OpenACC Based GPU Parallelization of Plane Sweep Algorithm for Geometric Intersection

Line segment intersection is one of the elementary operations in computational geometry. Complex problems in Geographic Information Systems (GIS) like finding map overlays or spatial joins using polygonal data require solving segment intersections. Plane sweep paradigm is used for finding geometric intersection in an efficient manner. However, it is difficult to parallelize due to its in-order processing of spatial events. We present a new fine-grained parallel algorithm for geometric intersection and its CPU and GPU implementation using OpenMP and OpenACC. To the best of our knowledge, this is the first work demonstrating an effective parallelization of plane sweep on GPUs. We chose compiler directive based approach for implementation because of its simplicity to parallelize sequential code. Using Nvidia Tesla P100 GPU, our implementation achieves around 40X speedup for line segment intersection problem on 40K and 80K data sets compared to sequential CGAL library

Multi-Step Processing of Spatial Joins

Spatial joins are one of the most important operations for combining spatial objects of several relations. In this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by the following two steps. First of all, sophisticated approximations are used to identify answers as well as to filter out false hits from the set of candidates. For this purpose, we investigate various types of conservative and progressive approximations. In the last step, the exact geometry of the remaining candidates has to be tested against the join predicate. The time required for computing spatial join predicates can essentially be reduced when objects are adequately organized in main memory. In our approach, objects are first decomposed into simple components which are exclusively organized by a main-memory resident spatial data structure. Overall, we present a complete approach of spatial join processing on complex spatial objects. The performance of the individual steps of our approach is evaluated with data sets from real cartographic applications. The results show that our approach reduces the total execution time of the spatial join by factors

Pattern Matching for sets of segments

In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and measures that relate to collections of orthogonal line segments in the plane. Such collections arise naturally from problems in mapping buildings and robot exploration. We propose a new measure of segment similarity called a \emph{coverage measure}, and present efficient algorithms for maximising this measure between sets of axis-parallel segments under translations. Our algorithms run in time O(n^3\polylog n) in the general case, and run in time O(n^2\polylog n) for the case when all segments are horizontal. In addition, we show that when restricted to translations that are only vertical, the Hausdorff distance between two sets of horizontal segments can be computed in time roughly O(n^{3/2}{\sl polylog}n). These algorithms form significant improvements over the general algorithm of Chew et al. that takes time $O(n^4 \log^2 n)$. In the second part of this paper we address the problem of matching polygonal chains. We study the well known \Frd, and present the first algorithm for computing the \Frd under general translations. Our methods also yield algorithms for computing a generalization of the \Fr distance, and we also present a simple approximation algorithm for the \Frd that runs in time O(n^2\polylog n).Comment: To appear in the 12 ACM Symposium on Discrete Algorithms, Jan 200

The combination of spatial access methods and computational geometry in geographic database systems

Geographic database systems, known as geographic information systems (GISs) particularly among non-computer scientists, are one of the most important applications of the very active research area named spatial database systems. Consequently following the database approach, a GIS hag to be seamless, i.e. store the complete area of interest (e.g. the whole world) in one database map. For exhibiting acceptable performance a seamless GIS hag to use spatial access methods. Due to the complexity of query and analysis operations on geographic objects, state-of-the-art computational geomeny concepts have to be used in implementing these operations. In this paper, we present GIS operations based on the compuational geomeny technique plane sweep. Specifically, we show how the two ingredients spatial access methods and computational geomeny concepts can be combined für improving the performance of GIS operations. The fruitfulness of this combination is based on the fact that spatial access methods efficiently provide the data at the time when computational geomeny algorithms need it für processing. Additionally, this combination avoids page faults and facilitates the parallelization of the algorithms.

Articular human joint modelling

Copyright @ Cambridge University Press 2009.The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints