中国科学院沈阳自动化研究所机构知识库
Advanced  
SIA OpenIR  > 装备制造技术研究室  > 学位论文
题名: 自由曲线曲面重建方法及形状微调技术研究
其他题名: Study on the Reconstruction of Free Form Curves & Surfaces and Its Shape Modification
作者: 程仙国
导师: 刘伟军
分类号: TP391.72
关键词: 逆向工程 ; 自由曲线 ; 自由曲面 ; B样条曲线 ; B样条曲面
索取号: TP391.72/C56/2011
学位专业: 机械电子工程
学位类别: 博士
答辩日期: 2011-12-06
授予单位: 中国科学院沈阳自动化研究所
学位授予地点: 中国科学院沈阳自动化研究所
作者部门: 装备制造技术研究室
中文摘要: 随着计算机技术和测量技术的快速发展,逆向工程已经成为产品设计和制造的一种重要手段。曲线曲面重建是逆向工程中两个重要问题,也是几何造型的核心问题。同时,一个复杂形体的几何建模往往不能一蹴而就,它需要在曲线曲面模型重建的基础上进行反复编辑、不断修改。因此,高精度的曲线曲面重建方法和一个简单实用的曲线曲面形状微调技术对缩短产品设计周期、提高建模效率具有重要的意义。本文对B样条曲线曲面重建关键技术及形状微调技术进行了深入的研究,主要研究内容及成果如下: 1. 研究了截面测量数据的B样条曲线重建问题。分析了激光线扫描测量数据噪声处理方法,引入了一种随机滤波法对激光线测量数据进行降噪;研究了数据点不同参数化方法对拟合曲线形状的影响,运用累积弦长参数化方法对数据点进行参数化,并给出了一种初始曲线的逼近算法;利用数据点的曲率信息提取曲率局部极值点,将曲率局部极值点和两个端点作为形状曲线的初始特征点,给出了一种新的节点配置算法用于逼近初始特征点,并引入了B样条曲线段复杂度的方法对特征点进行细分和节点的更新,克服了传统的节点插入方法对曲线重建结果的影响,得到了满足给定拟合误差的逼近曲线,且逼近曲线的节点数目等于细分后的特征点数目,较好地保留了形状曲线的细小特征。 2. 研究了基于截面测量数据的曲面重建方法。分析了呈矩阵拓扑点阵数据的B样条曲面拟合过程中数据点的参数化、节点矢量的计算方法,将B样条曲面的控制顶点的求解问题转化为两阶段B样条曲线的控制顶点求解问题,避免了求解B样条曲面控制顶点的复杂问题。分析了逆向工程中截面测量数据点特点,利用基于特征点的B样条曲线逼近算法对各截面线进行精确逼近;提出了一种候选节点和节点容差的方法对各截面线进行相容处理,得到了完全相容的截面线,利用曲面蒙皮法进行曲面重建,并运用节点删除算法删除逼近曲面的冗余节点,得到紧凑的B样条曲面。 3. 研究了基于三角网格模型的B样条曲面重建方法。分析了三角网格模型的数学描述,给出了散乱数据点的网格模型的重建方法,讨论了网格模型的参数化方法及其应用。针对单边界的三角网格模型,提出了一种基于均值坐标映射的参数化方法将其网格的顶点一一映射到指定的平面参数域,给出了一种平面参数域的规则采样的方法,利用逆映射技术将平面域的规则采样点映射到网格模型上,得到规则的三维空间采样点,构造插值于三维采样点B样条曲面,实现了三角网格模型的B样条曲面重建。 4. 研究基于外载荷的B样条曲线形状微调方法。分析了修改控制顶点对B样条曲线形状影响的规律,给出了曲线移点微调的数学表达式;研究了修改单个节点值和连续多个节点值对B样条曲线形状的影响规律;给出了一种等效B样条曲线上外载荷的力学模型,并建立了二阶的曲线能量方程,利用求解B样条曲线能量方程的最小值,得到了在外载荷作用下B样条控制顶点的变化量,实现了B样条曲线形状的微调。 5. 研究基于外载荷的B样条曲面形状微调方法。分析了修改控制顶点和节点矢量对B样条曲面形状影响的规律,给出了B 样条曲面移点微调的数学表达式;建立了四阶的曲面能量方程,给出了B样条曲面上的外载荷等效成曲面片端点力的力学模型,通过求解B样条曲面能量方程的最小值,得到在外载荷作用下B样条曲面控制顶点的变化量,实现了B样条曲面形状的整体和局部微调。
英文摘要: With the rapid development of computer technology and data acquisition technology, reverse engineering (RE) has become one of the import technologies for product design and manufacture. Curve and surface reconstruction are two important issues in RE, and also the core issues of the geometric modeling. At the same time, a complex geometric shape modeling often can not be done overnight, it needs to repeatly edit and constantly revise on the basis of curve and surface reconstruction. Therefore, the accuracy reconstruction methods of curve and surface, and a simple and practical technology of curve and surface shape minor adjustion are great significant to shorten the design cycle of new products and improve the modeling efficiency. This dissertation discusses and studies the reconstruction and shape modification of B-spline curve and surface.The main topics and contributions are as follows: 1. The B-spline curve rereconstruction of digitized section data is researched. The paper anlysises the data processing method of the laser line scanner data with the noise errors, introduces the random filter method to remove the noise errors, and studies the different parameterization methods of the data to influence the fitting curve shape. Using the cumulative chord parameterization to parameterize the data, we give an approximating algorithm to fit the initial curve. The local curvature maximum points are extracted by the curvature information of the curve. The local curvature maximum points and two end points of the data are viewed as the seed points of feature points. Base on the seed points, a new algorithm of calculating knot vectors is proposed for the approximating curve. Then we present the method of B-spline curve segment complexity to refine the feature points and update the knot vectors, overcoming the influence of the traditional method of knot insert on the result curve. Meawhile, the number of the knot vectors is eaqul to the number of the refinemented feature points. The small features of the result curve can be well retainded. 2. We discuss the problem of B-spline surface reconstruction of the digitized section data. We investigate the parameterization method and the knot vectors calculation of the lattice data for B-spline surface fitting. The inverse problem of the B-spline surface is transformed into two stages of the inverse problem of the B-spline curve, avoiding the complex problems of the calculation of the B-spline surface control points. We analyse the characteristics of digitized section data, use the method of B-spline curve approximation based on feature points to construct the sectional curves, propose the method of the candidate knot vectors and the method of the knot tolerance interval to make the sectional curves compatible, and get a B-spline surface by the skinning method. The surface can be compressed by the way of removing to remove the redundant knot vectors under the given error limits. 3. The problem of B-spline surface reconstruction based on the triangular mesh model is investigated. This dissertation argues the mathematical expressions of the mdoel, offers some construction techniques of he mesh model for the scattered data, and discusses the parameterization of the mesh model and its application. For the triangular mesh model with the single boundary, we suggest the method of mean coordinate mapping to map the vertices of the model into the specified plane parameter field, provide the regular sampling method for the plane parameter domain.Based on the inverse mapping technology, we obtain the regular three-dimensional space sampling points and construct the B-spline surface interpolating them. 4. We research the problem of the shape modification of B-spline curve based on external load. The paper analyses the impact law of the curve shape modification when the control points are changed, and presents the mathematical expression of moveing the point of the curve to the specified position. The altering law of the curve shape is discussed when a knot and continuous multiple knots are changed. The mechanical model of external load on B-spline curve is proposed, the curve energy function of second-order is established, the variation of the control points can be gained by solving the minmum value of the function. The shape modification of B-spline curve can be accomplished, avoiding the smoothing problem of B-spline curve. 5. We investigate the problem of the shape modification of B-spline surface based on external loads. The paper argues the influence of the changes of control points and knot vectors on the B-spline surface shape, offers the mathematical expressions of moving the point of the surface to the specified position. We establish the fourth-order energy function for the surface and supply the method of equaling the external loads into surface patch endpoint force. The variation of the control points can be acquired by solving the minmun value of the function.
语种: 中文
产权排序: 1
内容类型: 学位论文
URI标识: http://ir.sia.cn/handle/173321/9310
Appears in Collections:装备制造技术研究室_学位论文

