基于n边形折叠的网格简化算法

提出在三角网格中利用多个三角形组合及检索n边形(n为正整数)的规则,并提出一种具有相似折叠规律的n边形折叠的网格简化算法,该算法以n边形折叠为基本简化操作,并以二次误差作为误差度量,每次n边形折叠操作可以减少,n-1个顶点以及2(n-1)个三角形,n越大达到某一简化目标所需的折叠次数越少,因此简化速度也可能越快.通过选取适当的n值及新顶点位置,新算法可以转化成顶点删除、边折叠及三角形折叠3种已知的几何元素删除算法,因此也可以视做为基于二次误差度量的几何元素删除简化算法的总括算法.最后分别对几种n取值情况列举实验数据,说明该算法的有效性.     

用C-C细分法和流形方法构造G2连续的自由型曲面

通过改进Cotrina等利用流形方法构造n边曲面片的算法,以C-C细分网格奇异点的5一环作为控制网构造出了带有均匀三次B样条边界的n边曲面片,使得该曲面片和C-C细分曲面G^2拼接．在此基础上,讨论了C-C细分曲面中n边域的构造和填充,从而为基于任意拓扑网格构造低次G^2连续曲面的问题给出了一个有效的解决方案,实现了用流形方法构造的曲面和C-C细分曲面的融合．最后,给出了几个具体算例．     

软件学报2002年第13卷总目次

第l期基于密度的增量式网格聚类算法(英文)……………………………… 陈 宁 陈 安基于关系数据库系统的空间数据处理方法(英文)…………………… 朱铁稳 钟志农塑造,l边形曲面的外形(英文)…………………………………………………· 郑津津基于规则的软件过程事务模型(英文)……………………………………· 沈备军 陈 诚带有时钟变量的线性时序逻辑与实时系统验证………………………………· 李广元路由查找算法研究综述………………………………… 徐 恪 徐明伟 吴建平一种新的实时多处理器系统的动态调度算法………………………· 乔 颖 …     

STL三角形网格模型曲面特征边的提取

针对STL网格模型曲面特征边识别困难的问题,提出一种基于边和面的特征边提取方法。首先遍历网格模型,自适应地获取二面角阈值并根据该阈值识别显性特征边;然后利用最小二乘法估算曲面上顶点的平均曲率,由此计算出三角形面片的近似曲率,并利用相邻三角形的曲率差值来判别其公共的隐性特征边是否为特征边,最后采用改进的断点处特征边提取算法形成完整的特征边界。实验结果表明该方法能够有效地提取STL网格模型曲面网格的特征边,具有很好的鲁棒性。     

基于移动最小二乘曲面的点云拼接算法

针对现有点云拼接方法受被测零件复杂外形和测量噪声影响的问题,提出基于移动最小二乘( Moving Least-Squares,MLS)曲面的点云拼接算法.该算法利用一种极值投影方法来有效计算点到MLS曲面的对应点,并结合迭代最近点(Iterative Closest Point,ICP)算法将各个视角的点云统一到该ML...     

基于任意骨架的隐式曲面造型技术

给出了一个新的基于任意多面体网格骨架的构造性自由曲面造型算法.算法首先由每个给定骨架构造出一个距离场,然后利用隐函数光滑过渡技术和CSG(constructive solid geometry)表示技术将所构造的隐式曲面自由地两两粘合成一张光滑曲面.隐式曲面的多边形化算法则用来生成最终曲面网格.以任意骨架作为基本体素,突破了传统隐式曲面以点为基本骨架的限制.而且,距离曲面很好地逼近了原骨架形状,使用户可直观地对复杂曲面进行交互设计.而形变函数的引入,则极大地丰富了此方法的造型能力.实验结果表明,基于该算法的原型系统能够方便、直观地构造复杂的自由曲面.     

基于隐函数插值的连续多分辨率模型

提出了一种基于变分隐函数插值的连续多分辨率模型生成算法,通过递归地删除网格模型中的边得到连续的简化模型.算法采用变分隐函数插值的方法对网格模型分区域插值,生成原始模型的区域插值隐函数曲面,并以对应隐函数曲面上的采样点作为边折叠的目标点.算法建立了可调加权控制函数来控制边的简化顺序.在模型简化过程中,可通过交互调节控制函数的权值执行不同的简化原则,使得重要度低的边优先删除.此外,通过建立独立集,避免了模型的局部过度简化.实验结果表明,此算法能实现较理想的简化效果.     

Delaunay三角网表示和点删除方法

对于三角网的表示方法,提出了一种双循环链表结构,这种结构能够方便的表示三角网的边拓扑和面拓扑信息,以及多边形结构.基于这种结构,对三角网点删除算法进行了改进.以前的点删除算法是基于连续的凸耳删除,提出的方法是基于多边形边的构建方法,利用D-三角网的空外接圆属性.与其它方法相比,这种方法具有容易理解,效率高的优点.     

