Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Using distance maps for accurate surface representation in sampled volumes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
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
Kizamu: a system for sculpting digital characters
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Simulation of wrinkled surfaces
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Computing Voronoi skeletons of a 3-D polyhedron by space subdivision
Computational Geometry: Theory and Applications
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Penalized-Distance Volumetric Skeleton Algorithm
IEEE Transactions on Visualization and Computer Graphics
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
A subdivision algorithm for computer display of curved surfaces.
A subdivision algorithm for computer display of curved surfaces.
Efficient collision detection for animation and robotics
Efficient collision detection for animation and robotics
Efficient algorithms for solving static hamilton-jacobi equations
Efficient algorithms for solving static hamilton-jacobi equations
Interactive Deformation and Visualization of Level Set Surfaces Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Interactive 3D distance field computation using linear factorization
I3D '06 Proceedings of the 2006 symposium on Interactive 3D graphics and games
Fast proximity computation among deformable models using discrete Voronoi diagrams
ACM SIGGRAPH 2006 Papers
Short paper: approximating distance fields in image space
EGVE - JVRC'10 Proceedings of the 16th Eurographics conference on Virtual Environments & Second Joint Virtual Reality
Computing local signed distance fields for large polygonal models
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Approximating functions on a mesh with restricted Voronoï diagrams
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a new parameterized representation called surface distance maps for distance computations on piecewise 2-manifold primitives. Given a set of orientable 2-manifold primitives, the surface distance map represents the (non-zero) signed distance-to-closest-primitive mapping at each point on a 2-manifold. The distance mapping is computed from each primitive to the set of remaining primitives. We present an interactive algorithm for computing the surface distance map of triangulated meshes using graphics hardware. We precompute a surface parameterization and use the it to define an affine transformation for each mesh primitive. Our algorithm efficiently computes the distance field by applying this affine transformation to the distance functions of the primitives and evaluating these functions using texture mapping hardware. In practice, our algorithm can compute very high resolution surface distance maps at interactive rates and provides tight error bounds on their accuracy. We use surface distance maps for path planning and proximity query computation among complex models in dynamic environments. Our approach can perform planning and proximity queries in a dynamic environment with hundreds of objects at interactive rates and offer significant speedups over prior algorithms.