Afonso Paiva

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.

Robust adaptive meshes for implicit surfaces

This work introduces a robust algorithm for computing good polygonal approximations of implicit surfaces, where robustness entails recovering the exact topology of the implicit surface. Furthermore, the approximate triangle mesh adapts to the geometry and to the topology of the real implicit surface. This method generates an octree subdivided according to the interval evaluation of the implicit function in order to guarantee the robustness, and to the interval automatic differentiation in order to adapt the octree to the geometry of the implicit surface. The triangle mesh is then generated from that octree through an enhanced dual marching

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

Spectral Image Segmentation Using Image Decomposition and Inner Product-Based Metric

Image segmentation is an indispensable tool in computer vision applications, such as recognition, detection and tracking. In this work, we introduce a novel user-assisted image segmentation technique which combines image decomposition, inner product-based similarity metric, and spectral graph theory into a concise and unified framework. First, we perform an image decomposition to split the image into texture and cartoon components. Then, an affinity graph is generated and the weights are assigned to its edges according to a gradient-based inner-product function. From the eigenstructure of the affinity graph, the image is partitioned through the spectral cut of the underlying graph. The computational effort of our framework is alleviated by an image coarsening process, which reduces the graph size considerably. Moreover, the image partitioning can be improved by interactively changing the graph weights by sketching. Finally, a coarse-to-fine interpolation is applied in order to assemble the partition back onto the original image. The efficiency of the proposed methodology is attested by comparisons with state-of-art spectral segmentation methods through a qualitative and quantitative analysis of the results.

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.

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.

Concentric RadViz: Visual Exploration of Multi-task Classification

The discovery of patterns in large data collections is a difficult task. Visualization and machine learning techniques have emerged as a way to facilitate data analysis, providing tools to uncover relevant patterns from the data. This paper presents Concentric Rad Viz, a general purpose class visualization system that takes into account multi-class, multi-label and multi-task classifiers. Concentric Rad Viz uses a force attenuation scheme, which minimizes cluttering and ambiguity in the visual layout. In~addition, the user can add concentric circles to the layout in order to represent classification tasks. Our validation results and the application of Concentric Rad Viz for two real collections suggest that this tool can reveal important data patterns and relations. In our application, the user can interact with the visualization by selecting regions of interest according to specific criteria and changing projection parameters.