【作者】 周晓杰；

【导师】 苏志勋； 刘秀平；

【作者基本信息】 大连理工大学 ， 计算数学， 2008， 博士

【摘要】 曲线曲面造型是计算机辅助几何设计和计算机图形学等领域的重要研究内容、主要研究在计算机的环境下曲线曲面的表示、设计、显示和分析等.经过近半个世纪的发展、传统的曲线曲面造型技术已经比较成熟。但是,随着人们对图形显示的真实性、实时性要求的日益增强和几何设计对象向多样性、复杂性的靠拢,曲线曲面造型技术又面临着很多新的问题和挑战,比如对于柔性物体的刻画,变形造型方法正是在这样的背景下产生的。本文首先对基于能量的曲线曲面变形方法进行了研究,并将其应用于人体模型的参数化建模以及针织布缩水预测问题中,取得了较好的效果,然后针对点采样曲面的造型问题,给出了一种新的基于物理的造型方法,本文主要工作及贡献如下:1.本文首先提出了一种基于内在(Intrinsic)表示的折线变形算法.将线段长度与线段之间的角度作为表示参数,既有利于能量函数的构造,又便于处理位移约束和长度内蕴约束条件,利用这一优势,将其应用于三维人体的参数化建模,可以方便地产生具有不同特征尺寸参数的人体模型,由于这种方法只适用于折线变形,具有较大局限性,因此,本文进一步提出一种较通用的离散曲线曲面变形方法,通过分析变形前后的位置关系来构造能量函数,再加上位移约束条件,将变形问题转化为一个凸二次规划问题,并且给出了约束点应满足的必要条件及模型解唯一的充分条件,这种方法还可以与骨架驱动变形的思想相结合,能更好的控制变形。2.空间曲线是造型中最基本的几何元素之一,对其有效的表示是造型的基础,而特征参数化表示是其中一种包含语义信息的高层次表示,本文对空间自由曲线的特征参数化表示进行研究,建立了一种针织物线圈的特征参数化几何模型,采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系,并将该模型与能量极小化的方法相结合,得到了一种能较好地预测针织物缩水率的新模型,对随机选取的一些针织布缩水预测实验表明了算法的可行性。3.对点采样曲面的变形问题进行了研究,提出了一种新的基于物理的点采样曲面变形方法一点采样曲面仿真的质点-弹簧模型,采用基于切平面投影和Delaunay三角剖分的方法对点采样曲面进行简化得到仿真点,进一步利用该三角剖分给出仿真点的弹簧结构,从而解决在拓扑信息缺失的情况下弹簧结构的构造问题,最终点采样曲面的变形通过仿真点的变形拟合得到,对一些典型曲面的变形验证了算法的可行性和有效性。更多还原

【Abstract】 Curve and surface modeling is an important topic in Computer Aided Geometric Design and Computer Graphics, whose major components are the representation, design, display and analysis of curves and surfaces using computer. In the past fifty years, traditional curve and surface modeling techniques have been developed deeply. However, with the enhancement of the demands for reality and real-timeliness in graphics display, and with the trends of variety and complexity of geometrical objects, curve and surface modeling faces many new problems and challenges, such as the description of soft objects. So the researchers began to study deformable modeling methods. In this dissertation, energy based deformation methods for curves and surfaces are studied first, and the proposed methods are applied to parametric modeling of human body and shrinkage predication of knitted fabrics. Then a novel physically-based modeling methods is presented for point-sampled surfaces. The main work and contributions are as follows:1. A new deformation method for polylines is first presented based on the intrinsic representation of the polylines. Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.2. Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.3. Deformation methods for point-sampled surfaces are studied in Chapter 5. A new physically-based method, mass-spring based simulation, is proposed for point-sampled surfaces. A tangent plane projection and Delaunay triangulation based simplification algorithm is applied to the original point-sampled surface to produce the simulation points, and then the mass-spring system for the simulation points is also constructed based on the Delaunay triangulation, which overcomes the lack of connectivity information. Deformation of the original point-sampled surface can be obtained from the deformed simulation surface by fitting. Experiments on some typical point-sampled surfaces indicate the feasibility and effectiveness.更多还原