# Boundary particle resampling for surface reconstruction in liquid animation

### Resumo

In this paper, we present a novel adaptive particle resampling method tailored for surface reconstruction of level-sets defined by the boundary particles from a particle-based liquid simulation. The proposed approach is simple and easy to implement, and only requires the positions of the particles to identify and refine regions with small and thin fluid features accurately. The method comprises four main stages: boundary detection, feature classification, particle refinement and surface reconstruction. For each simulation frame, firstly the free-surface particles are captured through a boundary detection method. Then, the boundary particles are classified and labeled according to the deformation and the stretching of the free-surface computed from the Principal Component Analysis (PCA) of the particle positions. The particles placed at feature regions are refined according to their feature classification. Finally, we extract the free-surface of the zero level-set defined by the resampled boundary particles and its normals. In order to render the free-surface, we demonstrate how the traditional methods of surface fitting in Computer Graphics and Computational Physics literature can benefit from the proposed resampling method. Furthermore, the results shown in the paper attest the effectiveness and robustness of our method when compared to state-of-the-art adaptive particle resampling techniques.

**Palavras-chave:**Particle resampling, Boundary particles, Surface reconstruction, Particle-based fluids, Liquid animation

### Referências

M. Berger, A. Tagliasacchi, L.M. Seversky, P. Alliez, J.A. Levine, A. Sharf, C. Silva. State of the art in surface reconstruction from point clouds. Proceedings of the Eurographics 2014 - state of the art reports (2014), pp. 161-185

M. Ihmsen, J. Orthmann, B. Solenthaler, A. Kolb, M. Teschner. SPH fluids in computer graphics. Proceedings of the Eurographics 2014 - state of the art reports (2014), pp. 21-42

Y. Zhu, R. Bridson. Animating sand as a fluid. ACM Trans Graph, 24 (3) (2005), pp. 965-972

M. Müller, D. Charypar, M. Gross. Particle-based fluid simulation for interactive applications. Proceedings of the symposium on computer animation (SCA’03) (2003), pp. 154-159

J. Yu, G. Turk. Reconstructing surfaces of particle-based fluids using anisotropic kernels. ACM Trans Graph, 32 (1) (2013), pp. 5:1-5:12

B. Solenthaler, Y. Zhang, R. Pajarola. Efficient refinement of dynamic point data. Proceedings of the EG symposium on point-based graphics (2007), pp. 65-72

Y. Zhang, B. Solenthaler, R. Pajarola. Adaptive sampling and rendering of fluids on the GPU. Proceedings of the IEEE/ EG symposium on volume and point-based graphics (2008), pp. 137-146

R. Ando, N. Thürey, R. Tsuruno. Preserving fluid sheets with adaptively sampled anisotropic particles. IEEE Trans Vis Comput Graph, 18 (8) (2012), pp. 1202-1214

T. Jang, J. Noh. A geometric approach to animating thin surface features in smoothed particle hydrodynamics water. Comput Animat Virtual Worlds, 26 (2) (2015), pp. 161-172

S. Marrone, A. Colagrossi, D. Le Touzé, G. Graziani. Fast free-surface detection and level-set function definition in SPH solvers. J Comput Phys, 229 (10) (2010), pp. 3652-3663

J.C. Carr, R.K. Beatson, J.B. Cherrie, T.J. Mitchell, W.R. Fright, B.C. McCallum, T.R. Evans. Reconstruction and representation of 3D objects with radial basis functions. Proceedings of the SIGGRAPH ’01 (2001), pp. 67-76

Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, H.-P. Seidel. Multi-level partition of unity implicits. ACM Trans Graph, 22 (3) (2003), pp. 463-470

M. Kazhdan, H. Hoppe. Screened poisson surface reconstruction. ACM Trans Graph, 32 (3) (2013), pp. 29:1-29:13

I.T. Jolliffe. Principal component analysis. (2nd), Springer (2002)

B. Adams, M. Pauly, R. Keiser, L.J. Guibas. Adaptively sampled particle fluids. ACM Trans Graph, 26 (3) (2007)

W. Hong, D.H. House, J. Keyser. Adaptive particles for incompressible fluid simulation. Vis Comput, 24 (7) (2008), pp. 535-543

B. Solenthaler, M. Gross. Two-scale particle simulation. ACM Trans Graph, 30 (4) (2011), pp. 81:1-81:8

J. Orthmann, A. Kolb. Temporal blending for adaptive SPH. Comput Graph Forum, 31 (8) (2012), pp. 2436-2449

R. Ando, N. Thürey, C. Wojtan. Highly adaptive liquid simulations on tetrahedral meshes. ACM Trans Graph, 32 (4) (2013), pp. 103:1-103:10

