Motivated by the needs of a scalable out-of-core surface reconstruction algorithm available on the cloud, this paper addresses the computation of distributed Delaunay triangulations of massive point sets. The proposed algorithm takes as input a point cloud and first partitions it across multiple processing elements into tiles of relatively homogeneous point sizes. The distributed computation and communication between processing elements is orchestrated so that each one discovers the Delaunay neighbors of its input points within the theoretical overall Delaunay triangulation of all points and computes locally a partial view of this triangulation. This approach prevents memory limitations by never materializing the global triangulation. This efficiency is due to our proposed uncentralized model to represent, manage and locally construct the triangulation corresponding to each tile. The point set is first partitioned into non-overlapping tiles, then we construct within each tile the Delaunay triangulation of the local points and a minimal set of replicated foreign points in order to capture the simplices spanning multiple tiles. Inspired by the star splaying approach for Delaunay triangulation computation/repair, communication is limited to exchanging points of potential Delaunay neighbors across tiles. Therefore, our method is guaranteed to reconstruct, within each tile, a triangulation that contains the star of its local points, as though it were computed within the Delaunay triangulation of all points. The proposed algorithm is implemented with Spark for the scheduling and C ++ for the geometric computations. This allows both an optimal scheduling on multiple machines and efficient low-level computation. The results show the efficiency of our algorithm in terms of speedup and strong scaling on a classical Spark configuration with both synthetic and real use case datasets.
This paper addresses the creation and maintenance of partitions of city surfaces for mapping and transportation applications. It proposes a hierarchical spatial surface partitioning, encoding the spatial partition with a 2D arrangement and structuring a generic hierarchy of semantic objects with a directed acyclic graph (DAG), in which the leaves point to the partition elements (polygonal regions, line strings, points). Semantic objects such as buildings, sidewalks and roads are described by grouping other objects and partition elements with their semantic relationships. In the proposed generic data model, geometry and spatial relationships of the semantic objects are respectively described by the geometry and topology of the planar partition. The proposed geometric data structure for creating and maintaining this partition is a 2D arrangement. In addition, the hierarchical object model encodes the thematic and semantic relationships between the objects. Besides the data model, methods and algorithms are discussed for leveraging existing vector datasets to create and maintain such partitions. These partitions are then fit to further processing and analysis using computational geometry and graph theory algorithms. For this purpose, three application-wise generic algorithms were integrated into our system called Streetmaker: two skeleton operators for centerline generation (straight skeleton and medial axis) and connectivity graphs for itinerary calculations. Moreover, specific algorithms can be integrated into Streetmaker for specific applications. We demonstrated an example usage of this framework for generating static obstacle avoiding pedestrian network graphs. The representation of the network graph and the process used to generate it, can be considered as the second contribution of our work besides the proposed data model.
, 115 pages Polygonal meshes are a common way of representing 3D surface models in many different areas of computer graphics and geometry processing. However, these models are becoming more and more complex which increases the cost of processing these models. In order to reduce this cost, mesh simplification algorithms are developed. Another important property of a polygonal mesh model is that whether it is regular or not. Regular meshes have many advantages over the irregular ones in terms of memory requirements, efficient processing, rendering etc. In this thesis work, both mesh simplification and regular remeshing algorithms are studied. Moreover, some of the popular mesh libraries are compared with respect to their approaches and performance to the mesh simplification. In addition, mesh models with disk topology are remeshed and converted to regular ones.
Abstract. This paper deals with the distributed computation of Delaunay triangulations of massive point sets, mainly motivated by the needs of a scalable out-of-core surface reconstruction workflow from massive urban LIDAR datasets. Such a data often corresponds to a huge point cloud represented through a set of tiles of relatively homogeneous point sizes. This will be the input of our algorithm which will naturally partition this data across multiple processing elements. The distributed computation and communication between processing elements is orchestrated efficiently through an uncentralized model to represent, manage and locally construct the triangulation corresponding to each tile. Initially inspired by the star splaying approach, we review the Tile& Merge algorithm for computing Distributed Delaunay Triangulations on the cloud, provide a theoretical proof of correctness of this algorithm, and analyse the performance of our Spark implementation in terms of speedup and strong scaling in both synthetic and real use case datasets. A HPC implementation (e.g. using MPI), left for future work, would benefit from its more efficient message passing paradigm but lose the robustness and failure resilience of our Spark approach.
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