Dynamic Sampling and Rendering of Algebraic Point Set Surfaces

Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least‐squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real‐time rendering system of such surfaces using a dynamic up‐sampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive up‐sampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.     

Simulation of two-phase flow with sub-scale droplet and bubble effects

We present a new Eulerian-Lagrangian method for physics-based simulation of fluid flow, which includes automatic generation of sub-scale spray and bubbles. The Marker Level Set method is used to provide a simple geometric criterion for free marker generation. A filtering method, inspired from Weber number thresholding, further controls the free marker generation (in a physics-based manner). Two separate models are used, one for sub-scale droplets, the other for sub-scale bubbles. Droplets are evolved in a Newtonian manner, using a density-extension drag force field, while bubbles are evolved using a model based on Stokes' Law. We show that our model for sub-scale droplet and bubble dynamics is simple to couple with a full (macro-scale) Navier-Stokes two-phase flow model and is quite powerful in its applications. Our animations include coarse grained multiphase features interacting with fine scale multiphase features.     

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C¹ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.     

Advection‐Based Function Matching on Surfaces

A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non‐linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.     

Direct boolean intersection between acquired and designed geometry

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data).We use the moving least-squares (MLS) surface as the underlying surface representation for acquired point-sampled geometry. Based on the MLS surface definition, we derive closed formula for computing curvature of planar curves on the MLS surface. A set of intersection algorithms including line and MLS surface intersection, curvature-adaptive plane and MLS surface intersection, and polygonal mesh and MLS surface intersection are successively developed. Further, an algorithm for NURBS and MLS surface intersection is then developed. It first adaptively subdivides NURBS surfaces into polygonal mesh, and then intersects the mesh with the MLS surface. The intersection points are mapped to the NURBS surface through the Gauss-Newton method.Based on the above algorithms, a prototype system has been implemented. Through various examples from the system, we demonstrate that direct Boolean intersection between designed geometry and acquired geometry offers a useful and effective means for the shape modeling applications where point-cloud data is involved.     

Hydraulic Erosion Using Smoothed Particle Hydrodynamics

This paper presents a new technique for modification of 3D terrains by hydraulic erosion. It efficiently couples fluid simulation using a Lagrangian approach, namely the Smoothed Particle Hydrodynamics (SPH) method, and a physically-based erosion model adopted from an Eulerian approach. The eroded sediment is associated with the SPH particles and is advected both implicitly, due to the particle motion, and explicitly, through an additional velocity field, which accounts for the sediment transfer between the particles. We propose a new donor-acceptor scheme for the explicit advection in SPH. Boundary particles associated to the terrain are used to mediate sediment exchange between the SPH particles and the terrain itself. Our results show that this particle-based method is efficient for the erosion of dense, large, and sparse fluid. Our implementation provides interactive results for scenes with up to 25,000 particles.     

基于网格的流体界面追踪方法分析与改进

对于流体运动,需要去求解其自由表面,才能将其与周围的环境分开,目前许多人都对界面追踪进行了相关研究,并提出了许多方法,其中早期的主要有PIC法、MAC法和VOF法等。LevelSet方法可以有效地实现动态的界面,并且对计算机图形学的研究起到关键的作用,但是LevelSet方法对界面的尖角部分会有较强的抹平效应。ParticleLevelSet方法是在kvdSet方法的基础上,在界面附近引入示踪粒子,从而可以弥补这一缺陷。本文分另q介绍这几种方法,并提出一些改进与几种方法的综合应用。     

Asynchronous Eulerian Liquid Simulation

We present a novel method for simulating liquid with asynchronous time steps on Eulerian grids. Previous approaches focus on Smoothed Particle Hydrodynamics (SPH), Material Point Method (MPM) or tetrahedral Finite Element Method (FEM) but the method for simulating liquid purely on Eulerian grids have not yet been investigated. We address several challenges specifically arising from the Eulerian asynchronous time integrator such as regional pressure solve, asynchronous advection, interpolation, regional volume preservation, and dedicated segregation of the simulation domain according to the liquid velocity. We demonstrate our method on top of staggered grids combined with the level set method and the semi-Lagrangian scheme. We run several examples and show that our method considerably outperforms the global adaptive time step method with respect to the computational runtime on scenes where a large variance of velocity is present.     

