【作者】 李博；

【导师】 吴丽娟；

【作者基本信息】 沈阳师范大学 ， 无线电物理， 2020， 硕士

【摘要】 三维曲面构造研究是计算机辅助几何设计研究的热点之一,它通过计算机辅助系统设计分析曲面,完成对模型表面的模拟绘制。随着三维曲面构造技术的发展,曲面构建及曲面拼接技术在工程设计中的应用越来越广泛,是计算机辅助几何设计和制造的理论基础和关键。在曲面拼接问题上,很多学者进行了深入的研究,主要包括两种:Bézier曲面间的拼接和B样条曲面间的拼接。本文在查阅大量参考文献的基础上,设计了基于N-1条边的C~1连续的B样条曲面拼接算法。本文首先介绍了B样条曲面拼接技术的研究背景、选题意义以及国内外的研究现状,并介绍了论文的结构安排。其次介绍了B样条曲线、曲面的定义,详细分析了曲线、曲面的性质和分类,基于曲线和曲面的定义模型,定义了控制点,生成了均匀和准均匀曲面并给出了运行结果。然后重点介绍了曲面连续性,阐述了B样条曲面光顺方法的分析与研究,同时介绍了曲面光顺方法以及曲面光顺的重要性;最后,介绍了曲面拼接的方法,详细阐述了基于N-1条边的C~1连续的曲面拼接算法,通过给定的控制点构建三片待拼接的B样条曲面,求出待拼接曲面边界曲线上的型值点,通过反算生成控制点,再用控制点生成跨界曲线,并求出跨界曲线的跨界导矢,基于映射和约束条件生成拼接曲面。本算法在windows操作系统下,采用openGL,在VC++2010编译环境下进行算法的程序编写调试,并给出了运行结果,证明了算法的可行性。更多还原

【Abstract】 The research of 3d surface structure is one ofthe hot topics in the research ofcomputer-aided geometric design.With the development of 3d surface construction technology,surface construction and surface splicing technology are widely used in engineering design.On surface splicing,many scholars have conducted in-depth research,mainly including two kinds:Bezier surface splicing and b-spline surface splicing.In this paper,a continuous b-spline surface splicing algorithm based on n-1 edges is designed based on a large numberof references.First of all,the research background,the significance ofthe topic and the research status at home and abroad of b-spline surface splicing technology,and introduces the structure of the paper are introduced,Secondly,the definition of b-spline curve and surface is introduced,and the properties and classification of curve and surface are analyzed in detail.Then,the surface continuity,expounds the analysis and research of the b-spline surface smoothing method are introduced mainly,and the surface smoothing method and the importance of surface smoothing are expounded.Finally,the methods of surface splicing based on the continuous surface,on the edge ofN-1 the stitching algorithm are stated in detail,through the given control points to build three splicing b-spline curved surface,the type ofstay stitching on the curved surface boundarycurve value point,through generated by inverse calculation of control points,and cross-border curve is generated by a control point,and the crossover ofcross-border curve guide bolts,based on the mapping and constraintconditions to generate Mosaic surface.The algorithm in the Windows operating system,the use ofopenGL,in VC++2010 compilation environment for the algorithm programming debugging,and gave the running results,proved the feasibility ofthe algorithm.更多还原