【作者】 计忠平；

【导师】 王国瑾； 刘利刚；

【作者基本信息】 浙江大学 ， 应用数学， 2008， 博士

【摘要】 三维几何造型与处理是计算机辅助设计、计算机图形学中和计算机动画的非常重要的研究课题之一,它在三维游戏、医学可视化、影视特效、数值仿真、计算机辅助制造和建筑等应用领域都有着广泛的应用.外形建模速度的快慢、操作手段的灵活性以及建模结果的质量高低等问题是这一课题的焦点所在.在传统的几何造型系统中,用户不仅需要具有较高的专业知识和建模技能,而且进行高逼真度的三维建模非常费时费力.因此,之前的建模方法和手段并不能很好地满足上述几个方面的应用需求.随着三维数据获取技术及图形建模方法的快速发展,已经产生了越来越多的三维模型.对已有的三维模型进行分割、组合、编辑和优化的复用建模方式将节省大量的人力和物力.本文围绕着三维网格曲面的轻松建模方法这一主题展开了深入的研究,建立起一系列简易高效的曲面建模算法,取得了以下丰富的创新性实用成果:1.提出了一种基于轻松勾画交互的网格分割技术.该方法交互简单自然,用户只需用鼠标在物体表面上通过勾画的方式大致标明希望获取的部分和抛除的部分,该技术就能很快地从三维网格模型中提取出用户希望获取的有意义的部分.由于模拟了人们日常生活中通过笔在纸上表达意图的操作方式,这种勾画交互方式很容易让人操作和接受.基于人体感知学中的极小值法则,解决了交互式分割模型上有意义部位的难题.基于区域增长法,使得分割算法效率非常高,完全能够胜任实时交互.基于该技术,通过泊松融合等方法将从不同模型上提取出来的子部分重新组合生成新的三维模型,从而对已知三维模型进行高效的复用.这种轻松交互的勾画式网格分割方法在降低建模难度和提高模型利用率及建模效率方面具有特别重要的实用意义.2.提出了通过勾画的统一网格分割和编辑的交互方式.该编辑方法不仅交互方式简单自然,而且充分利用了分割时的勾画线条来辅助引导模型的变形,因为线条可以认为带有模型的“姿势”信息.结合拉普拉斯网格编辑方法,保持了网格曲面上的细节.此外,利用一维骨架跟用户勾画的线条之间的相似关系,提出了一种勾画式的基于骨架的网格编辑方法,用勾画结果引导骨架,再以骨架驱动物体的变形.首先检测了模型上的突起特征顶点,在这些顶点的辅助下抽取了形式简洁的但是反映了物体拓扑结构的一维骨架.在抽取模型骨架的同时,还建立了模型的骨架-球表示,从而解决了如何将勾画与骨架相结合的问题.骨架-球表示既有一维骨架简单的表示形式,又带有占据物体空间的球体,提供了一种更加灵活的编辑手段,可以制作出更加丰富的编辑效果.3.提出了两种各具特色的非迭代的全局优化算法.一种是基于拉普拉斯算子的全局优化算法,目的是均匀化网格的三角形,可用于光顺网格或提高网格的三角形质量.在顶点约束、面重心约束以及共面约束等约束条件下,优化网格的同时还保持了模型表面的特征以及整体形状.另一种是曲率驱动的顶点流动算法,在保持网格的连接关系不变的前提下让顶点从平坦部位自动流向特征区域,从而增强了模型的视觉感观特征.两种方法都是只需一次性求解一个稀疏线性方程组,不需要迭代步骤,使用正定矩阵的Cholesky分解,使得算法效率很高.由于经过分割和融合等操作产生的新网格往往需要提高三角形的质量,而本文的全局优化方法正是为了这个目的,可以大大改善融合网格的质量,从而保障了本文方法能够制作高质量的网格模型.本文结合了勾画式的分割、编辑以及保持或者增强特征的优化方法,提出了轻松交互式的网格曲面建模方法,适合用于快速建模.本文方法改善了传统的建模方式,减少了交互量,大大提高了建模效率.更多还原

【Abstract】 Three-dimensional geometric modeling and processing is an important research topic in computer-aided design, computer graphics and computer animation. It has been widely used in various applications including computer games, medical visualization, entertainment industry, simulation, computer-aided manufacturing, architecture and so on. The efficiency, flexibility, and the quality of the modeling method are the primary challenges. The previous geometric modeling systems generally require much professional skills and efforts from the user to model complex and high-quality 3D models. On the other hand, a large number of 3D models have been created in recent years with the fast development of 3D data acquisition technologies. It appears that a compound approach using decomposing, merging, editing, and optimization would become useful and powerful in a modeling tool. In this paper, we have studied on the interactive approach for easy 3D modeling and developed a series of simple and efficient modeling algorithms. Our contributions are summarized as follows.1. Based on sketching mesh decomposing, an interactive mesh cutting tool is proposed, which is an intuitive and easy-to-use mesh cutout tool. Users can cut meaningful components from meshes instantly by simply drawing freehand sketches to roughly specify which parts of the mesh are wanted or unwanted. Sketch-based interfaces offer a natural method of interaction with computer applications because they mimic traditional expression on paper using pencils. The segmentation is based on the minima rule in human cognitive vision theory, which solves the problem on decomposing meshes into meaningful components interactively. Based on an improved region growing algorithm, instant visual feedback can be provided for users. Combined with the Poisson merging approach, it reuses existing models efficiently. It presents its importance in practical to improve the reusability of models and the efficiency of the three-dimensional modeling, and to reduce the difficulty of 3D modeling.2. A unified sketch-based mesh decomposing and editing approach is proposed. On one hand, the sketch-based interfaces are simple and natural for mesh editing; on the other hand, the sketches using to decompose the model are reused to guide the deformation, because they can be considered as a model of "gesture" information. Combined with Laplacian mesh editing, our method can preserve details of the source mesh. In addi- tion, considering the similarity between the sketch and the one-dimensional skeleton, we proposed a sketch-base mesh editing method combined with the skeleton. Prong feature points correspond to tips of the branches of the shape are detected, then the skeleton is computed with the assistance of prong features. A novel representation—skeleton and balls are constructed simultaneously, which gives a solution to combining the skeleton and sketching. This representation is simple but preserves the topological structure of the object, and provides a more flexible form with which one can produce more editing results.3. Two different types of non-iterative and global optimization algorithms are proposed. One is the global optimization algorithm based on Laplacian operator, which is designed to unify the triangle shape of meshes, and can be used to smooth or improve the quality of triangular meshes. The global shape and features of the original mesh can be preserved by adding a variety of constraints in the system such as vertex position, face barycenter constraints and coplanar constraints. The other one is the curvature-driven vertices flow algorithm which is designed to make mesh vertices flow from low-curvature regions to high-curvature regions, thus to enhance features of the mesh. It only needs to solve a linear least squares without any iterative scheme, which is efficient using the Cholesky factorization of symmetric positive definite matrices. Our global optimization algorithms are designed to improve the quality of triangles on new meshes produced by the decomposing and merging operations. After optimization, the mesh quality is greatly improved, which ensures that our method can produce high-quality mesh models.This paper provides an intuitive and simple sketch-based interface for both expert users and untrained users to model 3D meshes in an easy manner. We have proposed couples of interactive approaches for easy geometric modeling including the sketch-based mesh decomposition, editing, and feature aware optimization. Our approaches improve traditional modeling approach by involving human users in the process, yet minimizing user input and providing real time feedback.更多还原