A Geometric Approach to Animating Thin Surface Features in SPH Water

Transcription

1 A Geometric Approach to Animating Thin Surface Features in SPH Water Taekwon Jang et al. Computer Animation and Social Agents 2013 (CASA) Jong-Hyun Kim

2 Abstract We propose a geometric approach to animating thin surface features of SPH based water. Fluid thin sheet Liquid ligament Jong-Hyun Kim # 2

3 Introduction Particle fluids approach polygonization: low sampling density problem (ex: evaluation of isovalue) Low sampling density High sampling density One remedy is to increase the number of particles adaptively at such area. 1. Symmetrically - Adaptively sampled particle fluids - ACM SIGGRAPH Adams et al. Previous method Our method Jong-Hyun Kim # 3

4 Introduction 2. Spherically - Efficient refinement of dynamic point data - IEEE VGTC Solenthaler et al. 3. Cubically - Two-scale particle simulation - ACM SIGGRAPH Solenthaler and Gross Original Upsampling Two-scale Original droplets ligaments sheets Jong-Hyun Kim # 4

5 Introduction In order to circumvent the issue of unresolved target geometry, we introduce explicit inter-particle connections Create linear connections among surface particles in sparsely sampled regions Along with our inter-particle connections, we propose the following components to reproduce animations of thin surface features in SPH fluids (3 components) Jong-Hyun Kim # 5

6 Introduction Surface breakup animation method determines whether the unresolved regions experience surface breakup or not using each inter-particle connections. Dynamic upsampling method accuracy checking of the continuity status of each connection by incorporating more accurate surface normals this application of the Poisson-disk sampling method serves this purpose Thin surface reconstruction method reconstructs surfaces including thin features by using SPH particles and inter-particle connections. Jong-Hyun Kim # 6

7 Introduction Animation of small-scale surfaces Figure 1 liquid ligaments liquid sheets Figure 2 Zhu and bridson (2005) Our method Zhu and bridson (2005) Our method Jong-Hyun Kim # 7

8 Introduction Inter-particle Connections The connections represents a stored set of neighbor lists of the surface particles surface particles: fewer than 10 neighbors For every simulation frame, new connections can be generated generated connections are updated or disconnected according to predefined geometric condition (Section 3) Jong-Hyun Kim # 8

9 Related Work SPH Water (introduced SPH model to the CG fields) Smoothed Particles: A new paradigm for animating highly deformable bodies Eurographics 1996 Desbrum and Gascule (simulation of water) Particle-based fluid simulation for interactive application SCA 2003 Muller et al. (fluid-fluid interaction) Particle-based fluid-fluid interaction SCA 2005 Muller et al. (frothing bubbles) Bubbling and frothing liquids ACM SIGGRAPH 2007 Cleary et al. (under water bubbles) Animation of air bubbles with SPH GRAPP (Computer Graphics Theory and Applications) 2011 Ihmsen et al. (liquid-liquid mixture) Realistic simulation of mixing fluids Visual Computer 2011 Liu et al. Jong-Hyun Kim # 9

10 Related Work SPH Water (porous flow) Porous flow in particle-based fluid simulation ACM SIGGRAPH 2008 Lenaerts et al. (interfaces between multiple fluids) Density contrast SPH interfaces SCA 2008 Solenthaler and Pajarola (water turbulence) Simulating SPH fluid with multi-level vorticity CASA 2011 Jang et al. Incorporating stochastic turbulence in particle-based fluid simulation Visual Computer 2011 Yuan et al. (enforcing incompressibility) Predictive-corrective incompressible SPH ACM SIGGRAPH 2009 Solenthaler and Pajarola (adaptive sampling) Two-scale particle simulation ACM SIGGRAPH 2011 Solenthaler and Gross Jong-Hyun Kim # 10