基于车身曲面离散点的三角形网格生成

基于车身曲面的离散点,文章利用稀疏阵法搜寻法来自动生成三角形曲面。该方法首先通过曲面离散点在投影面上的投影点来生成稀疏矩阵,接着利用环形边表和边界搜寻盒来进行离散点的自动三角化。该方法算法简单,生成三角形的速度快,且生成的三角形网格适用于有限元分析和车身曲面的反求问题。文章最后给出的具体算例证明了该算法的有效性。     

基于SVG的动态函数作图研究及其实现

可伸缩矢量图(SVG)是一种基于XML的语言,用于绘制二维图形以及用户定制图形的呈现.利用这种新型网络图形标准,可以构建出初等数学函数的基本结构.应用该结构,实现了支持Web的动态函数作图.详尽讨论了基于SVG的函数表示方法和动态作图的策略及算法,同时确定了一种能够根据用户数据自动确定最佳比例,以缩放SVG图形的方法.     

Interactive Sculpting with Deformable Nonuniform B-splines

This paper describes an efficient method for manipulating deformable B-spline surfaces, based on minimizing an energy functional. The major benefit of the proposed new fairness norm is that it preserves the natural representation of the B-spline surface control points (a two dimensional array) which has an efficiency advantage over other methods. The designer uses forces as a main sculpting tool and is free to specify a single force, a set of isolated forces, forces situated on a line or curve or area of the deformable surface. The user is allowed to modify several parameters and in this way to change the physical properties of the object.     

An Interactive Designing System with Virtual Sculpting and Virtual Woodcut Printing

In this paper, we propose an interactive designing method and a system based on it to create 3D objects and 2D images. This system consists of two subsystems for virtual sculpting to create a 3D shape and virtual printing to produce a picture with a printing block. In the virtual sculpting subsystem, a user can form solid objects with curved surfaces as if sculpting them. The user operates virtual chisels, and can remove or attach arbitrary shapes of ellipsoids or cubes from or to the workpiece. A 3D object generated by virtual sculpting looks like a real wooden sculpture. If using a board as a workpiece, a user can generate a virtual printing block. In the virtual printing subsystem, a user can synthesize a woodcut printing image from the virtual printing block mentioned above, a virtual paper sheet, and a printing brush. The user can synthesize a realistic woodcut print with a procedure similar to the actual woodcut printing.     

Freestyle: Sculpting meshes with self-adaptive topology

We present a real-time method for sculpting triangular manifold meshes while enabling arbitrary surface deformation with seamless topological changes. Our insight is that the use of quasi-uniform mesh sampling, an interesting option now that very large meshes can be edited and displayed in real-time, provides the right framework for expressing and efficiently processing arbitrary changes of topological genus. The user controls deformation by gesture: he sweeps tools that apply a variety of deformation fields, from smoothing and trimming ones to local inflation and constant volume deformation tools. Meanwhile, the quasi-regular mesh seamlessly splits or locally blends when and where needed, while still following the user-specified deformation. Our method guarantees a closed, self-intersection-free mesh, whatever the user action. We demonstrate the practical usability of the resulting, interactive sculpting system through the sculpture of models that would have been extremely difficult to achieve with both current research methods and state of the art professional software.     

Warp sculpting

The task of computer-based free-form shape design is fraught with practical and conceptual difficulties. Incorporating elements of traditional clay sculpting has long been recognized as a means of shielding the user from these complexities. We present warp sculpting, a variant of spatial deformation, which allows deformations to be initiated by the rigid body transformation or uniform scaling of volumetric tools. This is reminiscent of a tool imprinting, flexing, and molding clay. Unlike previous approaches, the deformation is truly interactive. Tools, encoded in a distance field, can have arbitrarily complex shapes. Although individual tools have a static shape, several tools can be applied simultaneously. We enhance the basic formulation of warp sculpting in two ways. First, deformation is toggled to automatically overcome the problem of "sticky" tools, where the object's surface clings to parts of a tool that are moving away. Second, unlike many other spatial deformations, we ensure that warp sculpting remains foldover-free and, hence, prevent self-intersecting objects.     

Deformation Grammars: Hierarchical Constraint Preservation Under Deformation

Deformation grammars are a novel procedural framework enabling to sculpt hierarchical 3D models in an object‐dependent manner. They process object deformations as symbols thanks to user‐defined interpretation rules. We use them to define hierarchical deformation behaviours tailored for each model, and enabling any sculpting gesture to be interpreted as some adapted constraint‐preserving deformation. A variety of object‐specific constraints can be enforced using this framework, such as maintaining distributions of subparts, avoiding self‐penetrations or meeting semantic‐based user‐defined rules. The operations used to maintain constraints are kept transparent to the user, enabling them to focus on their design. We demonstrate the feasibility and the versatility of this approach on a variety of examples, implemented within an interactive sculpting system.     

