Meshless Animation of Fracturing Solids

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.     

Turbulent flow computations on a hybrid cartesian point distribution using meshless solver LSFD-U

This paper may be considered as a sequel to one of our earlier works pertaining to the development of an upwind algorithm for meshless solvers. While the earlier work dealt with the development of an inviscid solution procedure, the present work focuses on its extension to viscous flows. A robust viscous discretization strategy is chosen based on positivity of a discrete Laplacian. This work projects meshless solver as a viable cartesian grid methodology. The point distribution required for the meshless solver is obtained from a hybrid cartesian gridding strategy. Particularly considering the importance of an hybrid cartesian mesh for RANS computations, the difficulties encountered in a conventional least squares based discretization strategy are highlighted. In this context, importance of discretization strategies which exploit the local structure in the grid is presented, along with a suitable point sorting strategy. Of particular interest is the proposed discretization strategies (both inviscid and viscous) within the structured grid block; a rotated update for the inviscid part and a Green-Gauss procedure based positive update for the viscous part. Both these procedures conveniently avoid the ill-conditioning associated with a conventional least squares procedure in the critical region of structured grid block. The robustness and accuracy of such a strategy is demonstrated on a number of standard test cases including a case of a multi-element airfoil. The computational efficiency of the proposed meshless solver is also demonstrated.     

Properties of a Level Set Algorithm for the Visibility Problems

We study an implicit visibility formulation and show that the corresponding closed form formula satisfies a dynamic programming principle, and is the viscosity solution of a Hamilton-Jacobi type equation involving jump discontinuities in the Hamiltonian. We derive the corresponding discretization in multi-dimensions and prove convergence of the corresponding numerical approximations. Finally, we introduce a generalization of the original Hamilton-Jacobi equation and the corresponding discretization that can be solved efficiently using either the fast sweeping or the fast marching methods. Thus, the visibility of an observer in non-constant media can be computed. We also introduce a specialization of the algorithms for environments in which occluders are described by the graph of a function.     

Real‐time cutting simulation of meshless deformable object using dynamic bounding volume hierarchy

This paper proposes a novel method for a real‐time cutting simulation of deformable objects using meshless method. The method utilizes a rapid refinement of topological relations among the simulation nodes of meshless deformable objects. Topological relations are defined as an undirected graph based on a visibility criterion. The graph connects the adjacent nodes that lie within a support of each node. The topological relations are refined by removing the edges of the graph that is intersected by the cut surface during the cutting simulation. Our approach utilizes a bounding volume hierarchy (BVH) to accelerate the computation of the intersection test. The BVH reconstruction algorithm is proposed to account for the cases where pieces of the object are completely cut out from the object. Algorithms to examine the connectivity among simulation nodes and accordingly reconstructing the BVH using two‐level BVH are presented. The proposed approach achieves real‐time cutting simulation of deformable objects through the rapid refinement of the topological relation. In addition, the computational performance of the cutting procedure is preserved during the entire simulation, thanks to the real‐time reconstruction of the BVH. Copyright © 2012 John Wiley & Sons, Ltd.     

Non‐Rigid Registration Under Isometric Deformations

We present a robust and efficient algorithm for the pairwise non‐rigid registration of partially overlapping 3D surfaces. Our approach treats non‐rigid registration as an optimization problem and solves it by alternating between correspondence and deformation optimization. Assuming approximately isometric deformations, robust correspondences are generated using a pruning mechanism based on geodesic consistency. We iteratively learn an appropriate deformation discretization from the current set of correspondences and use it to update the correspondences in the next iteration. Our algorithm is able to register partially similar point clouds that undergo large deformations, in just a few seconds. We demonstrate the potential of our algorithm in various applications such as example based articulated segmentation, and shape interpolation.     

