消除二次曲面纹理映射的图像失真的方法

二次曲面是一类常用的物体，文章利用三角剖分纹理映射及仿射变换的原理，分别对圆柱曲面、球面实现了纹理映射，有效地消除了二次曲面的纹理映射的图像失真问题。     

带纹理映射的牙膏体构造法及其OpenGL实现

在探讨三维Morphing(形状过渡)技术的基础上,提出了一种带不失真纹理映射的牙膏体构造法,较详尽地阐述了三角网格剖分算法的思想.牙膏体是一个包含帽体和膏体两部分的复杂曲面体,从顶部圆台过渡到中间圆面、最后过渡到底部一条直线,它们在拓扑结构上是同构的,因此能通过OpenGL的顶点数组编程加以实现.这种组合曲面造型法不仅方便,还提供丰富的参数选择,具有一定的应用意义,也能有效应用于二维半形状、火箭体和鱼类等绘制.     

基于弹簧-质点模型的不规则曲面纹理映射

针对三角网格表示的不规则曲面的纹理映射问题,提出一种基于弹簧-质点模型的简单、高效、失真小的纹理映射算法。结合调和映射的参数化方法以及弹簧-质点模型的复杂平面展开方法,保持拓扑关系地将三维曲面投影于平面内;通过建立三角网格表示的投影面的弹簧-质点模型,将不规则曲面参数化于给定大小的矩形域;利用参数化的结果计算不规则曲面各顶点的纹理坐标,进行纹理贴图。实验结果表明,该算法能够实现纹理高效、均匀、变形小地映射于任意不规则曲面上。     

基于两步法的交互式纹理映射研究

两步纹理映射方法将映射过程分解为S映射与O映射两步进行.针对两步纹理映射方法研究中复杂物体表面纹理映射时出现的变形问题,采用B样条曲面代替简单的中间映射媒介,用它近似地包裹在三维物体的外表面,将纹理通过某种方式映射到曲面上实现参数化.基于两步映射方法提出了一种交互式纹理映射的算法.该算法允许用户交互选择贴图范围,通过控制B样条曲面实现对映射效果的调整.实验结果表明,该算法可显著提高纹理映射质量,纹理贴图效果良好.     

环形物体的两步纹理映射算法

鉴于现有的两步纹理映射技术对环形物体表面的纹理映射均不适用,为此提出了一种两步纹理映射方法,用于解决环形物体的纹理映射问题。该算法选择圆环表面为中介曲面,首先运用面积等比约束方法将两块相同类型的纹理分别映射到圆环的上下两侧表面,并通过对纹理拼接区域进行插值预处理来消除纹理接缝;然后采用中介表面法向法将圆环表面的纹理进一步映射至物体表面。实验结果表明,该算法可将平面纹理映射至多种环形物体表面,不仅纹理形变小,且保持连续,能够较好地满足虚拟现实与真实感绘制对环形物体表面的纹理映射要求。     

一种带不失真纹理映射的船形曲面造型法

提出了一种带不失真纹理映射的船形曲面造型法，详尽地阐述了算法的思想，并通过OpenGL实现该算法。这种曲面造型法能有效应用于各种二次曲面、牙膏体等的造型中。     

基于OpenGL的复杂曲面的纹理映射

介绍利用OpenGL和Visual C 6.0进行复杂曲面的纹理映射。利用解二次随圆偏微分方程的方法，得到任意曲面到平面的共形映射。此方法可以自动分配纹理坐标到复杂的没有起伏的曲面，有效地克服复杂曲面的自动纹理映射的变形，避免了纹理扰动。     

一般参数曲面的纹理映射技术

本文提出了一种适用于一般参数曲面的纹理映射算法。该算法通过绘制一系列非常靠近的曲线来生成曲面，应用向前差分算法来调节曲线绘制时的参数变化步长，以保证在生产的曲面上不留下任何一个没有绘制的象素。另外，由于该算法将曲面绘制问题转化成曲线绘制问题，从而也把对曲面的纹理映射问题转化为对曲线进行纹理映射，简化了纹理映射算法，易于实现。     

