一种基于几何约束的插值曲线的参数连续性
|
摘要
针对计算机辅助几何设计中工程造型需用曲线曲面拼接来构造的问题,研究了一种基于几何约束的插值曲线的参数连续性.通过分析这种插值曲线的性质及端点处切向量,研究了曲线间的光滑拼接条件,得到了两条插值曲线的C1,C2连续条件及几何意义.最后,给出了该插值曲线光滑拼接的步骤和应用实例.实例表明,该插值曲线在曲线曲面造型中具有一定的应用价值.
Focusing on the problem that the engineering modeling can be constructed by the connections of curve and surface in computer aided geometric design,parametric continuity for a class of interpolation curves with geometric constraints were investigated.Based on the analysis of the properties of the interpolation curves and the tangent vector at the end point,the smooth connection conditions between curves were investigated.The continuity conditions of two interpolation curves C1,C2 and geometric meanings of the curves were presented.Finally,the steps of the continuity condition for the interpolation curves and application examples of the interpolation curves were given.Experimental examples show that the interpolation curves have a certain application value in the curve and surface design.
Focusing on the problem that the engineering modeling can be constructed by the connections of curve and surface in computer aided geometric design,parametric continuity for a class of interpolation curves with geometric constraints were investigated.Based on the analysis of the properties of the interpolation curves and the tangent vector at the end point,the smooth connection conditions between curves were investigated.The continuity conditions of two interpolation curves C1,C2 and geometric meanings of the curves were presented.Finally,the steps of the continuity condition for the interpolation curves and application examples of the interpolation curves were given.Experimental examples show that the interpolation curves have a certain application value in the curve and surface design.
引文
[1]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,2001:306-454.SHI F Z.Computer aided geometric design&NURBS[M].Beijing:Higher Education Press,2001:306-454.
[2]胡钢,戴芳,秦新强,等.四次带参Bezier曲线曲面的光滑拼接[J].上海交通大学学报,2010,44(11):1481-1485,1490.HU G,DAI F,QIN X Q,et al.On continuity conditions for quartic Bezier curves and surfaces with shape parameters[J].Journal of Shanghai Jiaotong University,2010,44(11):1481-1485,1490.
[3]刘植,陈晓彦,江平.带多形状参数的广义Bézier曲线曲面[J].计算机辅助设计与图形学学报,2010,22(5):838-844.LIU Z,CHEN X Y,JIANG P.A class of generalized Bezier curves and surfaces with multiple shape parameters[J].Journal of Computer Aided Design&Computer Graphics,2010,22(5):838-844.
[4]陈军.一类带三个形状参数的三角曲面[J].计算机集成制造系统,2013,19(11):2680-2685.CHEN J.Triangular surface with three shape parameter[J].Computer Integrated Manufacturing Systems,2013,19(11):2680-2685.
[5]师晶.一类二次TC-Bezier曲线的光滑拼接[J].新乡学院学报,2016,33(12):12-14.SHI J.Smooth connections for a class of quadratic TC-Bezier Curve[J].,2016,33(12):12-14.
[6]邱宁.时间分数阶延迟微分方程在流体力学中的应用[J].沈阳大学学报(自然科学版),2016,28(2):170-172.QIU N.Application of time fractional delay differential equations in fluid dynamics[J].Journal of Shenyang University(Natural Science),2016,28(2):170-172.
[7]郭海杰.非线性Dirichlet型三点边值问题正解的存在性[J].沈阳大学学报(自然科学版),2016,28(4):340-344.GUO H J.Existence of positive solutions for nonlinear Dirichlet type three point boundary value problems[J].Journal of Shenyang University(Natural Science),2016,28(4):340-344.
[8]吴雪蓉.一类常微分方程和Volterra积分方程解的存在唯一性[J].沈阳大学学报(自然科学版),2017,29(2):168-172.WU X R.Existence and uniqueness of solutions for ordinary differential equations and Volterra integral equations[J].Journal of Shenyang University(Natural Science),2017,29(2):168-172.
[2]胡钢,戴芳,秦新强,等.四次带参Bezier曲线曲面的光滑拼接[J].上海交通大学学报,2010,44(11):1481-1485,1490.HU G,DAI F,QIN X Q,et al.On continuity conditions for quartic Bezier curves and surfaces with shape parameters[J].Journal of Shanghai Jiaotong University,2010,44(11):1481-1485,1490.
[3]刘植,陈晓彦,江平.带多形状参数的广义Bézier曲线曲面[J].计算机辅助设计与图形学学报,2010,22(5):838-844.LIU Z,CHEN X Y,JIANG P.A class of generalized Bezier curves and surfaces with multiple shape parameters[J].Journal of Computer Aided Design&Computer Graphics,2010,22(5):838-844.
[4]陈军.一类带三个形状参数的三角曲面[J].计算机集成制造系统,2013,19(11):2680-2685.CHEN J.Triangular surface with three shape parameter[J].Computer Integrated Manufacturing Systems,2013,19(11):2680-2685.
[5]师晶.一类二次TC-Bezier曲线的光滑拼接[J].新乡学院学报,2016,33(12):12-14.SHI J.Smooth connections for a class of quadratic TC-Bezier Curve[J].,2016,33(12):12-14.
[6]邱宁.时间分数阶延迟微分方程在流体力学中的应用[J].沈阳大学学报(自然科学版),2016,28(2):170-172.QIU N.Application of time fractional delay differential equations in fluid dynamics[J].Journal of Shenyang University(Natural Science),2016,28(2):170-172.
[7]郭海杰.非线性Dirichlet型三点边值问题正解的存在性[J].沈阳大学学报(自然科学版),2016,28(4):340-344.GUO H J.Existence of positive solutions for nonlinear Dirichlet type three point boundary value problems[J].Journal of Shenyang University(Natural Science),2016,28(4):340-344.
[8]吴雪蓉.一类常微分方程和Volterra积分方程解的存在唯一性[J].沈阳大学学报(自然科学版),2017,29(2):168-172.WU X R.Existence and uniqueness of solutions for ordinary differential equations and Volterra integral equations[J].Journal of Shenyang University(Natural Science),2017,29(2):168-172.