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31
Matching Fluid Simulation Elements to Surface Geometry and Topology
"... Figure 1: Sphere Splash. Coupling an explicit surface tracker to a Voronoi simulation mesh built from pressure points sampled in a geometryaware fashion lets us capture very fine details in this sphere splash animation that uses only 314K tetrahedra. We introduce an Eulerian liquid simulation frame ..."
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Cited by 35 (7 self)
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Figure 1: Sphere Splash. Coupling an explicit surface tracker to a Voronoi simulation mesh built from pressure points sampled in a geometryaware fashion lets us capture very fine details in this sphere splash animation that uses only 314K tetrahedra. We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples. Constructing the simulation mesh in this way allows us to place samples anywhere in the computational domain; we exploit this by choosing samples that accurately capture the geometry and topology of the liquid surface. When combined with highresolution explicit surface tracking this allows us to simulate nearly arbitrarily thin features, while eliminating noise and other artifacts that arise when there is a resolution mismatch between the simulation and the surface—and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh. In addition, we present a simplified Voronoi/Delaunay mesh velocity interpolation scheme, and a direct extension of embedded free surfaces and solid boundaries to Voronoi meshes.
G.: Reconstructing surfaces of particlebased fluids using anisotropic kernels
 In Proc. of the 2010 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim
, 2010
"... In this paper we present a novel surface reconstruction method for particlebased fluid simulators such as Smoothed Particle Hydrodynamics. In particlebased simulations, fluid surfaces are usually defined as a level set of an implicit function. We formulate the implicit function as a sum of anisotr ..."
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Cited by 24 (3 self)
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In this paper we present a novel surface reconstruction method for particlebased fluid simulators such as Smoothed Particle Hydrodynamics. In particlebased simulations, fluid surfaces are usually defined as a level set of an implicit function. We formulate the implicit function as a sum of anisotropic smoothing kernels, and the direction of anisotropy at a particle is determined by performing Principal Component Analysis (PCA) over the neighboring particles. In addition, we perform a smoothing step that repositions the centers of these smoothing kernels. Since these anisotropic smoothing kernels capture the local particle distributions more accurately, our method has advantages over existing methods in representing smooth surfaces, thin streams and sharp features of fluids. Our method is fast, easy to implement, and our results demonstrate a significant improvement in the quality of reconstructed surfaces as compared to existing methods.
TopologyAdaptive Mesh Deformation for Surface Evolution, Morphing, and MultiView Reconstruction
, 2009
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Exact and robust (self)intersections for polygonal meshes
, 2010
"... We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and selfintersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for me ..."
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Cited by 15 (1 self)
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We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and selfintersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate meshbased front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness ( = correctness) and robustness ( = completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a planebased BSPrepresentation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency.
WOJTAN C.: Tracking surfaces with evolving topology
 ACM Trans. Graph. (SIGGRAPH
, 2012
"... Figure 1: Our method recovers a sequence of highquality, temporally coherent triangle meshes from any sequence of closed surfaces with arbitrarily changing topology. We reliably extract correspondences from a level set and track textures backwards through a fluid simulation. We present a method for ..."
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Cited by 13 (2 self)
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Figure 1: Our method recovers a sequence of highquality, temporally coherent triangle meshes from any sequence of closed surfaces with arbitrarily changing topology. We reliably extract correspondences from a level set and track textures backwards through a fluid simulation. We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multiresolution nonrigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process.
C.: Explicit mesh surfaces for particle based fluids
 Computer Graphics Forum (Proc. Eurographics
, 2012
"... Figure 1: A drop falling into a shallow pool creates a water crown. We introduce the idea of using an explicit triangle mesh to track the air/fluid interface in a smoothed particle hydrodynamics (SPH) simulator. Once an initial surface mesh is created, this mesh is carried forward in time using near ..."
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Cited by 12 (2 self)
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Figure 1: A drop falling into a shallow pool creates a water crown. We introduce the idea of using an explicit triangle mesh to track the air/fluid interface in a smoothed particle hydrodynamics (SPH) simulator. Once an initial surface mesh is created, this mesh is carried forward in time using nearby particle velocities to advect the mesh vertices. The mesh connectivity remains mostly unchanged across timesteps; it is only modified locally for topology change events or for the improvement of triangle quality. In order to ensure that the surface mesh does not diverge from the underlying particle simulation, we periodically project the mesh surface onto an implicit surface defined by the physics simulation. The mesh surface gives us several advantages over previous SPH surface tracking techniques. We demonstrate a new method for surface tension calculations that clearly outperforms the state of the art in SPH surface tension for computer graphics. We also demonstrate a method for tracking detailed surface information (like colors) that is less susceptible to numerical diffusion than competing techniques. Finally, our temporallycoherent surface mesh allows us to simulate highresolution surface wave dynamics without being limited by the particle resolution of the SPH simulation.
