Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Octree-based decimation of marching cubes surfaces
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Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Fast and simple 2D geometric proximity queries using graphics hardware
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
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Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Photon mapping on programmable graphics hardware
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
ACM SIGGRAPH 2003 Papers
Accurate Computation of the Medial Axis of a Polyhedron
Accurate Computation of the Medial Axis of a Polyhedron
Efficient collision detection for animation and robotics
Efficient collision detection for animation and robotics
Efficient algorithms for solving static hamilton-jacobi equations
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Resolution independent curve rendering using programmable graphics hardware
ACM SIGGRAPH 2005 Papers
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
ACM SIGGRAPH 2005 Papers
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Feature-Sensitive Subdivision and Isosurface Reconstruction
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Fast proximity computation among deformable models using discrete Voronoi diagrams
ACM SIGGRAPH 2006 Papers
ACM SIGGRAPH 2006 Sketches
GI '07 Proceedings of Graphics Interface 2007
Programmable shaders for deformation rendering
Proceedings of the 22nd ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Real-time navigation of independent agents using adaptive roadmaps
Proceedings of the 2007 ACM symposium on Virtual reality software and technology
Single-pass GPU solid voxelization for real-time applications
GI '08 Proceedings of graphics interface 2008
Real-time path planning for virtual agents in dynamic environments
ACM SIGGRAPH 2008 classes
Real-time navigation of independent agents using adaptive roadmaps
ACM SIGGRAPH 2008 classes
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Parallel Banding Algorithm to compute exact distance transform with the GPU
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Discrete construction of order-k voronoi diagram
ICICA'10 Proceedings of the First international conference on Information computing and applications
Novel geometrical voxelization approach with application to streamlines
Journal of Computer Science and Technology
Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids
Journal of Computational Physics
Discrete construction of power network voronoi diagram
ICICA'11 Proceedings of the Second international conference on Information Computing and Applications
SMI 2012: Full GPU accelerated convex hull computation
Computers and Graphics
Efficient Image-Based Proximity Queries with Object-Space Precision
Computer Graphics Forum
Short paper: approximating distance fields in image space
EGVE - JVRC'10 Proceedings of the 16th Eurographics conference on Virtual Environments & Second Joint Virtual Reality
Efficient collision detection for brittle fracture
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Particle level set advection for the interactive visualization of unsteady 3D flow
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Computing local signed distance fields for large polygonal models
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Efficient collision detection for brittle fracture
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Accurate and efficient rendering of detail using directional distance maps
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
CHOMP: Covariant Hamiltonian optimization for motion planning
International Journal of Robotics Research
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We present an interactive algorithm to compute discretized 3D Euclidean distance fields. Given a set of piecewise linear geometric primitives, our algorithm computes the distance field for each slice of a uniform spatial grid. We express the non-linear distance function of each primitive as a dot product of linear factors. The linear terms are efficiently computed using texture mapping hardware. We also improve the performance by using culling techniques that reduce the number of distance function evaluations using bounds on Voronoi regions of the primitives. Our algorithm involves no preprocessing and is able to handle complex deforming models at interactive rates. We have implemented our algorithm on a PC with NVIDIA GeForce 7800 GPU and applied it to models composed of thousands of triangles. We demonstrate its application to medial axis approximation and proximity computations between rigid and deformable models. In practice, our algorithm is more accurate and almost one order of magnitude faster as compared to previous distance computation algorithms that use graphics hardware.