毛发的结构造型方法

人物的绘制是当今计算机图形学中的一项重要任务,特别吸引人的是头发的生成技术.头发生成技术的难点在于其精细的形状和庞大的数量.文章针对头发提出了弯曲纹元和三维纹理体的概念,并给出了它们的数学表达式以及对不同发型的描述方法.弯曲纹元和三维纹理体是一般三维纹理的结构.带三维纹理的景物是由弯曲纹元和三维纹理体构成的,三维纹理体可再分成多个弯曲纹元,因而指明了三维纹理空间的结构,并解决了三维纹理曲面的造型问题.文章通过不同例子表明了结构造型方法在描述头发中的应用价值.     

三角和张量积Bézier曲面间相互转换的新方法

在计算机辅助几何设计中 ,已有的三角 Bézier曲面和张量积 Bézier曲面间的相互转换算法 ,通常是将一个三角 Bézier曲面转化为三个张量积 Bézier曲面 ,或将一个张量积 Bézier曲面转化为两个三角 Bézier曲面 ,但这样会增加系统存储和显示的负担 .针对这一问题 ,提出了一类新的转换方法 ,即 :将一个三角 Bézier曲面表示为一个张量积 Bézier曲面的 Trimm ed曲面 ,或者将一个张量积 Bézier曲面表示为一个三角 Bézier曲面的 Trimmed曲面 .理论分析和实验结果表明 ,当用基于广义 de Casteljau算法实现转换时 ,新方法与已有方法的数值精度相同 ,而在计算时间和存储量方面只有原来方法的 1/ 3或 1/ 2 .此外 ,新方法有利于在 Open GL的编程环境下显示三角Bézier曲面 .     

可展Bézier参数曲面

给出B啨ｚｉｅｒ参数曲面可展的特征 这里的B啨ｚｉｅｒ参数曲面包括三角域上的Ｂ B参数曲面和矩形域上的张量积B啨ｚｉｅｒ参数曲面 特别地 ,给出了三角域上可展二次B B参数曲面的具体形式及其构造方法 ,以及三角域上可展三次B B参数曲面为切线面的一种特例     

带有形状参数的B啨zier三角曲面片

给出了含有参数的二元(n+1)次多项式基函数,是三角域上二元n次Bernstein基函数的扩展;分析了该组基的性质并定义了带有形状参数的(n+1)次B啨zier三角曲面片·该曲面不仅具有n次B啨zier三角曲面片的特性,而且具有形状的可调性;其参数有明确的几何意义,参数越大,曲面越逼近控制网格;当参数为0时,曲面可退化为n次B啨zier三角曲面片·     

球域张量积Bézier曲面的降阶

讨论了球域张量积Bézier曲面的降阶问题。为了简单起见,只考虑了次数（m,n）的Bézier曲面的降阶到次数为（m-1,n-1）的情况。在降阶逼近过程中,要求低阶的张量积Bézier曲面为原有曲面的闭包。与已有的算法相比,该算法具有计算简单、逼近误差直接给出,几何直观性强等优点。     

两相邻张量积Bézier曲面的近似合并

Bézier曲面是 CAD/ CAM系统中的最常用的造型工具之一 ,因此在造型系统的发展过程中 ,对两相邻Bézier曲面近似合并算法进行研究是非常重要的。两相邻 Bézier曲面的近似合并就是 :在一定的误差允许范围内 ,用一片 k× l(k≥ m,l≥ n)次的 Bézier曲面去逼近相邻的两片 m× n次 Bézier曲面。但随着国际互联网越来越发展和跨国企业的大量建立 ,在产品设计中信息的交换越来越重要 ,且已能够实现。当前 ,产品模型数据的交换比以前更加频繁 ,但由于数据量特别巨大 ,因此如果在数据交换之前采用近似合并算法 ,则可减少几何数据。为了能较佳地进行 Bézier曲面近似合并 ,因此利用张量积 Bézier曲面细分后的矩阵表示 ,并根据所定义的原 Bézier曲面与合并Bézier曲面间的距离函数取最小值 ,给出了张量积 Bézier曲面近似合并的一种方法 ,以便得到合并 Bézier曲面控制顶点的显示表示式。该方法在合并过程中 ,由于考虑了原 Bézier曲面与合并 Bézier曲面在边界达到高阶连续的情形 ,因此利用该方法可直接完成两相邻 Bézier曲面的近似合并。     

基于扩展Bézier曲线拼接的曲线造型新方法

提出了一种基于扩展Bézier曲线拼接的曲线造型新方法。该方法首先构造了一种具有优良形状可调性和更好逼近性的带3个形状参数α, β, γ的三次扩展Bézier曲线(CE-Bézier曲线);并针对CE-Bézier曲线无法精确表示圆弧和椭圆弧等二次曲线的缺点,利用CE-Bézier曲线与C-Bézier曲线间的拼接技术,解决了CE-Bézier曲线造型中圆弧和椭圆弧的表示问题。最后讨论了该方法在曲线曲面设计中的应用。造型实例表明,该方法在计算机辅助几何设计中具有一定的应用价值。     