Low‐Complexity Intervisibility in Height Fields

Global illumination systems require intervisibility information between pairs of points in a scene. This visibility problem is computationally complex, and current interactive implementations for dynamic scenes are limited to crude approximations or small amounts of geometry. We present a novel algorithm to determine intervisibility from all points of dynamic height fields as visibility horizons in discrete azimuthal directions. The algorithm determines accurate visibility along each azimuthal direction in time linear in the number of output visibility horizons. This is achieved by using a novel visibility structure we call the convex hull tree. The key feature of our algorithm is its ability to incrementally update the convex hull tree such that at each receiver point only the visible parts of the height field are traversed. This results in low time complexity; compared to previous work, we achieve two orders of magnitude reduction in the number of algorithm iterations and a speedup of 2.4 to 41 on height fields, depending on geometric content.     

A voronoi diagram‐visibility graph‐potential field compound algorithm for robot path planning

Numerous methods have been developed to solve the motion planning problem, among which the Voronoi diagram, visibility graph, and potential fields are well‐known techniques. In this paper, a new path planning algorithm is presented where these three methods are integrated for the first time in a single architecture. After constructing the generalized Voronoi diagram of C‐space, we introduce a novel procedure for its abstraction, producing a pruned generalized Voronoi diagram. A broad freeway net is then developed through a new α‐MID (maximal inscribed discs) concept. A potential function is assigned to the net to form an obstacle‐free network of valleys. Afterwards we take advantage of a bidirectional search, where the visibility graph and potential field modules execute alternately from both start and goal configurations. A steepest descent mildest ascent search technique is used for local planning and avoiding local minima. The algorithm provides a parametric tradeoff between safest and shortest paths and generally yields shorter paths than the Voronoi and potential field methods, and faster than the visibility graph. It also performs well in complicated environments. © 2004 Wiley Periodicals, Inc.     

Texturing fluids

We present a novel technique for synthesizing textures over dynamically changing fluid surfaces. We use both image textures as well as bump maps as example inputs. Image textures can enhance the rendering of the fluid by either imparting realistic appearance to it or by stylizing it, whereas bump maps enable the generation of complex micro-structures on the surface of the fluid that may be very difficult to synthesize using simulation. To generate temporally coherent textures over a fluid sequence, we transport texture information, i.e. color and local orientation, between free surfaces of the fluid from one time step to the next. This is accomplished by extending the texture information from the first fluid surface to the 3D fluid domain, advecting this information within the fluid domain along the fluid velocity field for one time step, and interpolating it back onto the second surface -- this operation, in part, uses a novel vector advection technique for transporting orientation vectors. We then refine the transported texture by performing texture synthesis over the second surface using our "surface texture optimization" algorithm, which keeps the synthesized texture visually similar to the input texture and temporally coherent with the transported one. We demonstrate our novel algorithm for texture synthesis on dynamically evolving fluid surfaces in several challenging scenarios.     

A Posteriori Analysis of a Positive Streamwise Invariant Discretization of a Convection-Diffusion Equation

We consider the finite element discretization of a convection-diffusion equation, where the convection term is handled via a fluctuation splitting algorithm. We prove a posteriori error estimates which allow us to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.     

基于整数拆分的椭圆曲线密码体制上的快速点乘算法

在椭圆曲线密码系统中,其核心操作是点乘运算κP,P是椭圆曲线上的点,忌是整数。怎样提高点乘计算速度,已成为热点研究领域。本文提出了一种新的基于整数拆分与预计算相结合的快速点乘算法。     

Incremental Polygonization of Implicit Surfaces

This paper describes an incremental polygonization technique for implicit surfaces built from skeletal elements. Our method is dedicated to fast previewing in an interactive modeling system environment. We rely on an octree decomposition of space combined with Lipschitz conditions to recursively subdivide cells until a given level of precision is reached and converge to the implicit surface. We use a trilinear interpolation approximation of the field function to create a topologically consistent tessellation characterized by an adjacency graph. Our algorithm aims at updating the mesh locally in regions of space where changes in the potential field occurred. Therefore, we propose an octree inflating and deflating strategy to preserve the octree structure as much as possible and to avoid useless or redundant computations. Timings show that our incremental algorithm dramatically speeds up the overall polygonization process for complex objects.     

