B样条曲面拼接方法的设计与研究
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摘要
首先简单阐述了B样条曲线曲面生成的原理,并绘制成B样条曲线曲面。通过改变控制点的坐标或对控制点改变来实现局部的改变曲线曲面的形状,突出了B样条曲线曲面具有良好的局部性的特点。对B样条曲线曲面进行了简单的处理,绘制出散乱数据点下的B样条曲面,然后简单介绍现有的曲面拼接的方式方法,对曲面拼接方法的国内外研究现状进行了阐述,并设计了3个矢量参数的偏微分方程法,实现曲面拼接。详细阐述了在3个矢量参数下求解PDE的方法,并通过该方法实现了曲面的C~1连续拼接,较好地解决了曲面形状微调的问题,而且在曲面闭合的情况或非闭合情况下都可应用,具有广泛的应用价值。能够较好地满足实际,为接下来的研究提供了基础。最后总结该算法的优点以及不足。
This paper first briefly describes the principle of B-spline curve surface generation,and draw a B-spline curve surface.Locally changing the shape of the curved surface by changing the coordinates of the control point or changing the control point,projecting the B-spline curves and surfaces with good locality characteristics.Simple processing of B-spline curves and surfaces,draw a B-spline surface under a scattered data point,then briefly introduce the existing method of surface stitching,research on the present situation of surface blending method were elaborated,the partial differential equation method and the design parameters of the three vectors,achieve surface blending.This paper elaborates on the method of solving PDE under three vector parameters,and through this method,the C~1 continuous splicing of the surface is realized,solve the problem of the curved shape of the fine-tuning by a better way,and can be applied when the surface is closed or not closed,has a wide range of applications.Can better meet the reality and provide the basis for the next study.Finally,the advantages and disadvantages of the algorithm are summarized.
This paper first briefly describes the principle of B-spline curve surface generation,and draw a B-spline curve surface.Locally changing the shape of the curved surface by changing the coordinates of the control point or changing the control point,projecting the B-spline curves and surfaces with good locality characteristics.Simple processing of B-spline curves and surfaces,draw a B-spline surface under a scattered data point,then briefly introduce the existing method of surface stitching,research on the present situation of surface blending method were elaborated,the partial differential equation method and the design parameters of the three vectors,achieve surface blending.This paper elaborates on the method of solving PDE under three vector parameters,and through this method,the C~1 continuous splicing of the surface is realized,solve the problem of the curved shape of the fine-tuning by a better way,and can be applied when the surface is closed or not closed,has a wide range of applications.Can better meet the reality and provide the basis for the next study.Finally,the advantages and disadvantages of the algorithm are summarized.
引文
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[3]KAZMIIsmail Khalid,YOU Lihua,YANG Xiaosong,et al.Efficient sketch-based creation of detailed character models through data-driven mesh deformations[J].Computer Animation and Virtual Worlds,2015,26:3-4.
[4]KAZMIIsmail Khalid,YOU Lihua,ZHANG Jianjun.A hybrid approach for character modelling using geometric primitives and shape-from-shading algorithm[J].Journal of Computational Design and Engineering,2016(3):121-131.
[5]SHAO Jiayu,YOU Lihua.On some properties of three different types of triangular blocked tensors[J].Linear Algebra and its Applications,2016:S0024379516303901.
[6]陈亚娟,刘旭敏,关永.基于动态偏微分方程构造过渡面[J].计算机工程与设计,2009,30(14):3352-3355.
[7]WU Lijuan.The realization of B-spline surface reconstruction algorithm based on reverse control points[C]∥东北大学,IEEE新加坡工业电子分会,中国自动化学会信息物理系统控制与决策专业委员会.第29届中国控制与决策会议论文集(5).东北大学,IEEE新加坡工业电子分会,中国自动化学会信息物理系统控制与决策专业委员会:《控制与决策》编辑部,2017:5.
[8]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:高等教育出版社,2013:217-218.
[9]郭怀天.B样条曲线及曲面研究[D].合肥:合肥工业大学,2012.
[10]陈亚娟.过渡面生成算法及曲面光顺技术研究[D].北京:首都师范大学,2009.
[11]吴学毅.计算机图形学原理与实践[M].北京:印刷工业出版社,2008:103-104.
[12]李梦娇,袁晶,杜娜,等.准均匀B样条曲面重建的误差分析与改进方法[J].沈阳师范大学学报(自然科学版),2016,34(2):217-221.
[13]王洪艳.B-样条曲线曲面造型研究[D].哈尔滨:哈尔滨理工大学,2010.
[14]张宁蓉.计算机图形学[M].西安:西安电子科技大学出版社,2011:82-83.
[15]刘焕章.曲面拼接理论与技术的研究[D].北京:首都师范大学,2007.