Files in This Item:
File Name/ File Size Content Type Version Access License
自由曲线曲面重建方法及形状微调技术研究.pdf(2554KB)----限制开放 联系获取全文

Recommended Citation:
程仙国.自由曲线曲面重建方法及形状微调技术研究.[博士 学位论文 ].中国科学院沈阳自动化研究所 .2011
Service
Recommend this item
Sava as my favorate item
Show this item's statistics
Export Endnote File
Google Scholar
Similar articles in Google Scholar
[程仙国]'s Articles
CSDL cross search
Similar articles in CSDL Cross Search
[程仙国]‘s Articles
Related Copyright Policies
Null
Social Bookmarking
Add to CiteULike Add to Connotea Add to Del.icio.us Add to Digg Add to Reddit
所有评论 (0)
暂无评论
 
评注功能仅针对注册用户开放,请您登录
您对该条目有什么异议,请填写以下表单,管理员会尽快联系您。
内 容:
Email:  *
单位:
验证码:   刷新
您在IR的使用过程中有什么好的想法或者建议可以反馈给我们。
标 题:
 *
内 容:
Email:  *
验证码:   刷新

Items in IR are protected by copyright, with all rights reserved, unless otherwise indicated.

 

 

Valid XHTML 1.0!
Copyright © 2007-2016  中国科学院沈阳自动化研究所 - Feedback
Powered by CSpace