【作者】 张新宇；

【导师】 叶修梓；

【作者基本信息】 浙江大学 ， 计算机应用技术， 2004， 博士

【摘要】 三维几何已逐渐成为继声音、图像和视频之后的新一代数字媒体，这一媒体与其它数字媒体一样要求相应的工具和理论来支持自由、稳定和快速的造型和处理，这一直是CAD、计算机仿真和三维计算机动画等工业领域关注的问题，也是计算机图形学研究工作者们关心和关注的研究方向。就我们所知，三维几何造型和处理中所有的工作都是针对三维模型在计算机图形学中的两个主要属性——模型的几何形状和模型的纹理属性——展开的。本文，我们关注与网格模型的几何形状和纹理属性相关的研究内容，就网格的造型和处理领域的一些热点和难点问题，提出了相应的解决方法和理论。其中涉及几何和实体造型中的网格模型的扫描体逼近计算和网格模型的自由变形技术，外观造型和纹理设计中的交互式三维纹理彩绘，还有建立在几何图像之上的网格滤波理论。本文的主要贡献在于： 在扫描体逼近计算方面，在原有任意多边形网格模型沿任意路径运动生成扫描体逼近算法的基础上，提出了加入对扫描母体简化的预处理和用活动标架对扫描路径进行重采样等过程，算法的其它过程还包括：计算扫描体中几何基元的排列，用硬件加速构造无符号的有向距离场，将无符号距离场转化为有符号距离场，从有符号有向距离场提取等值面等。另外，我们还提出了对最终生成的扫描体进行简化的优化的处理过程。通过大量实验数据，着重分析了扫描母体的简化和利用活动标架对扫描路径进行重采样两个步骤对扫描体逼近的影响。实验结果表明，在一定的简化(扫描母体)范围内，扫描体生成的速度随着扫描母体的简化程度成线性关系提高，扫描体质量则基本保持不变，当达到某个临界点后，随着扫描母体的继续简化，扫描体质量迅速下降。同时，实验结果表明扫描路径的重采样操作也会得到类似的效果。 在自由变形技术方面，舍弃了原有的利用Bézier形式的偏移参考基准线，取而代之的是由基本函数定义的偏移曲线。这一方面弥补了受Bézier曲线在一个局部凸包内的约束，使得网格顶点可变形的范围更大，另一方面使得计算更稳定、变形后的曲面质量更好。其次，扩展了曲线几何约束。舍弃了原有的利用三角剖分带和局部参数化的方法，转而利用基本函数定义的偏移曲线来生成表面的凸凹变形。进而提出了利用曲线几何约束实现非均匀变形的方法，通过控制不同位置变形区域的大小和变形的幅值可以得到非均匀变形效果。另外，利用扩展的曲线几何约束变形方法，还可以模拟诸如椭球和圆环体的变形效果。 在网格滤波方面，提出了建立在几何图像之上的滤波理论，这种理论与其它的滤波技术在思想上完全不同。我们首先为任意的一个网格(在必要的情况下，需要切割为一个开网格)生成一幅几何图像。一旦得到几何图像，我们用传统的图像处理工具对几何图像进行处理。最后，我们用重构技术将处理后的几何图像重构为三维网格模型。我们通过实验结果为读者展现了大量的丰富多彩有趣的滤波效果，其中包括：模糊滤波、锐化滤波、晶格化滤波、像素化滤波和通过颜色调整滤波等。 在纹理造型方面，针对传统的三维彩绘技术利用纹理映射和参数化方法的缺陷，提出一种新颖的数据表示以实现在任意三角网格模型上直接进行三维彩绘。这是一种更为一般的数据表示，其思想也与用八叉树实现无参数化的纹理映射的方法不同。这种图像化几何的方法将每一个三角形视为一个三角形图像，可以直接对三角形内的几何点进行着色，而无须任何参数化和映射处理。系统的输出是原始网格加上附着其上的带有颜色信息的几何点。将这种数据表示用于三维模型彩绘可以很好地处理拓扑结构复杂的模型。 另外，设计并实现了一个三维媒体处理核心系统:Par目渐吮kS。为了适应各种应用，我们尽可能保持各种数据结构和算法的灵活性、时间左间的效率和易用性等特点。洲门的目标是:为实现上层的三维媒体处理技术(包括网格造型和处理、点集曲面绘制、逆向工程中的扫描线、基于栅格的体数据表示，还包括用于纹理映射和纹理合成的二维图像在内的各种媒体)提供底层数据结构和算法。更多还原

【Abstract】 3D geometry has become increasingly popular as a new form of digital media. Similar to other types of media, i.e., sound, image, and video, this requires tools and theories to model and process 3D geometry freely, robustly and fast in the fields of computer-aided design, computer simulation, computer animation and 3D games. It also has been the hot research topics in computer graphics. To author’s knowledge, almost all of research works in computer graphics have been proposed for two main kinds of properties of 3D models: geometric shape and texture property. The main focus of this thesis is on algorithms and theories for shape and texture modeling and processing of surfaces represented by meshes. This includes the techniques for swept volume approximation computation for arbitrary meshes and free-form deformation in geometric and solid modeling, the method for 3D interactive texture painting in appearance modeling and texture design and the theory for geometry image based filtering.In computation of swept volume approximation, an improved technique to generate the swept volume approximation for arbitrary meshes is presented by introducing generator simplification and path resample using Frenet moving frames along the discreted sweeping trajectory. Other steps, such as a directed distance field computation on a uniform grid based on the hardware accelerated computation technique and iso-surface extraction using Marching Cubes algorithm, are also included in this algorithm. In addition, the simplification scheme and smoothing technique are applied to the swept volume generated from iso-surface extraction. A large number of analytical data is extracted from well-designed experiments, with which the influence of the generator simplification and the trajectory resample to the last swept volume is analyzed. It shows that the generator simplification can do improve the sweeping speed of the last swept volume in linear time while preserving its quality, but after reaching a critical point, the quality of the swept volume declines sharply with simplification of the generator. So does the trajectory resample.In free-form deformation, the basic functions are implied to the displacement curve representation to replace the Bezier-shaped displacement reference curves used in our original system. To author’s knowledge, it can remedy the fact that the Bezier-shaped displacement reference curves are laid in local hulls in one hand, so that the deformation region can be further and larger; on other hand, it makes the computation and quality more robust and better. In addition, an extended curve constraint is presented to replace the original triangulation and parameterization techniques and instead of the Bezier-shaped displacement reference, the basic function with parameters to control the deformation area and the magnitude are used to surface deformation. Moreover, a nonuniform deformation technique is implemented by controlling the deformation region and magnitude nonuniformly. This technique also shows that it can simulate deformation effects constructed by other geometric primitives, such as ellipsoid and torus.In mesh filtering, the concept of geometry image is introduced into surface filter and a novel filter theory based on geometry images is illustrated, which is completely different in spirit Geometry images are created to represent 3D surfaces after cut and parameterization. Our improvement in resolution and reconstruction algorithms are presented while creating geometry images. These geometry images are then sent to the image processing toolboxes for varaints of filtering effects. 3D filtered models can be created via reconstruction from these filtered images. In our experiements, different and interesing surface filtering effects are achieved, such as blur, sharpen, crystallize, pixelize and variants of color adjustments.In appearance modeling, it is well known that the painting system based on texture mapping is often limited by the model’s parameterization into 2D texture space. For models with更多还原