基于相位恢复的三维可视化应用研究

空间曲面的三维数字化测量在工业检测、虚拟现实、影视艺术以及文物保护等领域具有重要的应用价值。提出一种实现自由曲面三维数字化的方法,该方法不仅能重建物体的几何模型,而且能实现物体表面色彩等纹理属性的恢复。利用结构光照明重建空间三维点云数据,并利用匹配算法建立物体的几何模型;然后通过交互式选取点优化策略进行纹理映射的方法实现目标物体的真实感三维重建。与传统的方法相比,该方法能够精确地实现目标物体的纹理重建,避免了特征检测困难或粘贴标准点等方法的数据处理困难以及后期数据的人工等操作,实验结果也验证了该方法的有效性。     

一种适用于球面局部区域的纹理映射算法

两步纹理映射和环境映射一般都采用球面作为中介曲面，由于球面映射算法是这两种纹理映射技术的重要组成部分，且球面映射算法还可应用于自由曲面的识别和视景生成等方面，因此，对球面映射算法进行研究具有重要的意义，为了进一步减少球面映射算法产生的纹理形变，从纹理不变形准则出发，分析了传统球面纹理映射算法及其不足之处，并在此基础上提出了一种适用于局部球面的纹理映射新算法，由于该算法考虑了面积等比约束关系，因此可显著提高纹理映射质量，实验结果表明，该算法十分有效，具有一定优势。     

Calculus of nonrigid surfaces for geometry and texture manipulation

We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting.     

Metamorphosis of arbitrary triangular meshes

Three-dimensional metamorphosis (or morphing) establishes a smooth transition from a source object to a target object. The primary issue in 3D metamorphosis is to establish surface correspondence between the source and target objects, by which each point on the surface of the source object maps to a point on the surface of the target object. Having established this correspondence, we can generate a smooth transition by interpolating corresponding points from the source to the target positions. We handle 3D geometric metamorphosis between two objects represented as triangular meshes. To improve the quality of 3D morphing between two triangular meshes, we particularly consider the following two issues: 1) metamorphosis of arbitrary meshes; 2) metamorphosis with user control. We can address the first issue using our recently proposed method based on harmonic mapping (T. Kanai et al., 1998). In that earlier work, we developed each of the two meshes (topologically equivalent to a disk and having geometrically complicated shapes), into a 2D unit circle by harmonic mapping. Combining those two embeddings produces surface correspondence between the two meshes. However, this method doesn't consider the second issue: how to let the user control surface correspondence. The article develops an effective method for 3D morphing between two arbitrary meshes of the same topology. We extend our previously proposed method to achieve user control of surface correspondence     

真实感人脸模型的细分曲面重建

提出一种利用2张正交照片和细分曲面进行真实感三维人脸建模的方法,并实现了不同模型间的三维变形.为了构造个性化的人脸几何模型,将网格简化、自由曲面变形和细分结合起来,得到多个层次细节下的人脸模型;再经过纹理融合和映射,完成个性化的真实感三维人脸建模;同时利用线性插值实现了同拓扑真实感模型间的光滑变形.实验结果表明：该方法不仅可以进行有效的真实感三维人脸建模,而且变形简单流畅,具有广阔的应用前景.     

