MATLAB逐步比较法的圆弧插补和直线插补写出汉字

内容采用逐步比较法的圆弧插补和直线插补写出汉字，具体原理不再解释，感兴趣的可以看一下计算机控制原理第四版，链接：百度网盘 请输入提取码

直线插补代码：Interpolation1.m文件

function Interpolation1(X0,Y0,Xe,Ye,h)
x=[X0,Xe];
y=[Y0,Ye]; 
plot(x,y,'--b','linewidth',2);%理想直线
hold on;
Xe = Xe-X0;%步长
Ye = Ye-Y0;
NXY= (abs(Xe)+abs(Ye))/h;%总步数
step=0;%移动步数
Fm=0;%偏差判别式
Xm=X0;%移动坐标变量，表示从(X0,Y0)开始移动
Ym=Y0;
if(Xe>0&&Ye>=0)%判断终点坐标系
XOY=1;
end
if(Xe<=0&&Ye>0)
XOY=2;
end
if(Xe<0&&Ye<=0)
XOY=3;
end
if(Xe>=0&&Ye<0)
XOY=4;
end
Xe=abs(Xe);%对终点坐标取绝对值
Ye=abs(Ye);
while (step<NXY)%开始画
switch XOY
case 1
if(Fm>=0)%  A+区域
x1=[Xm,Xm+h];
Fm=Fm-Ye;%更新偏差判别式
y1=[Ym,Ym];
else    %   A-区域
x1=[Xm,Xm];
y1=[Ym,Ym+h];
Fm=Fm+Xe;
end
case 2
if(Fm>=0)
x1=[Xm,Xm-h];
Fm=Fm-Ye;
y1=[Ym,Ym];
else
x1=[Xm,Xm];
y1=[Ym,Ym+h];
Fm=Fm+Xe;
end
case 3
if(Fm>=0)
x1=[Xm,Xm-h];
Fm=Fm-Ye;
y1=[Ym,Ym];
else
x1=[Xm,Xm];
y1=[Ym,Ym-h];
Fm=Fm+Xe;
end
case 4
if(Fm>=0)
x1=[Xm,Xm+h];
Fm=Fm-Ye;
y1=[Ym,Ym];
else
x1=[Xm,Xm];
y1=[Ym,Ym-h];
Fm=Fm+Xe;
end
end
step=step+1;%移动一次之后步数+1
plot(x1,y1,'r-','linewidth',2);%在前一点和移动后的点之间画直线
Xm=x1(2);%保存新起点坐标
Ym=y1(2);
hold on;
pause(0.0001);%延时程序形参为每走一步所用时间
end%画完
hold on;

圆弧插补代码：Interpolation2.m

function Interpolation2(X00,Y00,Xe,Ye,R,NorF,SorN,h)
%sorn:顺逆时针
%norf:是否远离圆心
if((Xe==X00)&&(Ye==Y00))
    x01 = 0;y01 = 0;
    x02= 2*Xe; y02 = 2*Ye;
    R= sqrt(Xe^2+Ye^2);
    mark = 0;
else
    mark = 1;
    k1 = (Ye-Y00)/(Xe-X00);        % 两点间线的斜率
    k2=-1/k1;                      % 垂直平分线斜率
Xz=(X00+Xe)/2;Yz=(Y00+Ye)/2;       % 两点中点坐标
L1=sqrt((X00-Xe)^2+(Y00-Ye)^2)/2 ; % 两点之间距离的一半
L2=sqrt(R^2-L1^2);
beta = atan(k2);                   % beta角度
x01 = Xz-L2*cos(beta); y01 = Yz-L2*sin(beta);       %靠近原点的圆心
x02= Xz+L2*cos(beta);y02 = Yz+L2*sin(beta);         %远离原点的圆心
end

if(NorF==1)         %判断圆心位置
    if((x01^2+y01^2-x02^2-y02^2)<=0)
    x0=x01;y0=y01;
    else
    x0=x02;y0=y02;
    end
else
    if((x01^2+y01^2-x02^2-y02^2)<=0)
    x0=x02;y0=y02;
    else
    x0=x01;y0=y01;
    end
end

axis equal;
Xm = X00;Ym = Y00;

step=0;
Fm=0;
while ((Xm-Xe)^2+(Ym-Ye)^2>h*h/2||(step==0&&mark==0))
if((Xm-x0)>0&&(Ym-y0)>=0) XOY=1;          %判断动点所在象限
end
if((Xm-x0)<=0&&(Ym-y0)>0) XOY=2;
end
if((Xm-x0)<0&&(Ym-y0)<=0) XOY=3;
end
if((Xm-x0)>=0&&(Ym-y0)<0) XOY=4;
end
switch XOY
case 1
if(SorN==1)
if(Fm>=0)
    x1=[Xm,Xm];y1=[Ym,Ym-h];
    else
    x1=[Xm,Xm+h];y1=[Ym,Ym];
    end
else if(Fm<=0)
    x1=[Xm,Xm];y1=[Ym,Ym+h];
    else
    x1=[Xm,Xm-h];y1=[Ym,Ym];
    end
end
case 2
if(SorN==1)
if(Fm>=0)
    x1=[Xm,Xm+h];y1=[Ym,Ym];
    else
    x1=[Xm,Xm];y1=[Ym,Ym+h];
    end
else
if(Fm>0)
    x1=[Xm,Xm];y1=[Ym,Ym-h];
    else
    x1=[Xm,Xm-h];y1=[Ym,Ym];
    end
end
case 3
if(SorN==1)
if(Fm>=0)
    x1=[Xm,Xm];y1=[Ym,Ym+h];
    else
    x1=[Xm,Xm-h];y1=[Ym,Ym];
    end
else
if(Fm>0)
    x1=[Xm,Xm+h];y1=[Ym,Ym];
    else
    x1=[Xm,Xm];y1=[Ym,Ym-h];
    end
end
case 4
if(SorN==1)
if(Fm>=0)
    x1=[Xm,Xm-h];y1=[Ym,Ym];
    else
    x1=[Xm,Xm];y1=[Ym,Ym-h];
    end
else
if(Fm>0)
    x1=[Xm,Xm];y1=[Ym,Ym+h];
    else
    x1=[Xm,Xm+h];y1=[Ym,Ym];
    end
end
end
step=step+1;
    plot(x1,y1,'r','linewidth',2);       %由此点和前一点坐标组成的2个向量画直线
Xm=x1(2);       %保存此点坐标供下次作图和比较时使用
Ym=y1(2);
Fm = (Xm-x0)^2+(Ym-y0)^2-R^2;
hold on;
pause(0.0001);     %延时程序形参为每走一步所用时间
end
hold on;

演示代码：Interpolation3.m

Interpolation1(152,1.5,216,4.8,0.1);
Interpolation2(183,19,160,-25,66,1,1,0.1);
Interpolation1(176,-5,176,-25,0.1);
Interpolation1(176,-25,213,-23,0.1);
Interpolation1(213,-23,207,-13,0.1);
Interpolation2(198,-4,182,-41,45,1,1,0.1);
Interpolation1(196,25,207,18,0.1);