gStar4D

gStar4D computes the 3D Delaunay triangulation on the GPU.

The gStar4D algorithm uses neighbourhood information in the 3D digital Voronoi diagram as an approximation of the 3D Delaunay triangulation. It uses this to perform massively parallel creation of stars of each input point lifted to 4D and employs an unique star splaying approach to splay these 4D stars in parallel and make them consistent. The result is the 3D Delaunay triangulation of the input constructed fully on the GPU.

Our CUDA implementation of gStar4D is robust and achieves a speedup of up to 5 times over the 3D Delaunay triangulator of CGAL.

Setup

This project has been primarily tested on Windows 7 64-bit OS using Visual Studio 2008 and CUDA 4.0. This is a workstation with Intel i7 2600K CPU and NVIDIA GTX 580 GPU.

On Windows

Open the GDelaunay solution file using Visual Studio and compile with the Release build for maximum performance.

On Linux

CMake is needed to build gStar4D on Linux. Make sure that the CUDA capability values in the CMakeLists.txt file matches that of your GPU.

To build and execute using CMake:

$ cd gstar4d
$ mkdir build
$ cd build
$ cmake ..
$ make
$ ./gstar4d --help

Documentation

Chapter 6 of my PhD thesis describes the details of the gStar4D algorithm.

Reference

To refer to gStar4D, please use:

Ashwin Nanjappa, "Delaunay triangulation in R3 on the GPU", PhD thesis,
School of Computing, National University of Singapore, 2012.

To cite gStar4D, please use this BibTeX entry:

@phdthesis{Ashwin2012GPUDelaunay,
    author = {Nanjappa, Ashwin},
    school = {National University of Singapore},
    title = {Delaunay triangulation in R3 on the {GPU}},
    year = {2012}
}

License

Author: Ashwin Nanjappa

Project: gStar4D

Copyright (c) 2013, School of Computing, National University of Singapore. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

Neither the name of the National University of Singapore nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission from the National University of Singapore.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.