11 Related Work SPH Surface Reconstruction (particle upsampling) Efficient refinement of dynamic point data IEEE VGTC 2007 Solenthaler et al. (density normalization scheme) SPH with small scale details and improve surface reconstruction SCCG 2011 Juraj et al. (minimize the thin-plate energy of surfaces) A level-set method for skinning animated particle data SCA 2011 Bhattacharya et al. (anisotropic kernel) Reconstructing surfaces of particle-based fluids using anisotropic kernels SCA 2010 Yu and Greg (isotropic kernel) Particle-based fluid simulation for interactive application SCA 2003 Muller et al. (triangle based surface tracking) Explicit mesh surfaces for particle based fluids Eurographics 2012 Yu et al. Jong-Hyun Kim # 11

12 Related Work Our Solution Main characteristic The utilization of explicit inter-particle connections to model the un-resolve surface features Overall computation cost required for managing the connections much less that that required for constructing an anisotropic kernel (anisotropic kernel) Reconstructing surfaces of particle-based fluids using anisotropic kernels SCA 2010 Yu and Greg The employed Poisson-disk sampling method is know to be fast compare to the dart-throwing technique (preserving fluid sheet on FLIP) Preserving fluid sheets with Adaptively Sampled Anisotropic Particles TVCG 2012 Ando et al. Jong-Hyun Kim # 12

13 Surface Breakup Animation Geometric conditions for connections Generation Reproducing breakable surface elements such as thin water sheets or ligaments. (angle condition) (distance condition) surface particle: neighboring surface particle: unit normal at : When the candidate satisfies Equations (1) and (2) : stored as a new connection is set : 0.15 : reset distance between particles : smoothing length of the employed SPH particles Jong-Hyun Kim # 13

14 Surface Breakup Animation Geometric conditions for connections Update In each simulation frame, update: length of each connection checking: either too long or too short maximum connectable range:, set In addition, a connection is removed if two connected SPH particles have more than 10 neighboring particles. Jong-Hyun Kim # 14

15 Surface Breakup Animation Geometric conditions for connections Disconnection Since thin surfaces in reality are prone to tearing and rupture by various physical factor We proposed to use a geometric approach Measure (over the connections) Strains of stretching deformations length of a connection in the previous frame: sudden stretching:, set 0.15 Thin surface can be torn when experience a large stretching deformation in a short time period. Jong-Hyun Kim # 15

16 Surface Breakup Animation Geometric conditions for connections Local curvature of bending deformations We approximate the curvature by using the surface normal and the length of a connection set : If a connection satisfies on of the two connections for disconnection, It is removed from our system color: magnitude of the stretching deformation, red(high) to blue(low) Jong-Hyun Kim # 16

17 Dynamic Upsampling Method Poisson-disk sampling method In our system, surface normal play important roles when animating the thin surface In particular, the conditions for generation and disconnection rely on the surface normal In order to increate the accuracy of the surface normal, We introduce a dynamic upsampling method. Basic idea: provide auxiliary samples in sparse regions Jong-Hyun Kim # 17

18 Dynamic Upsampling Method Poisson-disk sampling method While the geometry of thin surfaces is approximated by the connection, unresolved areas suffer from deficiency of samples due to local separations of particles. In order to add more sample efficiently: Poisson-disk sampling (sampling) Fast Poisson Disk Sampling in Arbitrary Dimensions ACM SIGGRAPH 2007 stetches Bridson Because 1. Generates and distributes samples while maintaining a minimum distance tween them 2. Achieves fast performance while maintaining the sampling quality Jong-Hyun Kim # 18

19 Dynamic Upsampling Method Upsampling over the connections Step 1. Traverse the grid and mark the voxels that contain as least one SPH particle. Step 2. Select a connection Step 3. Generate candidate points in the voxels that encounter using Poisson-Disk sampling method Step 4. If the candidate point is far from existing samples or SPH particles register the candidate point as a new sample In each frame, - our upsampling method iterates from Step 2 to Step 4 while visiting all the connections. - In step 3, when the candidate points do not align with the connection, - We move the generate samples in the direction of the normal. - Collision avoidance with existing SPH particles. Jong-Hyun Kim # 19