R. Winchenbach, H. Hochstetter, A. Kolb. Infinite continuous adaptivity for incompressible SPH. ACM Trans Graph, 36 (4) (2017), pp. 102:1-102:10

X. He, N. Liu, G. Wang, F. Zhang, S. Li, S. Shao, H. Wang. Staggered meshless solid-fluid coupling. ACM Trans Graph, 31 (6) (2012), pp. 149:1-149:12

J. Orthmann, H. Hochstetter, J. Bader, S. Bayraktar, A. Kolb. Consistent surface model for SPH-based fluid transport. Proceedings of the Symposium on Computer Animation (SCA’13) (2013), pp. 95-103

Barecasco A, Terissa H, Naa C. Simple free-surface detection in two and three-dimensional SPH solver. 2013. arXiv:1309.4290.

S. Katz, A. Tal, R. Basri. Direct visibility of point sets. ACM Trans Graph, 26 (3) (2007)

Guennebaud G, Jacob B, et al. Eigen v3. 2010. http://eigen.tuxfamily.org.

K. Museth. A flexible image processing approach to the surfacing of particle-based fluid animation. Mathematical progress in expressive image synthesis I, Springer (2014), pp. 81-84

G. Akinci, M. Ihmsen, N. Akinci, M. Teschner. Parallel surface reconstruction for particle-based fluids. Comput Graph Forum, 31 (6) (2012), pp. 1797-1809

A. Belyaev, Y. Ohtake. A comparison of mesh smoothing methods. Proceedings of the Israel-Korea bi-national conference on geometric modeling and computer graphics (2003), pp. 83-87

P. Cignoni, M. Callieri, M. Corsini, M. Dellepiane, F. Ganovelli, G. Ranzuglia. MeshLab: an open-source mesh processing tool. Proceedings of the Eurographics Italian chapter conference (2008), pp. 129-136

A.J.C. Crespo, J.M. Domínguez, B.D. Rogers, M. Gómez-Gesteira, S. Longshaw, R. Canelas, R. Vacondio, A. Barreiro, O. García-Feal. DualSPHysics: open-source parallel CFD solver based on smoothed particle hydrodynamics (SPH)

Comput Phys Commun, 187 (2015), pp. 204-216

K. Museth, J. Lait, J. Johanson, J. Budsberg, R. Henderson, M. Alden, P. Cucka, D. Hill, A. Pearce. OpenVDB: an open-source data structure and toolkit for high-resolution volumes. Proceedings of the ACM SIGGRAPH 2013 Courses (2013). 19:1–19:1. https://www.openvdb.org/

D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell. A hybrid particle level set method for improved interface capturing

J Comput Phys, 183 (1) (2002), pp. 83-116

Houdini. SideFX; 2019. https://www.sidefx.com/.

Jones D.K. editor. Diffusion MRI: theory, methods, and applications. Oxford University Press (2011)

C.F. Westin, S.E. Maier, H. Mamata, A. Nabavi, F.A. Jolesz, R. Kikinis. Processing and visualization for diffusion tensor MRI. Med Image Anal, 6 (2) (2002), pp. 93-108

A. Hérault, G. Bilotta, R.A. Dalrymple. SPH on GPU with CUDA. J Hydraul Res, 48 (2010), pp. 74-79

CUDA C Programming Guide. NVIDIA; 2019. https://docs.nvidia.com/cuda/pdf/CUDA_C_Programming_Guide.pdf.

M. Tang, J.-Y. Zhao, R.-F. Tong, D. Manocha. GPU accelerated convex hull computation. Comput Graph, 36 (5) (2012), pp. 498-506

R. Machado e Silva, C. Esperança, R. Marroquim, A.A.F. Oliveira. Image space rendering of point clouds using the HPR operator. Comput Graph Forum, 33 (1) (2014), pp. 178-189

Thrust Quick Start Guide. NVIDIA; 2019. https://docs.nvidia.com/cuda/pdf/Thrust_Quick_Start_Guide.pdf.

*In*: CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI), 32. , 2019, Rio de Janeiro.

**Anais**[...]. Porto Alegre: Sociedade Brasileira de Computação, 2019 . DOI: https://doi.org/10.5753/sibgrapi.2019.9811.