Fabiano Petronetto

Particle-based viscoplastic fluid/solid simulation

Simulations of viscoplastic materials are traditionally governed by continuum mechanics. The viscous behavior is typically modeled as an internal force, defined by diverse quantities. This work introduces a fluid model to simulate the viscoplastic effect of solid materials, such as plastic, wax, clay and polymer. Our method consists in modeling a solid object through a non-Newtonian fluid with high viscosity. This fluid simulation uses the Smoothed Particle Hydrodynamics method and the viscosity is formulated by using the General Newtonian Fluid model. This model concentrates the viscoplasticity in a single parameter. Our results show clear effects of creep, melting, hardening and flowing.

Meshless Helmholtz-Hodge Decomposition

Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility.

Particle-based non-Newtonian fluid animation for melting objects

This paper presents a new visually realistic animation technique for objects that melt and flow. It simulates viscoplastic properties of materials such as metal, plastic, wax, polymer and lava. The technique consists in modeling the object by the transition of a non-Newtonian fluid with high viscosity to a liquid of low viscosity. During the melting, the viscosity is formulated using the general Newtonian fluids model, whose properties depend on the local temperature. The phase transition is then driven by the heat equation. The fluid simulation framework uses a variation of the Lagrangian method called smoothed particle hydrodynamics. This paper also includes several schemes that improve the efficiency and the numerical stability of the equations

Fluid-based hatching for tone mapping in line illustrations

This paper presents a novel meshless, physically-based framework for line art rendering of surfaces with complex geometry and arbitrary topology. We apply an inviscid fluid flow simulation using Smoothed Particles Hydrodynamics to compute the global velocity and cross fields over the surface model. These fields guide the automatic placement of strokes while extracting the geometric and topological coherence of the model. Target tones are matched by tonal value maps allowing different hatching and cross-hatching effects. We demonstrate the simplicity and effectiveness of our method with sample renderings obtained for a variety of models.

SPH Fluids for Viscous Jet Buckling

We present a novel meshfree technique for animating free surface viscous liquids with jet buckling effects, such as coiling and folding. Our technique is based on Smoothed Particle Hydrodynamics (SPH) fluids and allows more realistic and complex viscous behaviors than the preceding SPH frameworks in computer animation literature. The viscous liquid is modeled by a non-Newtonian fluid flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross model. The proposed technique is efficient and stable, and our framework can animate scenarios with high resolution of SPH particles in which the simulation speed is significantly accelerated by using Computer Unified Device Architecture (CUDA) computing platform. This work also includes several examples that demonstrate the ability of our technique.

Uncovering representative groups in multidimensional projections

Multidimensional projection‐based visualization methods typically rely on clustering and attribute selection mechanisms to enable visual analysis of multidimensional data. Clustering is often employed to group similar instances according to their distance in the visual space. However, considering only distances in the visual space may be misleading due to projection errors as well as the lack of guarantees to ensure that distinct clusters contain instances with different content. Identifying clusters made up of a few elements is also an issue for most clustering methods. In this work we propose a novel multidimensional projection‐based visualization technique that relies on representative instances to define clusters in the visual space. Representative instances are selected by a deterministic sampling scheme derived from matrix decomposition, which is sensitive to the variability of data while still been able to handle classes with a small number of instances. Moreover, the sampling mechanism can easily be adapted to select relevant attributes from each cluster. Therefore, our methodology unifies sampling, clustering, and feature selection in a simple framework. A comprehensive set of experiments validate our methodology, showing it outperforms most existing sampling and feature selection techniques. A case study shows the effectiveness of the proposed methodology as a visual data analysis tool.

Mesh-Free Discrete Laplace-Beltrami Operator

In this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh‐free. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications. In particular, we use the eigenstructure of the discrete operator for filtering and shape segmentation. Point‐based surface deformation is another application that can be easily carried out from the proposed discretization method.

Particle-based fluids for viscous jet buckling

In this paper, we introduce a novel meshfree framework for animating free surface viscous liquids with jet buckling effects, such as coiling and folding. Our method is based on Smoothed Particle Hydrodynamics (SPH) fluids and allows more realistic and complex viscous behaviors than the previous SPH frameworks in computer animation literature. The viscous liquid is modeled by a non-Newtonian fluid flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross model. We demonstrate the efficiency and stability of our framework in a wide variety of animations, including scenarios with arbitrary geometries and high resolution of SPH particles. The interaction of the viscous liquid with complex solid obstacles is performed using boundary particles. Our framework is able to deal with different inlet velocity profiles and geometries of the injector, as well as moving inlet jet along trajectories given by cubic Hermite splines. Moreover, the simulation speed is significantly accelerated by using Computer Unified Device Architecture (CUDA) computing platform. Graphical abstractDisplay Omitted HighlightsOur method models viscous liquid in which the viscosity is governed by Cross model.We introduce a SPH first order approximation for viscous term.We use CUDA to simulate the jet buckling effect in affordable computational times.Our method allows different inlet velocities and geometries of the injector.Our implementation supports jet buckling on complex surfaces.

Wavelet-based visualization of time-varying data on graphs

Visualizing time-varying data defined on the nodes of a graph is a challenging problem that has been faced with different approaches. Although techniques based on aggregation, topology, and topic modeling have proven their usefulness, the visual analysis of smooth and/or abrupt data variations as well as the evolution of such variations over time are aspects not properly tackled by existing methods. In this work we propose a novel visualization methodology that relies on graph wavelet theory and stacked graph metaphor to enable the visual analysis of time-varying data defined on the nodes of a graph. The proposed method is able to identify regions where data presents abrupt and mild spacial and/or temporal variation while still been able to show how such changes evolve over time, making the identification of events an easier task. The usefulness of our approach is shown through a set of results using synthetic as well as a real data set involving taxi trips in downtown Manhattan. The methodology was able to reveal interesting phenomena and events such as the identification of specific locations with abrupt variation in the number of taxi pickups.

Visualizing and Interacting with Kernelized Data

Kernel-based methods have experienced a substantial progress in the last years, tuning out an essential mechanism for data classification, clustering and pattern recognition. The effectiveness of kernel-based techniques, though, depends largely on the capability of the underlying kernel to properly embed data in the feature space associated to the kernel. However, visualizing how a kernel embeds the data in a feature space is not so straightforward, as the embedding map and the feature space are implicitly defined by the kernel. In this work, we present a novel technique to visualize the action of a kernel, that is, how the kernel embeds data into a high-dimensional feature space. The proposed methodology relies on a solid mathematical formulation to map kernelized data onto a visual space. Our approach is faster and more accurate than most existing methods while still allowing interactive manipulation of the projection layout, a game-changing trait that other kernel-based projection techniques do not have.