Elsevier

Computers & Graphics

Volume 84, November 2019, Pages 55-65
Computers & Graphics

Special Section on SIBGRAPI 2019
Boundary particle resampling for surface reconstruction in liquid animation

https://doi.org/10.1016/j.cag.2019.08.011Get rights and content

Highlights

  • We present a novel particle resampling method for surface reconstruction of a liquid.

  • The first adaptive sampling tailored to level-sets defined by the boundary particles.

  • Our adaptive particle resampling preserves small and thin features of a liquid.

  • A new quality metric to evaluate the effectiveness of the resampling methods.

Abstract

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 then 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.

Introduction

An interface between a liquid and a gas (e.g., water and air) is known as a free-surface. The deformation and fragmentation of the free-surface caused by a liquid splashing is a ubiquitous phenomenon which generates not only an intricate surface but also important fluid features, such as thin sheets, liquid streams or ligaments, and small droplets. The numerical discretization imposes several limitations in the representation of these features, mainly for fluid details on a scale smaller than the numerical resolution. A plausible representation of these details is essential in fluid animation, demanding an intense research activity in the field of computer animation.

In the context of particle-based fluids, rendering of the free-surface usually involves the employment of a surface reconstruction technique which transforms particles into a polygonal mesh. Several surface reconstruction methods have been proposed in the Computer Graphics literature, not only for particle-based fluids but also for point clouds in general. The main concern of surface reconstruction techniques [2] is to create a watertight surface from oriented point cloud (i.e., a subset of 3D points and normals that sample the surface) typically acquired with 3D range scanners. On the other hand, in particle-based fluids, such as Smoothed Particle Hydrodynamics (SPH) [3] and Fluid-Implicit-Particle (FLIP) [4], the primary purpose is to extract a high-quality smooth free-surface from the particle positions. In this case, the free-surface is represented implicitly by a blobby-like model, i.e., the zero level-set of a signed distance field computed from a weighted sum of kernel evaluations over the distances between the particle positions [4], [5], [6]. For simplicity, we call this category of methods as volumetric surface reconstruction, because the smoothed signed distance function provided by these methods involve all particles of the system, i.e., without distinguishing whether a particle belongs to the free-surface or not.

The main drawback of the volumetric surface reconstruction methods is the difficulty in providing a representation of fluid features due to irregular and sparse distribution of the particles or by the numerical discretization. For this reason, many articles in the literature address the low particle resolution on the free-surface by using adaptive sampling methods [7], [8], [9], [10].

Recently, Marrone et al. [11] and Sandim et al. [1] proposed alternative frameworks for surface reconstruction. These frameworks rely on a level-set definition using only the particles on the free-surface, these particles are known as boundary particles (or surface particles). Firstly, these methods transform the volumetric shape defined by the fluid particles into a point cloud formed by surface particles through an accurate boundary detection method. Then, the surface reconstruction can be obtained efficiently from a level-set function which fits the boundary particles and its normals. The level-set is given by a closed formula [11] or by robust surface fitting algorithms [1], such as Radial Basis Functions (RBF) implicits [12], Multi-level Partition of Unity (MPU) implicits [13], and Screened Poisson surface reconstruction [14]. Despite reconstructing a watertight surface resilient to blobby artifacts (e.g., bumps or indentations), these methods also suffer from the problem of particle sampling with the disadvantage of lacking some adaptive resampling method tailored for free-surface fitting.

In this paper, we present a novel particle resampling method for surface reconstruction of a point cloud which represents the free-surface of a liquid, providing a significant improvement over the surface reconstruction methods based on a level-set definition from the boundary particles [1], [11]. Our approach is based on adaptive particle refinement of the free-surface according to its small and thin fluid features, preserving small droplets, streams, and thin sheets due to the insertion of new particles in poorly sampled regions. The detection of the fluid features and the positioning of the new sampled particles are provided by the Principal Component Analysis (PCA) [15] of the particle positions. Fig. 1 depicts our method in action.

In contrast to the previous adaptive sampling methods, our method is tailored to level-sets defined by the boundary particles. Besides being computationally efficient, simple and easy to implement, our resampling is independent of the boundary detection method used, allowing users to choose the detection method that better suit their needs. Moreover, we propose a quality metric in order to evaluate the effectiveness of our method against the state-of-the-art techniques in particle resampling by a set of experiments and comparisons.

