Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
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
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Implicit fairing of irregular meshes using diffusion and curvature flow
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
Journal of Computational Physics
Practical animation of liquids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Level set surface editing operators
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Progressive encoding of complex isosurfaces
ACM SIGGRAPH 2003 Papers
Geometric surface processing via normal maps
ACM Transactions on Graphics (TOG)
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Simulating water and smoke with an octree data structure
ACM SIGGRAPH 2004 Papers
A conservative level set method for two phase flow
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
ACM SIGGRAPH 2004 Course Notes
A semi-Lagrangian contouring method for fluid simulation
ACM Transactions on Graphics (TOG)
Hierarchical RLE level set: A compact and versatile deformable surface representation
ACM Transactions on Graphics (TOG)
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Physics based boiling simulation
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Interactive relighting of dynamic refractive objects
ACM SIGGRAPH 2008 papers
Fast viscoelastic behavior with thin features
ACM SIGGRAPH 2008 papers
Matching fluid simulation elements to surface geometry and topology
ACM SIGGRAPH 2010 papers
Technical Section: Interactive free-form level-set surface-editing operators
Computers and Graphics
Liquid simulation with mesh-based surface tracking
ACM SIGGRAPH 2011 Courses
Simulating free surface flow with very large time steps
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Mass-conserving eulerian liquid simulation
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Simulating free surface flow with very large time steps
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Mass-conserving eulerian liquid simulation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
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We present a purely Eulerian framework for geometry processing of surfaces and foliations. Contrary to current Eulerian methods used in graphics, we use conservative methods and a variational interpretation, offering a unified framework for routine surface operations such as smoothing, offsetting, and animation. Computations are performed on a fixed volumetric grid without recourse to Lagrangian techniques such as triangle meshes, particles, or path tracing. At the core of our approach is the use of the Coarea Formula to express area integrals over isosurfaces as volume integrals. This enables the simultaneous processing of multiple isosurfaces, while a single interface can be treated as the special case of a dense foliation. We show that our method is a powerful alternative to conventional geometric representations in delicate cases such as the handling of high-genus surfaces, weighted offsetting, foliation smoothing of medical datasets, and incompressible fluid animation.