High Reliefs from 3D Scenes

We present a method for synthesizing high reliefs, a sculpting technique that attaches 3D objects onto a 2D surface within a limited depth range. The main challenges are the preservation of distinct scene parts by preserving depth discontinuities, the fine details of the shape, and the overall continuity of the scene. Bas relief depth compression methods such as gradient compression and depth range compression are not applicable for high relief production. Instead, our method is based on differential coordinates to bring scene elements to the relief plane while preserving depth discontinuities and surface details of the scene. We select a user‐defined number of attenuation points within the scene, attenuate these points towards the relief plane and recompute the positions of all scene elements by preserving the differential coordinates. Finally, if the desired depth range is not achieved we apply a range compression. High relief synthesis is semi‐automatic and can be controlled by user‐defined parameters to adjust the depth range, as well as the placement of the scene elements with respect to the relief plane.     

Preventing self-intersection under free-form deformation

Free-Form Deformation (FFD) is a versatile and efficient modeling technique which transforms an object by warping the surrounding space. The conventional user-interface is a lattice of movable control points but this tends to be cumbersome and counterintuitive. Directly Manipulated Free-Form Deformation (DMFFD) allows the user to drag object points directly and has proven useful in an interactive sculpting context. A serious shortcoming of both FFD and DMFFD is that some deformations cause self-intersection of the object. This is unrealistic and compromises the object's validity and suitability for later use. An in-built self-intersection test is thus required for FFD and its extensions to be truly robust In this paper, we present the following novel results set of theoretical conditions for preventing self-intersection by ensuring the injectivity (one-to-one mapping) of FFD, an exact. (necessary and sufficient) injectivity test which is accurate but computationally costly, an efficient but approximate injectivity test which is a sufficient condition only, and a new form of DMFFD which acts by composing many small injective deformations. The latter expands the range of possible deformations without sacrificing the speed of the approximate test     

Crowd sculpting: A space‐time sculpting method for populating virtual environments

We introduce “Crowd Sculpting”: a method to interactively design populated environments by using intuitive deformation gestures to drive both the spatial coverage and the temporal sequencing of a crowd motion. Our approach assembles large environments from sets of spatial elements which contain inter‐connectible, periodic crowd animations. Such a “Crowd Patches” approach allows us to avoid expensive and difficult‐to‐control simulations. It also overcomes the limitations of motion editing, that would result into animations delimited in space and time. Our novel methods allows the user to control the crowd patches layout in ways inspired by elastic shape sculpting: the user creates and tunes the desired populated environment through stretching, bending, cutting and merging gestures, applied either in space or time. Our examples demonstrate that our method allows the space‐time editing of very large populations and results into endless animation, while offering real‐time, intuitive control and maintaining animation quality.     

Interactive Generation of Realistic Facial Wrinkles from Sketchy Drawings

Synthesizing facial wrinkles has been tackled either by a long process of manual sculpting on 3D models, or using automatic methods that do not allow for user interaction or artistic expression. In this paper, we propose a method that accepts interactive sketchy drawings depicting wrinkle patterns, and synthesizes realistic looking wrinkles on faces. The method inherits the simplicity of sketching, making it possible for artists as well as novice users to generate realistic facial detail very efficiently, allowing fast preview for physical makeup, or aging simulations for fun and professional applications. All strokes are used to infer the wrinkles, retaining the expressiveness of the sketches and realism of the final result at the same time. This is achieved by designing novel multi‐scale statistics tailored to the wrinkle geometry and coupled to the sketch interpretation method. The statistics capture the cross‐sectional profiles of wrinkles at different scales and parts of a face. The strokes are augmented with the statistics extracted from given example face models, and applied to an input face model interactively. The interface gives the user control over the shapes and scales of wrinkles via sketching while adding extra details required for realism automatically.     

Haptic sculpting of multi-resolution B-spline surfaces with shaped tools

In this paper, we first propose an implicit surface to B-spline surface haptic interface, which provides both force and torque feedback. We then present a new haptic sculpting system for B-spline surfaces with shaped tools of implicit surface. In the physical world, people touch or sculpt with their fingers or tools, instead of just manipulating points. Shaped virtual sculpting tools help users to relate the virtual modeling process to physical-world experience. Various novel haptic sculpting operations are developed to make the sculpting of B-spline surfaces more intuitive. Wavelet-based multi-resolution tools are provided to let modelers adjust the resolution of sculpture surfaces and thus the scale of deformation can be easily controlled. Moreover, sweep editing and 3D texture have been implemented by taking advantage of both the wavelet technique and haptic sculpting tools.