The algorithm can be applied to geospatial data and has been tested on data from the Google Open Buildings project and shapefile for the map of the Republic of Ghana from the Database of Global Administrative Areas. The article also discusses the concept of perpendicular distance and the equation of a line in vector form. The algorithm was found to work well on a Dell XPS 15 9570 with an Intel i7-8750H processor and 32GB of RAM, and on a Dell Optiplex 9020 with 8GB of RAM and an Intel i5-4590 CPU with 4 cores and 4 threads running Python 3.10.8, with significant improvements when combined with numba. The article includes figures and tables showing the execution time of the different algorithms and a map of Ghana demonstrating the accuracy of the algorithm in determining whether points are inside or outside a polygon. This document presents a comparison of different algorithms for calculating point in polygon using vector geometry, with the numba implementation with parallelization performing the fastest. Tables and figures show execution times for different numbers of points, and a linear least squares fit was used to predict execution times for larger numbers of points. The algorithm was tested on different computers and found to scale well. The document also includes references to resources related to point-in-polygon calculations and tables showing execution time and relative error of different implementations.
938 word summary
The document contains references to various resources related to point-in-polygon calculations using vector geometry. These resources include books, research papers, and software packages such as scikit-image, geopandas, and Shapely. Some of the references discuss algorithms for point-in-polygon testing, while others focus on related topics such as image processing and geometric object manipulation. The document also includes tables showing the execution time and relative error of different implementations of the algorithms. This document presents a point-in-polygon calculation algorithm using vector geometry. Tables and figures show the execution times and least squares fit of data for different implementations of the algorithm using different libraries and processors. The algorithm was tested on a Dell XPS 15 9570 with an Intel i7-8750H 6 core/12 thread processor and 32GB of RAM, as well as on an Optiplex 9020 with 8GB of RAM and Intel i5-4590 CPU with 4 cores and 4 threads running Python 3.10.8. The results show that the linear projection generally bounds the actual execution times and closely follows the lines. The least squares fit of the data in Table 7 is shown in Table 9. A point in polygon calculation using vector geometry was implemented and tested on a Dell XPS 15 computer with different numbers of points. The algorithm's execution time was found to be linear, allowing it to scale well. A linear least squares fit was used to predict execution times for a larger number of points. The algorithm was compared to other existing algorithms and found to be very useful. The numba implementation with parallelization had the highest relative error, while the opencv implementation had the largest errors in absolute terms. The largest deviations in execution times came from the numba algorithm with parallelization, possibly due to calls to multiple processor threads. A matrix equation was used to perform a linear least squares fit of the data to find the equation of the form ax + b = y, where x is the number of points and y is the execution time. The execution times for the numba implementations were absent due to numba not being supported on the new python 3.11 at the time of performing the simulations. The article compares the performance of different algorithms for calculating point in polygon calculations using vector geometry. The numba implementation with parallelization consistently performs the fastest, followed by the numba implementation without parallelization, then the OpenCV implementation, and finally Algorithm 2. Shapely and geopandas are the worst performing methods. Tables and figures show the execution times of the various algorithms for different numbers of points. Optimizing the algorithm with numba on 4 cores produces run times of 8min 59s and in 16min 3s without parallelization. The article presents an algorithm for point-in-polygon calculations using vector geometry. The algorithm was tested on a Dell Optiplex 9020 with 8GB of RAM and an Intel i5-4590 CPU with 4 cores and 4 threads running Python 3.10.8. The results showed that the algorithm had a faster execution time than the OpenCV implementation. When combined with numba, a high-performance Python compiler, the algorithm showed significant improvements, cutting the execution time from 18min 30s down to 3min 30s when all 12 processor threads were utilized. The algorithm was tested against the point-in-polygon algorithms used by shapely, geopandas, and OpenCV, and showed competitive results. The article includes figures and tables showing the execution time of the different algorithms and a map of Ghana demonstrating the accuracy of the algorithm in determining whether points are inside or outside a polygon. This document presents an algorithm for point-in-polygon calculation using vector geometry. The algorithm was tested on a Dell XPS 15 9570 with an Intel i7-8750H processor and 32GB of RAM, and was found to work well. The algorithm was tested against other algorithms. To test the algorithms, data was downloaded from the Google Open Buildings project and shapefile for the map of the Republic of Ghana from the Database of Global Administrative Areas. The initial data contained approximately 54 million points, which were reduced to 17,097,823 points by restricting to only points within the bounding box of Ghana and 0ff-buildings. The defined algorithm was implemented in python. The basic implementation is shown in Algorithms 1 and 2. The article presents a method for determining whether a point lies within a polygon using vector geometry. The method involves casting a ray from the point and testing for edge crossings. The equation of the line formed by the ray can be written as (r-p).n=0, where p is a point on the line and n is a normal vector. The direction of the ray can be chosen arbitrarily, but the article uses a horizontal ray with direction vector d=(1,0). The test for edge crossings involves computing the signs of f(r)=(r-p).n for each edge of the polygon. If the signs are opposite for adjacent edges, then the point lies within the polygon. The article also discusses the concept of perpendicular distance and the equation of a line in vector form. The article discusses the point in polygon problem and proposes an algorithm based on the ray casting method using vector geometry. The algorithm is more efficient than other methods and can take advantage of processor parallelization. The article includes a method section, implementation section with python code, and simulation section to test the algorithm on real-world data. The point in polygon problem is commonly used in computer graphics, painting simulation, robotics, geosciences, remote sensing, and geographic information systems. The proposed algorithm outperforms other methods, including those used by the shapely and OpenCV libraries. The algorithm's time complexity ranges from O(n) to O(n^2), and it can be applied to geospatial data.