A deformable surface model for real-time water drop animation

A water drop behaves differently from a large water body because of its strong viscosity and surface tension under the small scale. Surface tension causes the motion of a water drop to be largely determined by its boundary surface. Meanwhile, viscosity makes the interior of a water drop less relevant to its motion, as the smooth velocity field can be well approximated by an interpolation of the velocity on the boundary. Consequently, we propose a fast deformable surface model to realistically animate water drops and their flowing behaviors on solid surfaces. Our system efficiently simulates water drop motions in a Lagrangian fashion, by reducing 3D fluid dynamics over the whole liquid volume to a deformable surface model. In each time step, the model uses an implicit mean curvature flow operator to produce surface tension effects, a contact angle operator to change droplet shapes on solid surfaces, and a set of mesh connectivity updates to handle topological changes and improve mesh quality over time. Our numerical experiments demonstrate a variety of physically plausible water drop phenomena at a real-time rate, including capillary waves when water drops collide, pinch-off of water jets, and droplets flowing over solid materials. The whole system performs orders-of-magnitude faster than existing simulation approaches that generate comparable water drop effects.     

Procedural modeling of water caustics and foamy water for cartoon animation

We propose a method for procedural modeling and animation of cartoon water effects such as water caustics,foamy wake,and longshore currents.In our method we emulate the visual abstraction of these cartoon effects by the use of Voronoi diagrams and the motion abstraction by designing relevant controlling mechanisms corresponding to each effect.Our system enables the creation of cartoon effects withminimal intervention from the animator.Through high-level initial specification,the effects are animated procedurally in the style of hand-drawn cartoons.     

Skeleton-driven surface deformation through lattices for real-time character animation

In this paper, an efficient deformation framework is presented for skeleton-driven polygonal characters. Standard solutions, such as linear blend skinning, focus on primary deformations and require intensive user adjustment. We propose constructing a lattice of cubic cells embracing the input surface mesh. Based on the lattice, our system automatically propagates smooth skinning weights from bones to drive the surface primary deformation, and it rectifies the over-compressed regions by volume preservation. The secondary deformation is, in the meanwhile, generated by the lattice shape matching with dynamic particles. The proposed framework can generate both low- and high-frequency surface motions such as muscle deformation and vibrations with few user interventions. Our results demonstrate that the proposed lattice-based method is liable to GPU computation, and it is adequate to real-time character animation.     

Vector interpolation for surface normal calculation

The problem of approximating a surface normal by linear interpolation across a surface facet is considered from a geometric point of view. This point of view makes the coordinate independence for triangular facets particularly easy to see, and provides some insight into the problem of non-uniqueness for the non-triangular case.     

Markov-type velocity field for efficiently animating water stream

In computer graphics, one of the most challenging tasks is continuously varying phenomena such as waving, swaying, and flowing motions. In this paper, we present a novel hybrid model (physical-stochastic) to create an endless animation in which offline simulation is used to produce an infinitely varying real-time animated result. In this particular case, a water stream model is proposed. Most fully 3D physically based simulation methods for depicting fluid flows are very time and memory consuming. Thus, these methods are still reserved for offline simulations and small-domain real-time simulations, especially in the case of fluid flows with irregularly repeating patterns. The proposed model is based on the tracer particle technique, uses a non-static velocity field, and consists of two main phases. In the first phase, we construct the stochastic velocity field by using the physically based method. The second phase is the main part, in which we create real-time endless animation. Here, we introduce a new type of velocity field which we refer to as a Markov-type velocity field (MTVF). MTVF allows us to animate a water stream endlessly in real-time by avoiding the time-consuming process of solving the corresponding equations for every simulation step.     

Vector Field Path Following for Miniature Air Vehicles

In this paper, a method for accurate path following for miniature air vehicles is developed. The method is based on the notion of vector fields, which are used to generate desired course inputs to inner-loop attitude control laws. Vector-field path-following control laws are developed for straight-line paths and circular arcs and orbits. Lyapunov stability arguments are used to demonstrate asymptotic decay of path-following errors in the presence of constant wind disturbances. Experimental flight tests have demonstrated mean path-following errors on less than one wingspan for straight-line and orbit paths and less than three wingspans for paths with frequent changes in direction.     

