Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
Linear algebra operators for GPU implementation of numerical algorithms
ACM SIGGRAPH 2003 Papers
Real-time Voxelization for Complex Polygonal Models
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Inviscid and incompressible fluid simulation on triangle meshes: Research Articles
Computer Animation and Virtual Worlds - Special Issue: The Very Best Papers from CASA 2004
Adapted unstructured LBM for flow simulation on curved surfaces
Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation
3D Distance Fields: A Survey of Techniques and Applications
IEEE Transactions on Visualization and Computer Graphics
Fast Scene Voxelization and Applications
ACM SIGGRAPH 2006 Sketches
An Improvement of a Recent Eulerian Method for Solving PDEs on General Geometries
Journal of Scientific Computing
Solving general shallow wave equations on surfaces
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Fluid flow on interacting deformable surfaces
ACM SIGGRAPH 2007 posters
The Visual Computer: International Journal of Computer Graphics
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
Interactive Reaction-Diffusion on Surface Tiles
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Composite finite elements for 3D image based computing
Computing and Visualization in Science
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Surface processing methods for point sets using finite elements
Computers and Graphics
Finite Element Methods on Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces
SIAM Journal on Scientific Computing
Estimating the Laplace-Beltrami operator by restricting 3D functions
SGP '09 Proceedings of the Symposium on Geometry Processing
Segmentation on surfaces with the closest point method
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Geometry-based control of fire simulation
The Visual Computer: International Journal of Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Fast parallel surface and solid voxelization on GPUs
ACM SIGGRAPH Asia 2010 papers
SIAM Journal on Scientific Computing
VoxelPipe: a programmable pipeline for 3D voxelization
Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
A Hexahedral Multigrid Approach for Simulating Cuts in Deformable Objects
IEEE Transactions on Visualization and Computer Graphics
Solving PDEs on manifolds with global conformal parametriazation
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Closest point turbulence for liquid surfaces
ACM Transactions on Graphics (TOG)
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The Closest Point Method (CPM) is a method for numerically solving partial differential equations (PDEs) on arbitrary surfaces, independent of the existence of a surface parametrization. The CPM uses a closest point representation of the surface, to solve the unmodified Cartesian version of a surface PDE in a 3D volume embedding, using simple and well-understood techniques. In this paper, we present the numerical solution of the wave equation and the incompressible Navier-Stokes equations on surfaces via the CPM, and we demonstrate surface appearance and shape variations in real-time using this method. To fully exploit the potential of the CPM, we present a novel GPU realization of the entire CPM pipeline. We propose a surface-embedding adaptive 3D spatial grid for efficient representation of the surface, and present a high-performance approach using CUDA for converting surfaces given by triangulations into this representation. For real-time performance, CUDA is also used for the numerical procedures of the CPM. For rendering the surface (and the PDE solution) directly from the closest point representation without the need to reconstruct a triangulated surface, we present a GPU ray-casting method that works on the adaptive 3D grid. © 2012 Wiley Periodicals, Inc.