Eurographics/ ACM SIGGRAPH Symposium on Computer Animation (2010), pp. 1–9 M. Otaduy and Z. Popovic (Editors) Reconstructing Surfaces of Particle-Based Fluids Using Anisotropic Kernels Submission ID 1044 Abstract In this paper we present a novel surface reconstruction method for particle-based fluid simulators such as Smoothed Particle Hydrodynamics. In particle-based 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 re-positions 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. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation 1. Introduction It is becoming increasingly popular to create animated liq- uids using physics-based simulation methods for feature film effects and interactive applications. There exist two broad categories for simulation methods based on their different approaches to spatial discretization: mesh-based methods and mesh-free methods. In mesh-based methods, the sim- ulation domain is discretized into mesh grids and the val- ues of physical properties on grid points are determined by solving the governing equations. In mesh-free methods, on the other hand, the fluid volume is discretized into sam- pled particles that carry physical properties and that are ad- vected in space by the governing equations. In recent years, mesh-free methods have become a competitive alternative to mesh-based methods due to various advantages such as their inherent mass conservation, the flexibility of simula- tion in unbounded domains, and ease of implementation. Among various mesh free methods, Smoothed Particle Hy- drodynamics (SPH) is the most popular approach for simu- lating fluid since it is computationally simple and efficient compared to others. In computer graphics, SPH has been successfully used for the simulation of free-surface fluids [MCG03], fluid interface [MSKG05, SP08], fluid-solid cou- pling [MST * 04, LAD08, BTT09], deformable body [BIT09], multi-phase fluid [MKN * 04, KAG * 05, SSP07] and fluid con- trol [TKPR06]. Although SPH has been used to simulate various fluid phenomena, extracting high quality fluid surfaces from the particle locations is not straightforward. Classical surface re- construction methods have difficulties in producing smooth surfaces due to irregularly placed particles. Few researchers have successfully addressed this issue of reconstructing smooth fluid surfaces from particles. In this paper, we pro- pose a novel surface extraction method that significantly im- proves the quality of the reconstructed surfaces. Our new method can create smooth surfaces and thin streams along with sharp features such as edges and corners. The key to our method is to use a stretched, anisotropic smoothing ker- nel to represent each particle in the simulation. The orien- tation and scale of the anisotropy is determined by captur- ing each particle’s neighborhood spatial distribution. We ob- tain the neighborhood distribution in the form of covariance tensor and analyze it through Principle Component Analysis (PCA). We then use these principal components to orient and scale the anisotropic kernel. We adjust the centers of these kernels using a variant of Laplacian smoothing to counteract submitted to Eurographics/ ACM SIGGRAPH Symposium on Computer Animation (2010)