Discrete Viscous Sheets
"... Figure 1: A thin sheet of molten chocolate enrobes a spherical truffle. As viscous sheets deform they exhibit behaviors that combine both the fluidity of liquids, and the buckling and wrinkling instabilities of thin materials, as evidenced here in the beautiful spindly legs. We present the first red ..."
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Cited by 8 (1 self)
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Figure 1: A thin sheet of molten chocolate enrobes a spherical truffle. As viscous sheets deform they exhibit behaviors that combine both the fluidity of liquids, and the buckling and wrinkling instabilities of thin materials, as evidenced here in the beautiful spindly legs. We present the first reduceddimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the StokesRayleigh analogy to derive a simple yet consistent model for viscous forces. We incorporate nonlinear surface tension forces with a formulation based on minimizing discrete surface area, and preserve the quality of triangular mesh elements through local remeshing operations. Simultaneously, we track and evolve the thickness of each triangle to exactly conserve liquid volume. This approach enables the simulation of extremely thin sheets of viscous liquids, which are difficult to animate with existing volumetric approaches. We demonstrate our method with examples of several characteristic viscous sheet behaviors, including stretching, buckling, sagging, and wrinkling.
Approximate boolean operations on large polyhedral solids with partial mesh reconstruction
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract—We present a new approach to compute the approximate Boolean operations of two freeform polygonal mesh solids efficiently with the help of Layered Depth Images (LDI). After applying the LDI sampling based membership classification, the most challenging part, a trimmed adaptive contouring a ..."
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Cited by 8 (1 self)
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Abstract—We present a new approach to compute the approximate Boolean operations of two freeform polygonal mesh solids efficiently with the help of Layered Depth Images (LDI). After applying the LDI sampling based membership classification, the most challenging part, a trimmed adaptive contouring algorithm, is developed to reconstruct the mesh surface from the LDI samples near the intersected regions and stitch it to the boundary of the retained surfaces. Our method of approximate Boolean operations holds the advantage of numerical robustness as the approach uses volumetric representation. However, unlike other methods based on volumetric representation, we do not damage the facets in nonintersected regions, thus preserving geometric details much better and speeding up the computation as well. We show that the proposed method can successfully compute the Boolean operations of freeform solids with a massive number of polygons in a few seconds. Index Terms—Boolean operations, freeform solids, robust, approximation, Layered Depth Images. I.
Optimizing voronoi diagrams for polygonal finite element computations
 In Proceedings of the 19th International Meshing Roundtable
, 2010
"... Summary. We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectiv ..."
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Cited by 8 (0 self)
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Summary. We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities—short edges in the Voronoi diagram. We evaluate our method on a 2D Poisson problem and demonstrate that our simple but effective optimization achieves a significant improvement of the stiffness matrix condition number. 1
Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes
, 2010
"... We present a novel technique for the efficient boundary evaluation of sweep operations applied to objects in polygonal boundary representation. These sweep operations include Minkowski addition, offsetting, and sweeping along a discrete rigid motion trajectory. Many previous methods focus on the con ..."
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Cited by 6 (0 self)
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We present a novel technique for the efficient boundary evaluation of sweep operations applied to objects in polygonal boundary representation. These sweep operations include Minkowski addition, offsetting, and sweeping along a discrete rigid motion trajectory. Many previous methods focus on the construction of a polygonal superset (containing selfintersections and spurious internal geometry) of the boundary of the volumes which are swept. Only few are able to determine a clean representation of the actual boundary, most of them in a discrete volumetric setting. We unify such superset constructions into a succinct common formulation and present a technique for the robust extraction of a polygonal mesh representing the outer boundary, i.e. it makes no general position assumptions and always yields a manifold, watertight mesh. It is exact for Minkowski sums and approximates swept volumes polygonally. By using planebased geometry in conjunction with hierarchical arrangement computations we avoid the necessity of arbitrary precision arithmetics and extensive special case handling. By restricting operations to regions containing pieces of the boundary, we significantly enhance the performance of the algorithm.