Hybrid Particle‐grid Modeling for Multi‐scale Droplet/Spray Simulation

This paper presents a novel hybrid particle‐grid method that tightly couples Lagrangian particle approach with Eulerian grid approach to simulate multi‐scale diffuse materials varying from disperse droplets to dissipating spray and their natural mixture and transition, originated from a violent (high‐speed) liquid stream. Despite the fact that Lagrangian particles are widely employed for representing individual droplets and Eulerian grid‐based method is ideal for volumetric spray modeling, using either one alone has encountered tremendous difficulties when effectively simulating droplet/spray mixture phenomena with high fidelity. To ameliorate, we propose a new hybrid model to tackle such challenges with many novel technical elements. At the geometric level, we employ the particle and density field to represent droplet and spray respectively, modeling their creation from liquid as well as their seamless transition. At the physical level, we introduce a drag force model to couple droplets and spray, and specifically, we employ Eulerian method to model the interaction among droplets and marry it with the widely‐used Lagrangian model. Moreover, we implement our entire hybrid model on CUDA to guarantee the interactive performance for high‐effective physics‐based graphics applications. The comprehensive experiments have shown that our hybrid approach takes advantages of both particle and grid methods, with convincing graphics effects for disperse droplets and spray simulation.     

Geodesic-Controlled Developable Surfaces for Modeling Paper Bending

We present a novel and effective method for modeling a developable surface to simulate paper bending in interactive and animation applications. The method exploits the representation of a developable surface as the envelope of rectifying planes of a curve in 3D, which is therefore necessarily a geodesic on the surface. We manipulate the geodesic to provide intuitive shape control for modeling paper bending. Our method ensures a natural continuous isometric deformation from a piece of bent paper to its flat state without any stretching. Test examples show that the new scheme is fast, accurate, and easy to use, thus providing an effective approach to interactive paper bending. We also show how to handle non-convex piecewise smooth developable surfaces.     

A Practical Method for High‐Resolution Embedded Liquid Surfaces

Combining high‐resolution level set surface tracking with lower resolution physics is an inexpensive method for achieving highly detailed liquid animations. Unfortunately, the inherent resolution mismatch introduces several types of disturbing visual artifacts. We identify the primary sources of these artifacts and present simple, efficient, and practical solutions to address them. First, we propose an unconditionally stable filtering method that selectively removes sub‐grid surface artifacts not seen by the fluid physics, while preserving fine detail in dynamic splashing regions. It provides comparable results to recent error‐correction techniques at lower cost, without substepping, and with better scaling behavior. Second, we show how a modified narrow‐band scheme can ensure accurate free surface boundary conditions in the presence of large resolution mismatches. Our scheme preserves the efficiency of the narrow‐band methodology, while eliminating objectionable stairstep artifacts observed in prior work. Third, we demonstrate that the use of linear interpolation of velocity during advection of the high‐resolution level set surface is responsible for visible grid‐aligned kinks; we therefore advocate higher‐order velocity interpolation, and show that it dramatically reduces this artifact. While these three contributions are orthogonal, our results demonstrate that taken together they efficiently address the dominant sources of visual artifacts arising with high‐resolution embedded liquid surfaces; the proposed approach offers improved visual quality, a straightforward implementation, and substantially greater scalability than competing methods.     

Liquid-Gas Two-Phase Flow Simulation in Mold Filling Process with Level Set Method

Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking met...     

A Dimension‐reduced Pressure Solver for Liquid Simulations

This work presents a method for efficiently simplifying the pressure projection step in a liquid simulation. We first devise a straightforward dimension reduction technique that dramatically reduces the cost of solving the pressure projection. Next, we introduce a novel change of basis that satisfies free‐surface boundary conditions exactly, regardless of the accuracy of the pressure solve. When combined, these ideas greatly reduce the computational complexity of the pressure solve without compromising free surface boundary conditions at the highest level of detail. Our techniques are easy to parallelize, and they effectively eliminate the computational bottleneck for large liquid simulations.     

Online Motion Capture Marker Labeling for Multiple Interacting Articulated Targets

In this paper, we propose an online motion capture marker labeling approach for multiple interacting articulated targets. Given hundreds of unlabeled motion capture markers from multiple articulated targets that are interacting each other, our approach automatically labels these markers frame by frame, by fitting rigid bodies and exploiting trained structure and motion models. Advantages of our approach include: 1) our method is an online algorithm, which requires no user interaction once the algorithm starts. 2) Our method is more robust than traditional the closest point-based approaches by automatically imposing the structure and motion models. 3) Due to the use of the structure model which encodes the rigidity of each articulated body of captured targets, our method can recover missing markers robustly. Our approach is efficient and particularly suited for online computer animation and video game applications.     