基于多分辨率模型的三角曲面特征线辨识技术

由于特征线在反求工程 CAD建模中具有非常重要的作用 ,因此利用图形图象处理中的多分辨率模型概念 ,通过研究三角曲面模型的特征线 ,提出了一种三角曲面特征线的计算方法 .将计算得到的初始特征线通过编辑、修改等手段进行处理 ,得到清晰的特征线 ,并将其作为进一步划分重构 B样条曲面边界的依据和参考 ,从而为实现基于三角曲面模型的 B样条曲面重构奠定了基础 .实验结果证明 ,该算法能够在三角曲面上提取出令人满意的特征线 ,并据此重构出拓扑划分合理的 B样条曲面 .     

区间Bézier曲面逼近

在区间算术分析的基础上 ,引进了区间 Bézier曲面的概念 ,给出了利用区间 Bézier曲面逼近一般曲面和有理参数曲面的两套算法 ,并通过实例展示了区间 Bézier曲面在这两种曲面逼近中的应用 ,最后研究了区间 Bézier曲面的边界结构 .结论是 m× n次区间 Bézier曲面的边界必由分片裁剪形式的 m× n次 Bézier曲面片、母线平行于坐标轴的柱面片和平行于坐标平面的矩形平面片构成     

可调配广义Bézier曲线的构造及应用

构造了一类带有形状控制参数的可调配广义Bézier曲线,它们继承了Bézier曲线的优点.曲线表示简单、直观.此外由于它们还带有形状控制参数,当曲线的控制顶点固定时,可以通过形状参数的调整实现对曲线的形状进行调节.特别地,当控制参数λ=0时,由控制顶点所定义的曲线即为Bézier曲线.同时它们既可以精确表示直线段、二次多项式曲线段又可以精确表示圆弧、椭圆弧等二次曲线.     

虚拟人物实时毛发动画

提出了一个基于晶格的机械变形方法。晶格被作为一个粒子系统采用数学方法变形，毛发采用2次B样条插值方法绘制。用元球模型处理毛发和身体表面之间碰撞。发型机械模型具有很高的实时性能和通用性，可以用来模拟各种复杂发型。模型可达到各种绘制背景下准确性和计算速度之间的最佳折中。     

Real-time animation of complex hairstyles

True real-time animation of complex hairstyles on animated characters is the goal of this work, and the challenge is to build a mechanical model of the hairstyle which is sufficiently fast for real-time performance while preserving the particular behavior of the hair medium and maintaining sufficient versatility for simulating any kind of complex hairstyles. Rather than building a complex mechanical model directly related to the structure of the hair strands, we take advantage of a volume free-form deformation scheme. We detail the construction of an efficient lattice mechanical deformation model which represents the volume behavior of the hair strands. The lattice is deformed as a particle system using state-of-the-art numerical methods, and animates the hairs using quadratic B-spline interpolation. The hairstyle reacts to the body skin through collisions with a metaball-based approximation. The model is highly scalable and allows hairstyles of any complexity to be simulated in any rendering context with the appropriate trade off between accuracy and computation speed, fitting the need of level-of-detail optimization schemes.     

发带头发模型的快速渲染及发型控制

为了解决虚拟人头发仿真中由于头发数量巨大导致的实时渲染难、发型单一的问题,提出了一种改进的、可实现多种发型的发带头发模型仿真方法。对基于NURBS曲面的头发模型定位控制点时,采用悬梁臂模型表现出头发自然下垂的状态。对传统的Phong光照模型,提出一种快速精确计算反射方向的改进方法,并考虑头发纹理和Phong明暗处理的相互作用。此外,提出一种新颖的发型设计方法,即通过对alpha纹理的控制和对纹理映射施加扰动函数实现不同头发长短和弯曲的造型。实验结果表明,新的方法能快速实现具有高逼真度的虚拟人头发仿真,且支持多种发型。     

构建三维头发造型的层次多阶约束域算法

现有头发建模方法通常使用相互孤立的造型约束生成整体发型,当面对较复杂的待建发型时往往无法建立有效的造型约束。针对真实头发造型的层次性和沿发丝逐阶段形变等特点,提出控制显式发丝形变的层次多阶约束域算法,以有效解决采用造型约束交互式构建复杂发型的问题。该方法通过建立分别作用于全局和局部发簇的层次约束域队列,使用多约束域逐阶段控制样例发丝产生复杂形变。此外,结合发丝曲线的最小旋转标架(RMF)和可自定义的空间螺旋线参数方程,为发丝添加细节效果。实验结果表明,与现有方法相比,该方法能够更加有效地构建出丰富、自然的头发造型。     

采用手绘曲线的交互式发型生成方法

将矢量场发型生成方法和手绘曲线交互相结合,提出一种交互式发型生成方法.该方法将发型曲线和发型编辑笔画作为矢量场生成的约束条件,使用户可利用手绘曲线来生成或编辑不同的发型,为发型生成提供了交互手段;同时,采用插值方法对空间矢量场计算进行了简化,确保了交互式发型生成的实时性.实验结果表明:文中方法可满足多种发型交互生成的需要.     

