Computing Three-dimensional Constrained Delaunay Refinement Using the GPU

We propose the first GPU algorithm for the 3D triangulation refinement problem. For an input of a piecewise linear complex $\mathcal{G}$ and a constant $B$, it produces, by adding Steiner points, a constrained Delaunay triangulation conforming to $\mathcal{G}$ and containing tetrahedra mostly of radius-edge ratios smaller than $B$. Our implementation of the algorithm shows that it can be an order of magnitude faster than the best CPU algorithm while using a similar amount of Steiner points to produce triangulations of comparable quality

A parallel algorithm for Delaunay triangulation of moving points on the plane

Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very important in computational geometry for dealing with moving objects. However, when dealing with moving points, maintaining a dynamically changing Delaunay triangulation can be challenging. So, In this case, we have to update triangulation repeatedly. If points move so far, it is better to rebuild the triangulation. One approach to handle moving points is to use an incremental algorithm. For the case that points move slowly, we can give a faster algorithm than rebuilding it. Furthermore, sequential algorithms can be computationally expensive for large datasets. So, one way to compute as fast as possible is parallelism. In this paper, we propose a parallel algorithm for moving points. we propose an algorithm that divides datasets into equal partitions and give every partition to one block. Each block satisfay the Delaunay constraints after each time step and uses delete and insert algorithms to do this. We show this algorithm works faster than serial algorithms

Parallel constrained Delaunay triangulation

In this paper we propose a new GPU method able to compute the 2D constrained Delaunay triangulation of a planar straight line graph consisting of points and segments. The method is based on an incremental insertion, taking special care to avoid conflicts during concurrent insertion of points into the triangulation and concurrent edge flips.Ministerio de Ciencia e Innovació

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

Real-Time Dense Stereo Matching With ELAS on FPGA Accelerated Embedded Devices

For many applications in low-power real-time robotics, stereo cameras are the sensors of choice for depth perception as they are typically cheaper and more versatile than their active counterparts. Their biggest drawback, however, is that they do not directly sense depth maps; instead, these must be estimated through data-intensive processes. Therefore, appropriate algorithm selection plays an important role in achieving the desired performance characteristics. Motivated by applications in space and mobile robotics, we implement and evaluate a FPGA-accelerated adaptation of the ELAS algorithm. Despite offering one of the best trade-offs between efficiency and accuracy, ELAS has only been shown to run at 1.5-3 fps on a high-end CPU. Our system preserves all intriguing properties of the original algorithm, such as the slanted plane priors, but can achieve a frame rate of 47fps whilst consuming under 4W of power. Unlike previous FPGA based designs, we take advantage of both components on the CPU/FPGA System-on-Chip to showcase the strategy necessary to accelerate more complex and computationally diverse algorithms for such low power, real-time systems.Comment: 8 pages, 7 figures, 2 table

Characterization and surface reconstruction of objects in tomographic images of composite materials

Dissertação para obtenção do Grau de Mestre em Engenharia InformáticaIn the scope of the project Tomo-GPU supported by FCT / MCTES the aim is to build an interactive graphical environment that allows a Materials specialist to define their own programs for analysis of 3D tomographic images. This project aims to build a tool to characterize and investigate the identified objects, where the user can define search criteria such as size, orientation, bounding boxes, among others. All this processing will be done on a desktop computer equipped with a graphics card with some processing power. On the proposed solution the modules for characterizing objects, received from the identification phase, will be implemented using some existing software libraries, most notably the CGAL library. The characterization modules with bigger execution times will be implemented using OpenCL and GPUs. With this work the characterization and reconstruction of objects and their research can now be done on conventional machines, using GPUs to accelerate the most time-consuming computations. After the conclusion of this thesis, new tools that will help to improve the current development cycle of new materials will be available for Materials Science specialists