Sampling Bounds for 2-D Vector Field Tomography

The tomographic mapping of a 2-D vector field from line-integral data in the discrete domain requires the uniform sampling of the continuous Radon domain parameter space. In this paper we use sampling theory and derive limits for the sampling steps of the Radon parameters, so that no information is lost. It is shown that if Δx is the sampling interval of the reconstruction region and x _max? is the maximum value of domain parameter x, the steps one should use to sample Radon parameters ρ and θ should be: \(\Delta\rho\leq\Delta x/\sqrt{2}\) and \(\Delta\theta\leq\Delta x/((\sqrt{2}+2)|x_{\max}|)\). Experiments show that when the proposed sampling bounds are violated, the reconstruction accuracy of the vector field deteriorates. We further demonstrate that the employment of a scanning geometry that satisfies the proposed sampling requirements also increases the resilience to noise.     

一种非结构矢量场的线卷积积分方法

传统的结构化LIC方法不适用于非结构矢量场数据处理的主要原因有两个,一是矢量幅度的表现力不强,二是因分辨率等因素无法有效地应用于采样点位置随机的矢量场．为解决上述问题,可以采用如下方法：在DDA曲线的生成过程中,采用基于数值的计算方法替代结构化LIC中基于网格的计算方法,从而有效地保证了处理结果的分辨率;在DDA曲线的卷积积分（LIC）处理过程中,采用区域标记的策略替代快速LIC方法中的线标记策略,一方面,因为被标记的采样点不再作为以后各轮DAA曲线生成的起始点,从而可以有效地减少计算量;另一方面,区域标记方法能够使LIC处理的结果稀疏化,表现为矢量场中幅度大的区域矢量线密集,而幅度小的区域矢量线稀疏,从而有效地提高矢量场幅度、结构的表现力．     

Video-based running water animation in Chinese painting style

This paper presents a novel algorithm for synthesizing animations of running water,such as water-falls and rivers,in the style of Chinese paintings,for applications such as cartoon making. All video frames are first registered in a common coordinate system,simultaneously segmenting the water from background and computing optical flow of the water. Taking artists’ advice into account,we produce a painting structure to guide painting of brush strokes. Flow lines are placed in the water following an analysis of variance of optical flow,to cause strokes to be drawn where the water is flowing smoothly,rather than in turbulent areas: this allows a few moving strokes to depict the trends of the water flows. A variety of brush strokes is then drawn using a template determined from real Chinese paintings. The novel contributions of this paper are:a method for painting structure generation for flows in videos,and a method for stroke placement,with the necessary temporal coherence.     

矢量场可视化的研究现状与发展趋势

矢量场广泛存在于自然界并在科学计算和工程分析中扮演着重要的角色,试图为矢量场可视化研究领域提供一个清晰的概貌。阐述了矢量场可视化的基本流程,矢量场可视化的研究现状以及迄今为止的一些研究成果,并讨论了矢量场可视化的发展趋势及应重视的研究方向。     

Visualization of 4D Vector Field Topology

In this paper, we present an approach to the topological analysis of four‐dimensional vector fields. In analogy to traditional 2D and 3D vector field topology, we provide a classification and visual representation of critical points, together with a technique for extracting their invariant manifolds. For effective exploration of the resulting four‐dimensional structures, we present a 4D camera that provides concise representation by exploiting projection degeneracies, and a 4D clipping approach that avoids self‐intersection in the 3D projection. We exemplify the properties and the utility of our approach using specific synthetic cases.     

Isotropic Energies, Filters and Splines for Vector Field Regularization

The aim of this paper is to propose new regularization and filtering techniques for dense and sparse vector fields, and to focus on their application to non-rigid registration. Indeed, most of the regularization energies used in non-rigid registration operate independently on each coordinate of the transformation. The only common exception is the linear elastic energy, which enables cross-effects between coordinates. Cross-effects are yet essential to give realistic deformations in the uniform parts of the image, where displacements are interpolated.In this paper, we propose to find isotropic quadratic differential forms operating on a vector field, using a known theorem on isotropic tensors, and we give results for differentials of order 1 and 2. The quadratic approximation induced by these energies yields a new class of vectorial filters, applied numerically in the Fourier domain. We also propose a class of separable isotropic filters generalizing Gaussian filtering to vector fields, which enables fast smoothing in the spatial domain. Then we deduce splines in the context of interpolation or approximation of sparse displacements. These splines generalize scalar Laplacian splines, such as thin-plate splines, to vector interpolation. Finally, we propose to solve the problem of approximating a dense and a sparse displacement field at the same time. This last formulation enables us to introduce sparse geometrical constraints in intensity based non-rigid registration algorithms, illustrated here on intersubject brain registration.     

Discontinuity-Preserving Vector Smoothing of Multivariate MR Images Using Vector Mean Field Annealing

We consider PD-, T1-, and T2-weighted magnetic resonance images jointly as a vector-valued image and use the angle of this vector field to formulate maximum a posteriori restoration as a global optimization problem. We use Mean Field Annealing (MFA) to find restorations that are superior to those obtained by previous multivariate approaches when shading artifacts near the MRI antenna are significant. Local homogeneity of the vector field as well as the angle between the components or the ratio of the components of the field are shown to have potential use for improving segmentation.     

