Introduction to Solid Modeling
Introduction to Solid Modeling
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A comparison of tetrahedron quality measures
Finite Elements in Analysis and Design
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Three-Dimensional Front Tracking
SIAM Journal on Scientific Computing
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
A semi-Lagrangian contouring method for fluid simulation
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2006 Papers
Face offsetting: A unified approach for explicit moving interfaces
Journal of Computational Physics
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Fluid Simulation
Deforming meshes that split and merge
ACM SIGGRAPH 2009 papers
Robust Topological Operations for Dynamic Explicit Surfaces
SIAM Journal on Scientific Computing
TransforMesh: a topology-adaptive mesh-based approach to surface evolution
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
A multiscale approach to mesh-based surface tension flows
ACM SIGGRAPH 2010 papers
Dynamic local remeshing for elastoplastic simulation
ACM SIGGRAPH 2010 papers
Physics-inspired topology changes for thin fluid features
ACM SIGGRAPH 2010 papers
Topology-Adaptive Mesh Deformation for Surface Evolution, Morphing, and Multiview Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mathematical foundation of the optimization-based fluid animation method
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Cut Locus Construction Using Deformable Simplicial Complexes
ISVD '11 Proceedings of the 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering
Multiphase flow of immiscible fluids on unstructured moving meshes
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Multiphase flow of immiscible fluids on unstructured moving meshes
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Topology optimization using an explicit interface representation
Structural and Multidisciplinary Optimization
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We present a novel, topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex (DSC). In the DSC method, the interface is represented explicitly as a piecewise linear curve (in 2D) or surface (in 3D) which is a part of a discretization (triangulation/tetrahedralization) of the space, such that the interface can be retrieved as a set of faces separating triangles/tetrahedra marked as inside from the ones marked as outside (so it is also given implicitly). This representation allows robust topological adaptivity and, thanks to the explicit representation of the interface, it suffers only slightly from numerical diffusion. Furthermore, the use of an unstructured grid yields robust adaptive resolution. Also, topology control is simple in this setting. We present the strengths of the method in several examples: simple geometric flows, fluid simulation, point cloud reconstruction, and cut locus construction.