20 Dynamic Upsampling Method Computing surface normals After upsampling, We improve the accuracy of the computation of the surface normals by utilizing added PD samples. Basic idea To treat the PD-samples as adjacent SPH particles When computing the mass-density and the surface normal We first compute a new mass-density for connected particles and PD samples, as following: corrected mass-density SPH particles PD samples poly kernel in SPH Jong-Hyun Kim # 20

21 Dynamic Upsampling Method Computing surface normals An additional term is added to the typical equation in the same way as in the above density correction process. corrected surface normal corrected mass-density at SPH particles corrected mass-density at PD samples Ours Jong-Hyun Kim # 21

22 Thin surface reconstruction Contributions from the connections The breakup status of each connection, which is determined by the geometric condition. ( 앞에서설명 ) For example, when a connection is maintained, it is likely that water surfaces exist around the connection. Therefore, we reconstruct surface meshes connections exist. In order to obtain smooth surface, we adopt a moving avg. based method. (distance) Animating Sand as a Fluid ACM SIGGRAPH 2008 Zhu and Bridson grid pos. avg. pos. avg. radius Jong-Hyun Kim # 22

23 Thin surface reconstruction Contributions from the connections Differently from the original definition, We add the contributions from the PD samples grid pos. avg. pos. avg. radius nearby PD samples nearby PD samples Jong-Hyun Kim # 23

24 Thin surface reconstruction Rescaling the particle radius When evaluating the average radius in Equation 10, as PD samples area additionally involved, The overall volume of the surfaces may increase. We apply the following equation in order to preserve the volume By rescaling the radius of both SPH particles and the PD samples. SPH particles 0.25r PD sample involved in evaluating the isovalues, If no PD sample is involved, original particle radius is set to be the same as the The effect of rescaling is valid only in the surface reconstruction stage Jong-Hyun Kim # 24

25 Thin surface reconstruction Rescaling the particle radius Zhu and bridson (2005) Our method Zhu and bridson (2005) Our method Our method Jong-Hyun Kim # 25

26 Results and Discussion Implementation Our fluid solver: enforce incompressibility (enforcing incompressibility) Predictive-corrective incompressible SPH ACM SIGGRAPH 2009 Solenthaler and Pajarola Boundary handling: fluid-solid coupling (boundary particle) Predictive-corrective incompressible SPH ACM SIGGRAPH 2012 Akinci et al. Upsampling consumes around the 10% of time relative to the SPH solver Jong-Hyun Kim # 26

27 Results and Discussion Comparison with previous work Comparison: anisotropic kernel (anisotropic kernel) Reconstructing surfaces of particle-based fluids using anisotropic kernels SCA 2010 Yu and Greg Our method Jong-Hyun Kim # 27

28 Results and Discussion Comparison with previous work Comparison: previous adaptive sampling (preserving fluid sheet on FLIP) Preserving fluid sheets with Adaptively Sampled Anisotropic Particles TVCG 2012 Ando et al. Our method Jong-Hyun Kim # 28

29 Conclusions We presented a geometric approach to the animation of thin liquid surfaces of SPH fluid. Introduced inter-particle connection method Can represent the geometry of unresolved areas Allowing breakup simulation of SPH surfaces Applied Poisson-disk sampling method Adds PD samples to the connections for the purpose of increasing the accuracy of the breakup simulation. PD samples were exploited in the surface reconstruction stage to reproduce thin water surfaces. Jong-Hyun Kim # 29

30 Conclusions Limitation & Future work Animated surfaces may suffer from temporal inconsistency Water volumes in-bewteen particles may appear or disappear across frames resulting from the additions or deletions of PD samples In future work To reduce artifacts!!! more states, such as post connection/disconnection stage Jong-Hyun Kim # 30