Validation and automatic repair of planar partitions using a constrained triangulation

Planar partitions are frequently used to model, among others, land cover, cadastral parcels and administrative boundaries. In practice, they are often stored as a set of individual polygons to which attributes are attached (e.g. with the Simple Features paradigm), causing different errors and inconsistencies (e.g. gaps, overlaps and disconnected polygons), which are introduced during their creation, manipulation and exchange. These errors severely hamper the use of planar partitions in other software (e.g. due to false assumptions causing erroneous calculations). Existing approaches to validate planar partitions involve first building a planar graph of the polygons and enforcing constraints, then repair is done by snapping vertices and edges of this graph. We argue that these approaches have many shortcomings in terms of complexity, numerical robustness and difficulty of implementation, and do not guarantee valid results. Furthermore, they are semi-automatic, requiring manual user intervention. We propose in this paper a novel method to validate and automatically repair planar partitions. It uses a constrained triangulation of the polygons as a base-which by definition is a planar partition-and only simple operations are needed (i.e. labelling of triangles) to both validate and repair. Perhaps the biggest advantage of our method is that we can guarantee that a planar partition is valid after repair. In the paper we describe the details of our method, our implementation, and the experiments we have done with real-world datasets. We show that our implementation scales to big datasets and that it offers better capabilities and overall performance than existing solutions

On local heuristics to speed up polygon-polygon intersection tests

The polygon-polygon intersection operation is CPU-intensive. Many data structures look into decomposing the polygons into multiple yet simple pieces to speed up the polygon-polygon intersection operation. This paper addresses local heuristics that can be adopted in these data structures by using local information about the simple polygon pieces to decide upon polygon-polygon intersections without having to perform this costly operation. The significance and effectiveness of each of the heuristics is studied. The paper also shows how these heuristics can be put together to perform a polygon join operation. Experiments are given to demonstrate the savings both in CPU and in I/O that result from these local heuristics

Multi-Dimensional Joins

We present three novel algorithms for performing multi-dimensional joins and an in-depth survey and analysis of a low-dimensional spatial join. The first algorithm, the Iterative Spatial Join, performs a spatial join on low-dimensional data and is based on a plane-sweep technique. As we show analytically and experimentally, the Iterative Spatial Join performs well when internal memory is limited, compared to competing methods. This suggests that the Iterative Spatial Join would be useful for very large data sets or in situations where internal memory is a shared resource and is therefore limited, such as with today's database engines which share internal memory amongst several queries. Furthermore, the performance of the Iterative Spatial Join is predictable and has no parameters which need to be tuned, unlike other algorithms. The second algorithm, the Quickjoin algorithm, performs a higher-dimensional similarity join in which pairs of objects that lie within a certain distance epsilon of each other are reported. The Quickjoin algorithm overcomes drawbacks of competing methods, such as requiring embedding methods on the data first or using multi-dimensional indices, which limit the ability to discriminate between objects in each dimension, thereby degrading performance. A formal analysis is provided of the Quickjoin method, and experiments show that the Quickjoin method significantly outperforms competing methods. The third algorithm adapts incremental join techniques to improve the speed of calculating the Hausdorff distance, which is used in applications such as image matching, image analysis, and surface approximations. The nearest neighbor incremental join technique for indices that are based on hierarchical containment use a priority queue of index node pairs and bounds on the distance values between pairs, both of which need to modified in order to calculate the Hausdorff distance. Results of experiments are described that confirm the performance improvement. Finally, a survey is provided which instead of just summarizing the literature and presenting each technique in its entirety, describes distinct components of the different techniques, and each technique is decomposed into an overall framework for performing a spatial join