基于Normalized cut的矢量场分割方法

基于Normalized cut的矢量场分割方法融合了格林函数和Normalized cut两种基本技术,即先用格林函数和初始矢量做卷积得到可保持其拓扑结构的标量场,再用Normalized cut方法对标量场进行分割,最后将分割好的标量场对应映射到初始矢量场中,以完成矢量场的分割.这种基于Normalized cut方法的特点就是分割时能综合考虑矢量场的整体特征和局部特征,由于利用矢量场潜在的拓扑结构可把在某一奇异点周围的矢量划分到同一个区域中,因此可达到最佳分割效果.     

基于PVM的三维矢量场流面构造

文章提出一种三维矢量场自适应粒子跟踪快速算法和基于ＰＶＭ的流面并行计算策略。该算法采用改进的单元搜索方法,消除了原算法计算精度不高和流动特征容易丢失的缺陷。其自适应步长技术,在保证计算精度的前提下,大大减少了流线上的点数,提高了流面的生成速度。实践证明,这种基于ＰＶＭ的并行计算策略进一步加快了算法速度。     

An Operator Approach to Tangent Vector Field Processing

In this paper, we introduce a novel coordinate‐free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real values on edges, we argue that vector fields can also be naturally viewed as operators whose domain and range are functions defined on the mesh. Although this point of view is common in differential geometry it has so far not been adopted in geometry processing applications. We recall the theoretical properties of vector fields represented as operators, and show that composition of vector fields with other functional operators is natural in this setup. This leads to the characterization of vector field properties through commutativity with other operators such as the Laplace‐Beltrami and symmetry operators, as well as to a straight‐forward definition of differential properties such as the Lie derivative. Finally, we demonstrate a range of applications, such as Killing vector field design, symmetric vector field estimation and joint design on multiple surfaces.     

Vector Field Visualization of Advective‐Diffusive Flows

We propose a framework for unified visualization of advective and diffusive concentration fluxes, which play a key role in many phenomena like, e.g. Marangoni convection and microscopic mixing. The main idea is the decomposition of fluxes into their concentration and velocity parts. Using this flux decomposition, we are able to convey advective‐diffusive concentration transport using integral lines. In order to visualize superimposed flux effects, we introduce a new graphical metaphor, the stream feather, which adds extensions to stream tubes pointing in the directions of deviating fluxes. The resulting unified visualization of macroscopic advection and microscopic diffusion allows for deeper insight into complex flow scenarios that cannot be achieved with current volume and surface rendering techniques alone. Our approach for flux decomposition and visualization of advective‐diffusive flows can be applied to any kind of (simulation) data if velocity and concentration data are available. We demonstrate that our techniques can easily be integrated into Smoothed Particle Hydrodynamics (SPH) based simulations.     

有界区域流场拓扑Voronoi图可视化

特征可视化能揭示流场的拓扑结构,是流场可视化的重要手段之一.传统特征可视化侧重于描述流场中各临界点间的拓扑关系,而较少重视各特征的区域范围.作为特征的重要属性,合理定义描述特征的有效影响范围,对于研究流场特征性质及其变化非常重要.为此,分析了平面流场拓扑特征,定义了流场典型特征的有效区域范围,提出了一种描述流场性质及变...     

Vector Field Based Texture Mapping of Animated Implicit Objects

This paper shows that an adequate use of vectorfields can solve most inconsistencies related to texture mapping that appear in current animation and rendering systems based on implicit objects. The method used is based on the concept of a virtual skin. A skin with its own texture mapping is spread over an implicit object and is constrained to stick to the deformation of the implicit object. A vectorfield is used to compute the relationship between the motion of the skin and the deformation of the object. Visual and implementation issues are discussed with respect to typical applications of implicit objects in computer graphics.     

基于平面矢量场的可视化方法的研究

平面矢量场可视化是科学计算可视化的重要研究内容。矢量场以直观的图形图像显示场的运动,透过抽象数据有效洞察其内涵本质和变化规律,广泛应用于计算流体力学、航空动力学、大气物理和气象分析等领域。对平面矢量场进行可视化的方法有很多种,常见的有点图标法、流线法、线积分卷积法和拓扑分析法等。论文主要研究常见的可视化方法,分析它们的性能,并通过实际的例子,对具体的可视化结果图像进行比较。通过该研究,能够给人们在选择可视化方法时提供依据。