Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
Intrinsic scale space for images on surfaces: The Geodesic Curvature Flow
Graphical Models and Image Processing
Capturing the behavior of bubbles and drops using the variational level set approach
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Level set methods: an overview and some recent results
Journal of Computational Physics
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
Finding Shortest Paths on Surfaces Using Level Sets Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Computational Physics
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Visibility and its dynamics in a PDE based implicit framework
Journal of Computational Physics
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
A variational approach to path planning in three dimensions using level set methods
Journal of Computational Physics
Journal of Computational Physics
Geometric curve flows on parametric manifolds
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A semi-Lagrangian scheme for the curve shortening flow in codimension-2
Journal of Computational Physics
Diffusion generated motion of curves on surfaces
Journal of Computational Physics
Journal of Mathematical Imaging and Vision
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Discretizing delta functions via finite differences and gradient normalization
Journal of Computational Physics
A grid based particle method for evolution of open curves and surfaces
Journal of Computational Physics
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
SIAM Journal on Scientific Computing
A framework for intrinsic image processing on surfaces
Computer Vision and Image Understanding
A method for automated cortical surface registration and labeling
WBIR'12 Proceedings of the 5th international conference on Biomedical Image Registration
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The level-set method has been successfully applied to a variety of problems that deal with curves in R2 or surfaces in R3. We present here a combination of these two cases, creating a level-set representation for curves constrained to lie on surfaces. We study primarily geometrically based motions of these curves on stationary surfaces while allowing topological changes in the curves (i.e., merging and breaking) to occur. Applications include finding geodesic curves and shortest paths and curve shortening on surfaces. Further applications can be arrived at by extending those for curves moving in R2 to surfaces. The problem of moving curves on surfaces can also be viewed as a simple constraint problem and may be useful in studying more difficult versions. Results show that our representation can accurately handle many geometrically based motions of curves on a wide variety of surfaces while automatically enforcing topological changes in the curves when they occur and automatically fixing the curves to lie on the surfaces. The method can also be easily extended to higher dimensions.