Simulation of face/hairstyle swapping in photographs with skin texture synthesis

The modern trend of diversification and personalization has encouraged people to boldly express their differentiation and uniqueness in many aspects, and one of the noticeable evidences is the wide variety of hairstyles that we could observe today. Given the needs for hairstyle customization, approaches or systems, ranging from 2D to 3D, or from automatic to manual, have been proposed or developed to digitally facilitate the choice of hairstyles. However, nearly all existing approaches suffer from providing realistic hairstyle synthesis results. By assuming the inputs to be 2D photos, the vividness of a hairstyle re-synthesis result relies heavily on the removal of the original hairstyle, because the co-existence of the original hairstyle and the newly re-synthesized hairstyle may lead to serious artifact on human perception. We resolve this issue by extending the active shape model to more precisely extract the entire facial contour, which can then be used to trim away the hair from the input photo. After hair removal, the facial skin of the revealed forehead needs to be recovered. Since the skin texture is non-stationary and there is little information left, the traditional texture synthesis and image inpainting approaches do not fit to solve this problem. Our proposed method yields a more desired facial skin patch by first interpolating a base skin patch, and followed by a non-stationary texture synthesis. In this paper, we also would like to reduce the user assistance during such a process as much as possible. We have devised a new and friendly facial contour and hairstyle adjusting mechanism that make it extremely easy to manipulate and fit a desired hairstyle onto a face. In addition, our system is also equipped with the functionality of extracting the hairstyle from a given photo, which makes our work more complete. Moreover, by extracting the face from the input photo, our system allows users to exchange faces as well. In the end of this paper, our re-synthesized results are shown, comparisons are made, and user studies are conducted as well to further demonstrate the usefulness of our system.     

A trigonal prism-based method for hair image generation

The difficulties involved in modeling and rendering hair in computer graphics are described. An efficient method using a trigonal prism model to render individual human hairs is presented. A wisp model easily controls hair shape with a few parameters. The method also proves effective for rendering eyebrows, eyelashes, beards, moustaches, clothes and personal ornaments such as earrings and hair accessories. A double z-buffer generates the backlighting effect. A simple parabola approximates wisp loci for hair animation. The method makes it possible to draw an enormous number of hairs within a reasonably short time     

重建发型的真实感头部建模

提出了从几何模型和多视点彩色图像构造真实感三维头部模型的方法．作为输入数据的彩色图像不仅被用来构造全景纹理图，而且是发型重构的数据源．首先在模型空间定义对应于真实图像平面的虚拟图像平面，恢复不同视点图像中发型外轮廓点的相应三维位置；然后根据发根位置、生长方向和长度，在模型的头皮表面重建发型．另一种发型重构的方法是从多幅图像中抽取的二维发型轮廓线出发，通过立体匹配法恢复其三维位置．然后用Coons-patch法重构发型表面．实验结果显示了文中方法的头部重建效果．     

Natural Hairstyle Modeling and Animation

In this paper, we develop a hairstyle modeling and animation technique specifically designed for human hairs, and we report several experimental results. Using simplified cantilever beam model and one-dimensional projective differential equations of angular momenta, we give a practical solution to the problem of enormous complexity. Even though our hair animation algorithm is an approximate solution, it includes all the relevant dynamic elements such as gravity, wind, inertia, air-resistance, hair-to-head, and hair-to-hair friction forces. Collision is an important element that makes a collection of hair strands look like hair. We develop an accurate but efficient hair-to-head and hair-to-hair collision detection and treatment algorithm. The algorithm produces quite realistic results; still it runs at an interactive speed. An interesting contribution of our algorithm is that it unifies hairstyle modeling and animation into a single equation, so that (1) hairstyling can be done under the effects of gravity and other internal or external forces, and (2) original hairstyle is more or less restored even after the initial hair is tangled by the application of external forces or head movements.     

Hair image generation using connected texels

Generation of photo-realistic images of human hair is a challenging topic in computer graphics.The difficulty in solving the problem in this aspect comes mainly from the extremely large number of hairs and the high complexity of the hair shapes,Regarding to the modeling and rendering of hair-type objects,Kajiya proposed a so-called texel model for producing furry surfaces.However,Kajiya‘s model could be only used for the generation of short hairs.In this paper,a concise and practical approach is presented to solve the problem of rendering long haris,and is particular the method of rendering the smooth segmental texels for the generation of long hairs is addressed.