A variational approach to multi-phase motion of gas, liquid and solid based on the level set method

We propose a simple and robust numerical algorithm to deal with multi-phase motion of gas, liquid and solid based on the level set method [S. Osher, J.A. Sethian, Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys. 79 (1988) 12; M. Sussman, P. Smereka, S. Osher, A level set approach for capturing solution to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146; J.A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999; S. Osher, R. Fedkiw, Level Set Methods and Dynamics Implicit Surface, Applied Mathematical Sciences, vol. 153, Springer, 2003]. In Eulerian framework, to simulate interaction between a moving solid object and an interfacial flow, we need to define at least two functions (level set functions) to distinguish three materials. In such simulations, in general two functions overlap and/or disagree due to numerical errors such as numerical diffusion. In this paper, we resolved the problem using the idea of the active contour model [M. Kass, A. Witkin, D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision 1 (1988) 321; V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, International Journal of Computer Vision 22 (1997) 61; G. Sapiro, Geometric Partial Differential Equations and Image Analysis, Cambridge University Press, 2001; R. Kimmel, Numerical Geometry of Images: Theory, Algorithms, and Applications, Springer-Verlag, 2003] introduced in the field of image processing.     

A second-order curvilinear to Cartesian transformation of immersed interfaces and boundaries. Application to fictitious domains and multiphase flows

A global methodology dealing with fictitious domains of all kinds on curvilinear grids is presented. The main idea is to transform the curvilinear framework and its associated elements (velocity, immersed interfaces…) into a Cartesian grid. On such grids, many operations can be performed much faster than on curvilinear grids. The method is coupled with a Thread Ray-casting algorithm which works on Cartesian grids only. This algorithm computes quickly the Heaviside function related to the interior of an object on an Eulerian grid. The approach is also coupled with an immersed boundary method (L²-penalty) or with phase advection methods such as VOF–PLIC, VOF–TVD, Front-tracking or Level-set approaches. Applications, convergence and speed tests are performed for shape initializations, immersed boundary methods, and interface tracking.     

A Semi-Lagrangian CIP Fluid Solver without Dimensional Splitting

In this paper, we propose a new constrained interpolation profile (CIP) method that is stable and accurate but requires less amount of computation compared to existing CIP‐based solvers. CIP is a high‐order fluid advection solver that can reproduce rich details of fluids. It has third‐order accuracy but its computation is performed over a compact stencil. These advantageous features of CIP are, however, diluted by the following two shortcomings: (1) CIP contains a defect in the utilization of the grid data, which makes the method suitable only for simulations with a tight CFL restriction; and (2) CIP does not guarantee unconditional stability. There have been several attempts to fix these problems in CIP, but they have been only partially successful. The solutions that fixed both problems ended up introducing other undesirable features, namely increased computation time and/or reduced accuracy. This paper proposes a novel modification of the original CIP method that fixes all of the above problems without increasing the computational load or reducing the accuracy. Both quantitative and visual experiments were performed to test the performance of the new CIP in comparison to existing fluid solvers. The results show that the proposed method brings significant improvements in both accuracy and speed.     

结合均值聚类的窄带水平集曲线演化

水平集方法是目前常用的一种图像分割方法,但它在构造速度函数时仅使用了图像的梯度信息,对于MRI这类含有强噪音、弱边界等现象的图像很难取得理想的分割结果.针对这一问题,将图像的区域信息和梯度信息相结合,构造新的基于K-均值聚类的水平集速度函数,该速度函数有较强的抗噪性能,并且能够处理含有弱边界、低对比度的图像.对左心室MR图像的分割实验表明该方法具有良好的分割效果.     

Characterization of MLS 1/ fnoise parameters

Optimal filters provide minimum variance interpolation and smoothing of noisy data, but the form of the noise power spectrum must be known for their design. We analyse data from the Microwave Limb Sounder (MLS) experiment onboard the Upper Atmosphere Research Satellite (UARS) to quantify parameters describing the noise spectra. MLS views space as part of its calibration sequence providing regular samples of the radiometer output. From these samples we determine breakpoint frequencies at which the spectral power density of the low frequency l/ f equal to that of the white noise. Breakpoint frequencies were in the range from 0005 to 002Hz for the 90 filter channels of the MLS. A method was developed to distinguish between 11/ f and systematic disturbances caused by cyclic changes in the operating environment as the spacecraft traverses its orbit.     

基于混合瑞利分布的三维医学图像分割算法

水平集算法是当前比较重要的分割算法,研究该算法的三维分割技术.提出高斯分布和瑞利分布相结合的方法进行概率密度函数的确定与分析,通过随机极大似然算法(SEM)把瑞利分布引入到水平集三维分割演化模型中.该方法成功应用于多种医学组织的三维分割,提高了分割速度和分割效果,减少了参数的设置.