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[未答复] 迭代算法的实现

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发表于 2019-11-22 22:12:59 | 显示全部楼层 |阅读模式
本帖最后由 蜗牛111 于 2019-11-30 10:24 编辑

KNA{G5LA`5ZOQMW91CX6UTO.png
下面左图是实际效果图,右图是自己画出的图,但是差别太大。最下面附有自己写的代码,辛苦小伙伴帮忙看下

2.png 3.png
clear;
clc;
for i = 1:30
    x(i) = (0.033+0.000001*i)*i;
end
for i = 1:30
    if (x(i)<0.5)
        y(i)=sin(pi*x(i));
    else
        y(i)=-sin(pi*x(i));
    end
end


scatter(x(1,:),y(1,:),'*');
hold on

L=5;    %算法迭代次数
N=size(x,2);    %初始控点个数                    

    for k=1:L   
        nk=3^(k-1)*N;  %算法迭代后控制点的个数

           for i=1:nk-3

                 if   abs(y(k,i+2)-2*y(k,i+1)+y(k,i))>=abs(y(k,i+3)-2*y(k,i+2)+y(k,i+1))               
                  x(k+1,3*i-2)=(5/6)*x(k,i+1)+(1/6)*x(k,i+2)+(5/324)*(x(k,i+3)-2*x(k,i+2)+x(k,i+1))-(55/648)*2*(((x(k,i+2)-2*x(k,i+1)+x(k,i))*(x(k,i+3)-2*x(k,i+2)+x(k,i+1)))/(x(k,i+2)-2*x(k,i+1)+x(k,i)+x(k,i+3)-2*x(k,i+2)+x(k,i+1)));   
                  y(k+1,3*i-2)=(5/6)*y(k,i+1)+(1/6)*y(k,i+2)+(5/324)*(y(k,i+3)-2*y(k,i+2)+y(k,i+1))-(55/648)*2*(((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))/(y(k,i+2)-2*y(k,i+1)+y(k,i)+y(k,i+3)-2*y(k,i+2)+y(k,i+1)));  

                   x(k+1,3*i-1)=(1/2)*x(k,i+1)+(1/2)*x(k,i+2)-(1/8)*2*(((x(k,i+2)-2*x(k,i+1)+x(k,i))*(x(k,i+3)-2*x(k,i+2)+x(k,i+1)))/(x(k,i+2)-2*x(k,i+1)+x(k,i)+x(k,i+3)-2*x(k,i+2)+x(k,i+1)));  
                   y(k+1,3*i-1)=(1/2)*y(k,i+1)+(1/2)*y(k,i+2)-(1/8)*2*(((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))/(y(k,i+2)-2*y(k,i+1)+y(k,i)+y(k,i+3)-2*y(k,i+2)+y(k,i+1)));  

                    x(k+1,3*i)=(1/6)*x(k,i+1)+(5/6)*x(k,i+2)-(5/324)*(x(k,i+3)-2*x(k,i+2)+x(k,i+1))-(35/648)*2*(((x(k,i+2)-2*x(k,i+1)+x(k,i))*(x(k,i+3)-2*x(k,i+2)+x(k,i+1)))/(x(k,i+2)-2*x(k,i+1)+x(k,i)+x(k,i+3)-2*x(k,i+2)+x(k,i+1)));
                    y(k+1,3*i)=(1/6)*y(k,i+1)+(5/6)*y(k,i+2)-(5/324)*(y(k,i+3)-2*y(k,i+2)+y(k,i+1))-(35/648)*2*(((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))/(y(k,i+2)-2*y(k,i+1)+y(k,i)+y(k,i+3)-2*y(k,i+2)+y(k,i+1)));
                 else
                 x(k+1,3*i-2)=(5/6)*x(k,i+1)+(1/6)*x(k,i+2)-(5/324)*(x(k,i+2)-2*x(k,i+1)+x(k,i))-(35/648)*2*(((x(k,i+2)-2*x(k,i+1)+x(k,i))*(x(k,i+3)-2*x(k,i+2)+x(k,i+1)))/(x(k,i+2)-2*x(k,i+1)+x(k,i)+x(k,i+3)-2*x(k,i+2)+x(k,i+1)));   
                 y(k+1,3*i-2)=(5/6)*y(k,i+1)+(1/6)*y(k,i+2)-(5/324)*(y(k,i+2)-2*y(k,i+1)+y(k,i))-(35/648)*2*(((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))/(y(k,i+2)-2*y(k,i+1)+y(k,i)+y(k,i+3)-2*y(k,i+2)+y(k,i+1)));   

                  x(k+1,3*i-1)=(1/2)*x(k,i+1)+(1/2)*x(k,i+2)-(1/8)*2*(((x(k,i+2)-2*x(k,i+1)+x(k,i))*(x(k,i+3)-2*x(k,i+2)+x(k,i+1)))/(x(k,i+2)-2*x(k,i+1)+x(k,i)+x(k,i+3)-2*x(k,i+2)+x(k,i+1)));  
                  y(k+1,3*i-1)=(1/2)*y(k,i+1)+(1/2)*y(k,i+2)-(1/8)*2*(((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))/(y(k,i+2)-2*y(k,i+1)+y(k,i)+y(k,i+3)-2*y(k,i+2)+y(k,i+1)));  