A Finite Element Method on Convex Polyhedra

We present a method for animating deformable objects using a novel finite element discretization on convex polyhedra. Our finite element approach draws upon recently introduced 3D mean value coordinates to define smooth interpolants within the elements. The mathematical properties of our basis functions guarantee convergence. Our method is a natural extension to linear interpolants on tetrahedra: for tetrahedral elements, the methods are identical. For fast and robust computations, we use an elasticity model based on Cauchy strain and stiffness warping. This more flexible discretization is particularly useful for simulations that involve topological changes, such as cutting or fracture. Since splitting convex elements along a plane produces convex elements, remeshing or subdivision schemes used in simulations based on tetrahedra are not necessary, leading to less elements after such operations. We propose various operators for cutting the polyhedral discretization. Our method can handle arbitrary cut trajectories, and there is no limit on how often elements can be split.     

Direct extraction of surface meshes from implicitly represented heterogeneous volumes

This paper describes a novel algorithm to extract surface meshes directly from implicitly represented heterogeneous models made of different constituent materials. Our approach can directly convert implicitly represented heterogeneous objects into a surface model separating homogeneous material regions, where every homogeneous region in a heterogeneous structure is enclosed by a set of two-manifold surface meshes. Unlike other discretization techniques of implicitly represented heterogeneous objects, the intermediate surfaces between two constituent materials can be directly extracted by our algorithm. Therefore, it is more convenient to adopt the surface meshes from our approach in the boundary element method (BEM) or as a starting model to generate volumetric meshes preserving intermediate surfaces for the finite element method (FEM). The algorithm consists of three major steps: firstly, a set of assembled two-manifold surface patches coarsely approximating the interfaces between homogeneous regions are extracted and segmented; secondly, signed distance fields are constructed such that each field expresses the Euclidean distance from points to the surface of one homogeneous material region; and finally, coarse patches generated in the first step are dynamically optimized to give adaptive and high-quality surface meshes. The manifold topology is preserved on each surface patch.     

数字能见度仪中目标物自动定位技术

针对相机抖动和旋转造成的观测目标物定位不准确的问题, 提出了新颖的快速抗旋转匹配算法, 该方法利用与运算形成卷积运算的模式, 使匹配时间呈指数级下降. 大量实验结果表明, 利用该算法, 数字摄像能见度仪的目标物自动定标准确, 单次定标时间平均为24.2 ms, 在相同情况下比原始算法至少快200倍以上, 且观测准确度比普通算法提升7倍多, 比手动定位观测提升将近5倍. 基于该算法的数字摄像能见度仪测量结果符合世界气象组织对能见度仪研制标准的要求, 且价格更低, 具有广阔的应用前景.     

Patch layout from feature graphs

The structuring of surface meshes is a labor intensive task in reverse engineering. For example, in CAD, scanned triangle meshes must be divided into characteristic/uniform patches to enable conversion into high-level spline surfaces. Typical industrial techniques, like rolling ball blends, are very labor intensive.We provide a novel, robust and quick algorithm for the automatic generation of a patch layout based on a topology consistent feature graph. The graph separates the surface along feature lines into functional and geometric building blocks. Our algorithm then thickens the edges of the feature graph and forms new regions with low varying curvature. Further, these new regions-so-called fillets and node patches-will have highly smooth boundary curves, making the algorithm an ideal preprocessor for a subsequent spline fitting algorithm.     

挖掘最大频繁项集的改进蚁群算法

最大频繁项集挖掘用于发现频繁地出现在数据集中的最大子集,目前已经有许多有效的算法。应用蚁群算法挖掘最大频繁项集是一种新的方法,但是该算法往往迭代次数多,提取率低。结合频繁项集关联图和最大最小蚂蚁系统,提出一种新的蚁群算法。算法构造蚁群路径图,蚁群在动态的信息素和启发式因子指导下构造局部最大频繁项集,通过新的局部更新和全局更新机制发现全局最大频繁项集。对比实验表明,算法挖掘速度快,提取率高。     

