We present several simple representations of polygon and polyhedra that permit the efficient parallel computation of area and volume. They are particularly useful for computing the areas of the nonempty intersections between pairs of faces in two overlapping planar graphs in GIS, or the volumes of nonempty intersections between pairs of tetrahedra in two overlapping triangulations of a polyhedron in CAD. Both applications have been implemented on multicore Intel Xeons and tested on large datasets. The representations store the minimal types of information required for computation, and never need to store edge loops and face shells, or even most adjacency relations. The representations are sets of tuples or small fixed-size sets, and can be processed in parallel with map-reduce operations.
{"title":"Minimal Representations of Polygons and Polyhedra","authors":"W. Randolph Franklin","doi":"10.1145/3548732.3548738","DOIUrl":"https://doi.org/10.1145/3548732.3548738","url":null,"abstract":"We present several simple representations of polygon and polyhedra that permit the efficient parallel computation of area and volume. They are particularly useful for computing the areas of the nonempty intersections between pairs of faces in two overlapping planar graphs in GIS, or the volumes of nonempty intersections between pairs of tetrahedra in two overlapping triangulations of a polyhedron in CAD. Both applications have been implemented on multicore Intel Xeons and tested on large datasets. The representations store the minimal types of information required for computation, and never need to store edge loops and face shells, or even most adjacency relations. The representations are sets of tuples or small fixed-size sets, and can be processed in parallel with map-reduce operations.","PeriodicalId":330118,"journal":{"name":"Spatial Gems, Volume 1","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126111120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Menezes, S. V. G. Magalhães, M. A. D. Oliveira, W. Randolph Franklin, Bruno F. Coelho
This paper presents a technique to use GPUs to accelerate the computation of 3D geometric predicates. A common predicate is computing the orientation of four 3D points, which is a subproblem in applications such as intersecting two 3D meshes. Since the higher level application may require billions of evaluations, efficiency is important. Accuracy is required since floating roundoff errors can cause topological impossibilities. One solution is to compute with rational numbers, but that is difficult to implement on a GPU because rationals’ sizes vary. Our solution is to compute on the GPU with interval arithmetic, but fall back to using rationals on the CPU if the interval computed on the GPU includes the origin; i.e., its sign is unknown. Our experiment with a dataset of hard rock mining drill holes show that this fallback to the CPU is rarely necessary; so that our technique gave a 17 times speedup compared to a sequential implementation.
{"title":"Employing GPUs to Accelerate Exact Geometric Predicates for 3D Geospatial Processing","authors":"M. Menezes, S. V. G. Magalhães, M. A. D. Oliveira, W. Randolph Franklin, Bruno F. Coelho","doi":"10.1145/3548732.3548744","DOIUrl":"https://doi.org/10.1145/3548732.3548744","url":null,"abstract":"This paper presents a technique to use GPUs to accelerate the computation of 3D geometric predicates. A common predicate is computing the orientation of four 3D points, which is a subproblem in applications such as intersecting two 3D meshes. Since the higher level application may require billions of evaluations, efficiency is important. Accuracy is required since floating roundoff errors can cause topological impossibilities. One solution is to compute with rational numbers, but that is difficult to implement on a GPU because rationals’ sizes vary. Our solution is to compute on the GPU with interval arithmetic, but fall back to using rationals on the CPU if the interval computed on the GPU includes the origin; i.e., its sign is unknown. Our experiment with a dataset of hard rock mining drill holes show that this fallback to the CPU is rarely necessary; so that our technique gave a 17 times speedup compared to a sequential implementation.","PeriodicalId":330118,"journal":{"name":"Spatial Gems, Volume 1","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125517391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hao-Hsiang Wu, Ming-Shan Su, Thanh Dat Le, Nuo Xu, Guanfeng Wang, M. Stroe
{"title":"A Scalable In-Memory Solution for Real-Time K Nearest Search on Road Network","authors":"Hao-Hsiang Wu, Ming-Shan Su, Thanh Dat Le, Nuo Xu, Guanfeng Wang, M. Stroe","doi":"10.1145/3548732.3548743","DOIUrl":"https://doi.org/10.1145/3548732.3548743","url":null,"abstract":"","PeriodicalId":330118,"journal":{"name":"Spatial Gems, Volume 1","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132337182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many geospatial datasets can be represented as a heat map, such as rainfall, population density, terrain elevation, and others. These heat maps tend to form clusters of high density areas among a background of low density areas. This gem presents an automatic way to detect such clusters, and segment the heat map into areas. Experiments are conducted for two datasets which correlate to population density and show that the segmentation aligns with metropolitan areas and is stable to the choice of dataset. The segmentation described in this gem can potentially aid geospatial algorithms by supplying a smart divide-and-conquer strategy, such that the algorithm does not need to run for the entire Earth, but rather there can be a fine-grained model for each area.