                  x(k+1,3*i)=(1/6)*x(k,i+1)+(5/6)*x(k,i+2)+(5/324)*(x(k,i+2)-2*x(k,i+1)+x(k,i))-(55/648)*2*(((x(k,i+2)-2*x(k,i+1)+x(k,i))*(x(k,i+3)-2*x(k,i+2)+x(k,i+1)))/(x(k,i+2)-2*x(k,i+1)+x(k,i)+x(k,i+3)-2*x(k,i+2)+x(k,i+1)));
                  y(k+1,3*i)=(1/6)*y(k,i+1)+(5/6)*y(k,i+2)+(5/324)*(y(k,i+2)-2*y(k,i+1)+y(k,i))-(55/648)*2*(((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))/(y(k,i+2)-2*y(k,i+1)+y(k,i)+y(k,i+3)-2*y(k,i+2)+y(k,i+1)));

                 end
           end   

    end
plot(x(L+1,90:3*nk-1000),y(L+1,90:3*nk-1000),'r')
hold on;



NonlinearAlgorithm.m

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最佳答案
 楼主| 发表于 2019-12-2 20:10:20 | 显示全部楼层

for i = 1:30
    x(i) = (0.033+0.0001*i)*i;
    if (x(i)<0.5)
        y(i)=sin(pi*x(i));
    else
        y(i)=-sin(pi*x(i));
    end
end
scatter(x(1,:),y(1,:),'*');
hold on



L=8;   
N=size(x,2);   

for k=1:L
    nk=3^(k-1)*N;  
    for i=1:nk-3
        
        if ((y(k,i+2)-2*y(k,i+1)+y(k,i))*(y(k,i+3)-2*y(k,i+2)+y(k,i+1))>=0)
            d=harmmean([y(k,i+2)-2*y(k,i+1)+y(k,i),y(k,i+3)-2*y(k,i+2)+y(k,i+1)]);
        else
            d=0;
        end
        if (abs(y(k,i+2)-2*y(k,i+1)+y(k,i))>=abs(y(k,i+3)-2*y(k,i+2)+y(k,i+1)))
           

            x(k+1,3*i-2)=(5/6)*x(k,i+1)+(1/6)*x(k,i+2)+(5/324)*(x(k,i+3)-2*x(k,i+2)+x(k,i+1))-(55/648)*harmmean([x(k,i+2)-2*x(k,i+1)+x(k,i),x(k,i+3)-2*x(k,i+2)+x(k,i+1)]);
            y(k+1,3*i-2)=(5/6)*y(k,i+1)+(1/6)*y(k,i+2)+(5/324)*(y(k,i+3)-2*y(k,i+2)+y(k,i+1))-(55/648)*d;

            
            x(k+1,3*i-1)=(1/2)*x(k,i+1)+(1/2)*x(k,i+2)-(1/8)*harmmean([x(k,i+2)-2*x(k,i+1)+x(k,i),x(k,i+3)-2*x(k,i+2)+x(k,i+1)]);
            y(k+1,3*i-1)=(1/2)*y(k,i+1)+(1/2)*y(k,i+2)-(1/8)*d;
            
            x(k+1,3*i)=(1/6)*x(k,i+1)+(5/6)*x(k,i+2)-(5/324)*(x(k,i+3)-2*x(k,i+2)+x(k,i+1))-(35/648)*harmmean([x(k,i+2)-2*x(k,i+1)+x(k,i),x(k,i+3)-2*x(k,i+2)+x(k,i+1)]);
            y(k+1,3*i)=(1/6)*y(k,i+1)+(5/6)*y(k,i+2)-(5/324)*(y(k,i+3)-2*y(k,i+2)+y(k,i+1))-(35/648)*d;
            
        else
            x(k+1,3*i-2)=(5/6)*x(k,i+1)+(1/6)*x(k,i+2)-(5/324)*(x(k,i+2)-2*x(k,i+1)+x(k,i))-(35/648)*harmmean([x(k,i+2)-2*x(k,i+1)+x(k,i),x(k,i+3)-2*x(k,i+2)+x(k,i+1)]);
            y(k+1,3*i-2)=(5/6)*y(k,i+1)+(1/6)*y(k,i+2)-(5/324)*(y(k,i+2)-2*y(k,i+1)+y(k,i))-(35/648)*d;
            
            x(k+1,3*i-1)=(1/2)*x(k,i+1)+(1/2)*x(k,i+2)-(1/8)*harmmean([x(k,i+2)-2*x(k,i+1)+x(k,i),x(k,i+3)-2*x(k,i+2)+x(k,i+1)]);
            y(k+1,3*i-1)=(1/2)*y(k,i+1)+(1/2)*y(k,i+2)-(1/8)*d;
            
            x(k+1,3*i)=(1/6)*x(k,i+1)+(5/6)*x(k,i+2)+(5/324)*(x(k,i+2)-2*x(k,i+1)+x(k,i))-(55/648)*harmmean([x(k,i+2)-2*x(k,i+1)+x(k,i),x(k,i+3)-2*x(k,i+2)+x(k,i+1)]);
            y(k+1,3*i)=(1/6)*y(k,i+1)+(5/6)*y(k,i+2)+(5/324)*(y(k,i+2)-2*y(k,i+1)+y(k,i))-(55/648)*d;
       end
    end
end


plot(x(L+1,90:3*nk-30000),y(L+1,90:3*nk-30000),'r');
hold on
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