EWHU教学-武汉大学数学与统计学院.ppt

70年代，法国雷诺汽车公司的工程师贝齐尔（Bezier）创造出一种适用于几何体外形设计的新的曲线表示法。这种方法的优越性在于：对于在平面上随手勾画出的一个多边形（称为特征多边形），只要把其顶点坐标输入计算机，经过不到一秒钟的计算，绘图机就会自动画出同这个多边形很相像、又十分光滑的一条曲线。这种方法被人们称为贝齐尔(Bezier)方法(以下统称为Bezier方法)。 B样条函数 为了定义B样条曲线，首先给出n次截幂函数和n阶B样条函数的定义。我们称 为n次截幂函数，即 称Mn(x)为n阶B样条函数，即 * * * * Interpolation 向 华 武汉大学数学与统计学院 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Lagrangian polynomial interpolation 整体多项式插值 x = linspace(-5,5,13); y = 1./(1+x.^2); c = polyfit(x,y,12); t = linspace(x(1),x(end),100); p = polyval(c,t); plot(t,p,x,y,o) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. #include stdio.h #include math.h void main() { int i, j, kk; float xa, yans, z; static n = 3; /* n+1 is the number of data points. */ static float x[11]={1. , 2. , 3. , 4. }; static float f[11]={.671, .620, .567, .512}; printf( \nInput x ? ); scanf( %f, xa ); yans = 0; for( i = 0; i = n; i++ ) { z = 1.0; for( j = 0; j = n; j++ ) { if( i != j ) z = z*(xa - x[j])/(x[i] - x[j]); } yans = yans + z*f[i]; } printf( Answer: g( %g ) = %g \n, xa, yans ); } Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Chebyshev interpolation n = 8; a = -5; b = 5; x = (a+b)/2 + (b-a)/2* (-cos(pi*[0:n]/n)); f = 1./(1+x.^2); y = eval(f); c = polyfit(x,y,n); t = linspace(x(1),x(end),100); p = polyval(c,t); plot(t,p) hold on; fplot(1/(1+x^2),[-5,5]); Chebyshev interpolation :Runges phenomenon can be avoided if a suitable distribution of nodes is used. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 牛顿插值 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. xi x