{"title":"Heat Map Segmentation","authors":"G. Wolff","doi":"10.1145/3548732.3548734","DOIUrl":"https://doi.org/10.1145/3548732.3548734","url":null,"abstract":"Many geospatial datasets can be represented as a heat map, such as rainfall, population density, terrain elevation, and others. These heat maps tend to form clusters of high density areas among a background of low density areas. This gem presents an automatic way to detect such clusters, and segment the heat map into areas. Experiments are conducted for two datasets which correlate to population density and show that the segmentation aligns with metropolitan areas and is stable to the choice of dataset. The segmentation described in this gem can potentially aid geospatial algorithms by supplying a smart divide-and-conquer strategy, such that the algorithm does not need to run for the entire Earth, but rather there can be a fine-grained model for each area.","PeriodicalId":330118,"journal":{"name":"Spatial Gems, Volume 1","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130464682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When dealing with locations on the road network, geographic coordinates, com monly represented in the form of (latitude, longitude), can often be difficult to use and are hard to interpret. Not only do these coordinates omit any explicit road network information, such as what road segment the location belongs to, but even simple operations such as speed computation cannot be performed with out summing road distance over the segment geometry. In certain applications, map projection [Yang et al. 1999] and linear referencing [Scarponcini 2002] have been utilized to make locations easier to analyze or to associate certain attributes without compromising precision. We propose extending the concept of linear ref erencing to the entirety of road-based locations and show that we can perform local searches, speed computation, location prediction, and interpolation with simple, linear formulas. Using Segment Fraction for Road-Network Locations
在处理道路网络上的位置时，通常以(纬度、经度)的形式表示的地理坐标往往难以使用，也难以解释。这些坐标不仅忽略了任何明确的道路网络信息，例如位置属于哪个路段，而且即使是简单的操作，如速度计算，如果没有将路段几何上的道路距离相加，也无法执行。在某些应用中，地图投影[Yang et al. 1999]和线性参考[Scarponcini 2002]已被用于使位置更容易分析或在不影响精度的情况下将某些属性关联起来。我们建议将线性参考的概念扩展到整个基于道路的位置，并表明我们可以使用简单的线性公式进行局部搜索，速度计算，位置预测和插值。使用分段分数的道路网络位置
{"title":"Using Segment Fraction for Road-Network Locations","authors":"Yuanyuan Pao","doi":"10.1145/3548732.3548745","DOIUrl":"https://doi.org/10.1145/3548732.3548745","url":null,"abstract":"When dealing with locations on the road network, geographic coordinates, com monly represented in the form of (latitude, longitude), can often be difficult to use and are hard to interpret. Not only do these coordinates omit any explicit road network information, such as what road segment the location belongs to, but even simple operations such as speed computation cannot be performed with out summing road distance over the segment geometry. In certain applications, map projection [Yang et al. 1999] and linear referencing [Scarponcini 2002] have been utilized to make locations easier to analyze or to associate certain attributes without compromising precision. We propose extending the concept of linear ref erencing to the entirety of road-based locations and show that we can perform local searches, speed computation, location prediction, and interpolation with simple, linear formulas. Using Segment Fraction for Road-Network Locations","PeriodicalId":330118,"journal":{"name":"Spatial Gems, Volume 1","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130982538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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