Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations
SIAM Journal on Mathematical Analysis
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Fast tree-based redistancing for level set computations
Journal of Computational Physics
A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs
Journal of Computational Physics
Computer Vision and Image Understanding
A level set method for thin film epitaxial growth
Journal of Computational Physics
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A finite element technique for multifluid incompressible flow using Eulerian grids
Journal of Computational Physics
Differential equation-based wall distance computation for DES and RANS
Journal of Computational Physics
Journal of Mathematical Imaging and Vision
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Computer Vision and Image Understanding
Collision between deformable objects using fast-marching on tetrahedral models
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Visibility and its dynamics in a PDE based implicit framework
Journal of Computational Physics
Local or Global Minima: Flexible Dual-Front Active Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient active contour and K-means algorithms in image segmentation
Scientific Programming - Distributed Computing and Applications
Journal of Computational Physics
Bayesian surface reconstruction via iterative scan alignment to an optimized prototype
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Constrained curve fitting on manifolds
Computer-Aided Design
Fitting curves and surfaces to point clouds in the presence of obstacles
Computer Aided Geometric Design
Industrial geometry: recent advances and applications in CAD
Computer-Aided Design
SARDF: signed approximate real distance functions in heterogeneous objects modeling
Heterogeneous objects modelling and applications
Numerical Method for Interaction Among Multi-particle, Fluid and Arbitrary Shape Structure
Journal of Scientific Computing
Distance to objects built with set operations in constructive solid modeling
Proceedings of the 13th International Conference on Humans and Computers
Journal of Scientific Computing
Journal of Scientific Computing
Shortest path in a multiply-connected domain having curved boundaries
Computer-Aided Design
A uniformly second order fast sweeping method for eikonal equations
Journal of Computational Physics
A localized re-initialization equation for the conservative level set method
Journal of Computational Physics
Hi-index | 31.48 |
We present two fast and simple algorithms for approximating the distance function for given isolated points on uniform grids. The algorithms are then generalized to compute the distance to piecewise linear objects. By incorporating the geometry of Huygens' principle in the reverse order with the classical viscosity solution theory for the eikonal equation |∇u| = 1, the algorithms become almost purely algebraic and yield very accurate approximations. The generalized closest point formulation used in the second algorithm provides a framework for further extension to compute the distance accurately to smooth geometric objects on different grid geometries, without the construction of the Voronoi diagrams. This method provides a fast and simple translator of data commonly given in computational geometry to the volumetric representation used in level set methods.