Globally optimal surface mapping for surfaces with arbitrary topology

Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in computer graphics and such a method provides us a ubiquitous tool for geometric modeling and data visualization. Its vast variety of applications includes shape registration/matching, shape blending, material/data transfer, data fusion, information reuse, etc. The mapping quality is typically measured in terms of angular distortions among different shapes. This paper proposes and develops a novel quasi-conformal surface mapping framework to globally minimize the stretching energy inevitably introduced between two different shapes. The existing state-of-the-art inter-surface mapping techniques only afford local optimization either on surface patches via boundary cutting or on the simplified base domain, lacking rigorous mathematical foundation and analysis. We design and articulate an automatic variational algorithm that can reach the global distortion minimum for surface mapping between shapes of arbitrary topology, and our algorithm is sorely founded upon the intrinsic geometry structure of surfaces. To our best knowledge, this is the first attempt towards numerically computing globally optimal maps. Consequently, our mapping framework offers a powerful computational tool for graphics and visualization tasks such as data and texture transfer, shape morphing, and shape matching.     

有真实感图形的纹理映射算法

本文讨论了计算机生成真实感图形的纹理映射技术，根据模拟现实物体的表面细节特征提出了三种纹理映射方法。     

Fast and intuitive generation of geometric shape transitions

We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed. However, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely, specifying the morphing process intuitively with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Suitable 3D interaction techniques offer a simple and intuitive control over the whole morphing process.     

基于MPEG-4的人脸表情图像变形研究

为了实时地生成自然真实的人脸表情,提出了一种基于MPEG-4人脸动画框架的人脸表情图像变形方法。该方法首先采用face alignment工具提取人脸照片中的88个特征点;接着在此基础上,对标准人脸网格进行校准变形,以进一步生成特定人脸的三角网格;然后根据人脸动画参数（FAP）移动相应的面部关键特征点及其附近的关联特征点,并在移动过程中保证在多个FAP的作用下的人脸三角网格拓扑结构不变;最后对发生形变的所有三角网格区域通过仿射变换进行面部纹理填充,生成了由FAP所定义的人脸表情图像。该方法的输入是一张中性人脸照片和一组人脸动画参数,输出是对应的人脸表情图像。为了实现细微表情动作和虚拟说话人的合成,还设计了一种眼神表情动作和口内细节纹理的生成算法。基于5分制（MOS）的主观评测实验表明,利用该人脸图像变形方法生成的表情脸像自然度得分为3.67。虚拟说话人合成的实验表明,该方法具有很好的实时性,在普通PC机上的平均处理速度为66.67 fps,适用于实时的视频处理和人脸动画的生成。     

Feature-based 3D morphing based on geometrically constrained spherical parameterization

Current trends in free form editing motivate the development of a novel editing paradigm for CAD models beyond traditional CAD editing of mechanical parts. To this end, we need robust and efficient 3D mesh deformation techniques such as 3D structural morphing.In this paper, we present a feature-based approach to 3D morphing of arbitrary genus-0 polyhedral objects that is appropriate for CAD editing. The technique is based on a sphere parameterization process built on an optimization technique that uses a target function to maintain the correspondence between the initial polygons and the mapped ones, while preserving topology and connectivity through a system of geometric constraints. Finally, we introduce a fully automated feature-based technique that matches surface areas (feature regions) with similar topological characteristics between the two morphed objects and performs morphing according to this feature correspondence list. Alignment is obtained without user intervention based on pattern matching between the feature graphs of the two morphed objects.     

Texturing Internal Surfaces from a Few Cross Sections

We introduce a new appearance-modeling paradigm for synthesizing the internal structure of a 3D model from photographs of a few cross-sections of a real object. When the internal surfaces of the 3D model are revealed as it is cut, carved, or simply clipped, we synthesize their texture from the input photographs. Our texture synthesis algorithm is best classified as a morphing technique, which efficiently outputs the texture attributes of each surface point on demand. For determining source points and their weights in the morphing algorithm, we propose an interpolation domain based on BSP trees that naturally resembles planar splitting of real objects. In the context of the interpolation domain, we define efficient warping and morphing operations that allow for real-time synthesis of textures. Overall, our modeling paradigm, together with its realization through our texture morphing algorithm, allow users to author 3D models that reveal highly realistic internal surfaces in a variety of artistic flavors.