The remainder of the paper is organized as follows. Section 2 presents a brief review of related methods existing in the literature. The proposed method is described in Section 3. Sections 4 and 5 provide the results and a discussion about our method, respectively. Section 6 concludes the paper, giving a glimpse of future work.

Section snippets

Related work

In order to better contextualize our method and highlight its properties, we focused on reviewing previous works closely related to particle resampling methods in liquid animation.

Adams et al. [16] proposed an adaptive sampling method for SPH fluids based on geometric local feature size, computed using a particle approximation of the medial axis of the free-surface. Their approach allows increasing the number of particles in geometrically complex regions near the free-surface while reducing the

Boundary particle resampling

In this section, given a particle-based simulation (e.g., SPH or FLIP), we describe in details the proposed particle resampling method. Fig. 2 shows how we insert our resampling method in the surface reconstruction pipeline. This pipeline comprises four main stages: boundary detection, feature classification, particle refinement, and surface reconstruction. For each time-step of the simulation, since we are focused on rendering the free-surface, firstly the free-surface is captured through a

Results

We implemented our method in C++ using OpenMP multithreading API. The particle-based fluid simulations were generated using a weakly compressible SPH implementation provided by DualSPHysics [31]. For each simulation, the value of the parameter ρ is defined as the SPH smoothing length, as suggested by Sandim et al. [1]. All experiments have been performed on a 4-core 2.8 GHz Intel i7-4980HQ with 16 GB of RAM. The effectiveness of our approach is attested through quantitative and qualitative

About the parameter α

We chose α=0.2 in Eq. (2) empirically which was supported by the quality of the results obtained with the experiments reported in Section 4. However, one alternative to eliminate such a parameter could be interpreting the covariance matrix Ci as a diffusion tensor, a traditional tool in medical image analysis [35]. Among the diffusion measures, in particular, the Westin measures [36] capture the shape “DNA” of the PCA ellipsoid from Ci, i.e., there is a diffusion tensor basis {B1, B2, B3}

Conclusion and future work

We have presented a novel adaptive particle resampling method for free-surface reconstruction of zero level-sets defined by boundary particles from particle-based fluid simulations. Given a particle set which discretizes a liquid, firstly our method relies on Sandim et al. [1] to accurately identify the boundary particles. Each boundary particle is then classified and labeled regarding the local features of the fluid, where this classification is based on deformation of the free-surface and the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We want to thank the anonymous reviewers for their suggestions. We also thank Cristin Barghiel from SideFX for their kind donation of the Houdini software. This study was financed in part by the Coordenação de Aperfeiçcoamento de Pessoal de Nível Superior – Brasil (CAPES), National Council for Scientific and Technological Development – Brasil (CNPq) under grant #301642/2017-6, and São Paulo Research Foundation (FAPESP) under grants #2013/07375-0 and #2014/09546-9.

References (41)

  • J. Yu et al.

    Reconstructing surfaces of particle-based fluids using anisotropic kernels

    ACM Trans Graph

    (2013)
  • B. Solenthaler et al.

    Efficient refinement of dynamic point data

    Proceedings of the EG symposium on point-based graphics

    (2007)
  • Y. Zhang et al.

    Adaptive sampling and rendering of fluids on the GPU

    Proceedings of the IEEE/ EG symposium on volume and point-based graphics

    (2008)
  • R. Ando et al.

    Preserving fluid sheets with adaptively sampled anisotropic particles

    IEEE Trans Vis Comput Graph

    (2012)
  • T. Jang et al.

    A geometric approach to animating thin surface features in smoothed particle hydrodynamics water

    Comput Animat Virtual Worlds

    (2015)
  • J.C. Carr et al.

    Reconstruction and representation of 3D objects with radial basis functions

    Proceedings of the SIGGRAPH ’01

    (2001)
  • Y. Ohtake et al.

    Multi-level partition of unity implicits

    ACM Trans Graph

    (2003)
  • M. Kazhdan et al.

    Screened poisson surface reconstruction

    ACM Trans Graph

    (2013)
  • I.T. Jolliffe

    Principal component analysis

    (2002)
  • B. Adams et al.

    Adaptively sampled particle fluids

    ACM Trans Graph

    (2007)
  • Cited by (0)

    View full text