Simple feature model-based non-weighted polygon overlapping analysis operations include eight basic tools: intersection, difference, merge, symmetrical difference, union, update, identity, and spatial join. It is assumed that the determination of the "one-to-many" or "many-to-many" mapping relationships between polygons of the two overlapping layers is the primary prerequisite to the implementation of parallel polygon overlay toolset at the feature layer level. Polygon difference, intersection, identity, update, and spatial join algorithms must address the "one-to-many" mapping relationships between polygons of the overlapping layers. However, the "many-to-many" relationships must be handled by polygon merge, symmetrical difference, and union algorithms. In this research, we analyzed the differences and similarities among the parallel implementation approaches and optimization methods of the eight polygon overlapping tools from the perspective of data parallelism with the OpenMP parallel programming model. We proposed an improved group-relation-minimizing data partition method to realize complex data decomposition without geometry cutting and sewing, and adopted a vertex number indicator-based strategy for load balancing, and several optimization approaches, including the method of avoiding potential bottleneck in polygon merging, strategy for addressing the defect in polygon symmetrical differencing using the XOR operator of the Vatti polygon clipping algorithm, and the strategies of pre-filtering of features with R-tree and bulk loading of structural stored vector data in MySQL. We developed and implemented the parallel polygon overlapping toolset by systematically summarizing the applicative data decomposition method, characters of overlay operations, the Vatti polygon clipping algorithm, load balancing and parallel schedule strategies. The logical flow of parallel polygon union algorithm was introduced as an example to describe the general process of designing parallel polygon overlapping tools. Parallel overlapping case study was also conducted to analyze the effectiveness of the implementation and optimization methods. The experimental results show that the improved group-relation-minimizing data partition method can bring approximately 92% parallel acceleration and more parallel robustness for polygon union; different expected group size specified in the data division method proposed in this research can lead to different parallel speedup benchmarks; the vertex-number based load balancing strategy can give the parallel difference tool about 21% performance improvement; the two-way merge algorithm applied in the parallel merge tool can address the potential performance bottleneck; the dynamic schedule strategy of OpenMP can bring higher speedup than the static and guided schedule strategies; the pre-filtering approach can bring more than 20-fold acceleration for parallel polygon difference; the bulk loading strategy of structural stored vector data can effectively reduce the performance loss due to the disk I/O. The implementation approaches and optimization methods introduced in this study show different applicable features on the developing of the eight overlapping tools. The methods and strategies introduced above can be potential alternatives when launching similar parallelization tasks of other spatial analysis algorithms. This research not only provided theoretical basis and guidance of methodologies for the design and development of parallel polygon overlapping tools at the feature layer level in the multi-core environment, but also presented important practical significance in improving the system resource utilization and computational efficiency of spatial analyses for massive personal and low-cost GIS applications.

This historiographical article examines the ways by which geographers wrote about the history of geography in the past and provides suggestions for the future. We refer to the actual history of geography as "HG1" and the writings of historians about the history as "HG2". The essence of historiography of geography is to examine how HG1 record, explain HG2 in its places and times rather than it "should be" today. There are three types of historiographical methods in HG2: (1) positivism historiography, such as The Nature of Geography, All possible words: A history of geographical ideas, an "essentialist" historiography which postulates what geography is as a science "in essence", and construct geography's history base on this approach; (2) constructivism historiography, such as the contributions by Trevor J. Barnes, who insisted that geography is constructed by society; (3) historical contextualism historiography, emphasized by British historian of geography, Robert J. Mayhew, who drew on the ideas from so-called "Cambridge school" scholars, such as Michael Oakeshott and Quentin Skinner, etc., and the aim is to think how to write the histories of geographies, rather than history of geography. Both Robert J. Mayhew and Charles W. J. Withers insisted that geography was so different in different places and different times, implying that we should avoid an inevitable or progressive "essentialist" historiography which postulates what geography is as a science "in essence". Of course, historical contextualism historiography has been related to the works in China such as From dynastic geography to historical geography: A change in perspective towards the geographical past of China (in English) and From chaos to order: Palaeoid geographical thought in China (in Chinese), published by Xiaofeng Tang. Tang thinks that the history of Chinese geography should be concerned with the past for its own sake, which means in this context the ways by which Chinese geography was understood at the time, rather than the ways by which it can be understood in the light of the present-day practice of the discipline. So, Tang constructed the history of dynastic geography and explained it from the perspectives of Chinese ancient culture, words and concepts. The thought has been inherited by his student, Sheng Pan, in his doctoral thesis, Ideas, system and interest in the geography of the Sung dynasties (Peking University, 2008). Based on the discussions, we suggest that an effective way for the progress of historiography is to make a choice among these methods, and we think positivism historiographical method is a good choice for modern history; historical contextualism historiographical method is beneficial to ancient and early modern history, especially to non-western or non-Anglophone places like China.