求解区间图上的罗马控制数的动态规划算法

摘 要: 针对区间图的最小罗马控制函数和罗马控制数求解的困难性,本文提出了一个动态规划算法。从区间图的顶点排序开始,结合区间图的某些性质,采用逐步搜索的方法,不断扩大搜索的顶点集合范围,最终求出最优的罗马控制集和罗马控制数。为保证算法的正确性和科学性,对算法进行了严格的数学推理和证明。最后还给出了一个典型的区间图求解过程的演示示例,增强了算法的可读性和可操作性。结果表明该算法不仅运算速度快,而且简单易行。 关键词: 区间图;罗马控制函数;罗马控制数;权重;动态规划算法     

Accelerating unstructured finite volume computations on field‐programmable gate arrays

In the paper, an field‐programmable gate array (FPGA)‐based framework is described to efficiently accelerate unstructured finite volume computations where the same mathematical expression has to be evaluated at every point of the mesh. The irregular memory access patterns caused by the unstructured spatial discretization are eliminated by a novel mesh node reordering technique, and a special architecture is designed to fully utilize the benefits of the predictable memory access patterns. In the proposed architecture, a fixed‐size moving window of the input stream of the reordered state variables is cached into the on‐chip memory and a pipelined chain of processing elements, which gets input only from the fast on‐chip memory, is used to carry out the computations. The arithmetic unit (AU) of the processing elements is generated from the data flow graph extracted from the given mathematical expression. The data flow graph is partitioned with a novel graph partitioning algorithm to break up the AU into smaller locally controlled parts, which can be more efficiently implemented in FPGA than the globally controlled AU. The proposed architecture and algorithms are presented via a case study solving the Euler equations on an unstructured mesh. On the currently available largest FPGA, the generated architecture contains three processing elements working in a pipelined fashion to provide one order of magnitude speedup compared with a high performance microprocessor and three times speedup compared with a high performance graphics processing unit. Copyright © 2013 John Wiley & Sons, Ltd.     

CageR: Cage‐Based Reverse Engineering of Animated 3D Shapes

We present CageR: A novel framework for converting animated 3D shape sequences into compact and stable cage‐based representations. Given a raw animated sequence with one‐to‐one point correspondences together with an initial cage embedding, our algorithm automatically generates smoothly varying cage embeddings which faithfully reconstruct the enclosed object deformation. Our technique is fast, automatic, oblivious to the cage coordinate system, provides controllable error and exploits a GPU implementation. At the core of our method, we introduce a new algebraic algorithm based on maximum volume sub‐matrices (maxvol) to speed up and stabilize the deformation inversion. We also present a new spectral regularization algorithm that can apply arbitrary regularization terms on selected subparts of the inversion spectrum. This step allows to enforce a highly localized cage regularization, guaranteeing its smooth variation along the sequence. We demonstrate the speed, accuracy and robustness of our framework on various synthetic and acquired data sets. The benefits of our approach are illustrated in applications such as animation compression and post‐editing.     

Interactive High-Quality Soft Shadows in Scenes with Moving Objects

Interactive rendering of soft shadows (or penumbra) in scenes with moving objects is a challenging problem. High quality walkthrough rendering of static scenes with penumbra can be achieved using pre-calculated discontinuity meshes, which provide a triangulation well adapted to penumbral boundaries, and backprojections which provide exact illumination computation at vertices very efficiently. However, recomputation of the complete mesh and back-projection structures at each frame is prohibitively expensive in environments with changing geometry. This recomputation would in any case be wasteful: only a limited part of these structures actually needs to be recalculated. We present a novel algorithm which uses spatial coherence of movement as well as the rich visibility information existing in the discontinuity mesh to avoid unnecessary recomputation after object motion. In particular we isolate all modifications required for the update of the discontinuity mesh by using an augmented spatial subdivision structure and we restrict intersections of discontinuity surfaces with the scene. In addition, we develop an algorithm which identifies visibility changes by exploiting information contained in the planar discontinuity mesh of each scene polygon, obviating the need for many expensive searches in 3D space. A full implementation of the algorithm is presented, which allows interactive updates of high-quality soft shadows for scenes of moderate complexity. The algorithm can also be directly applied to global illumination.