VC use recursive method to draw fractal graph

Fractal geometry is a new subject in the field of mathematics, if each element of the graph is deformed according to some rules, the new figure is obtained, and so on, the graph obtained after several times of deformation is fractal shape. The couch curve is the most typical fractal shape:

To transform a line segment according to Figure 1, get figure 1, and then the figure 1 of each line in Figure 1 of the line transformation to get figure 2, and so on, 6 times to transform to get figure 6, if the infinite transformation, it is couch curve, couch curve of the dimension is not an integer dimension, For more details, see the fractal aspect of the book.

With fractal graphics can draw many beautiful patterns and is widely used, the following will be a few simple fractal graphics code and graphics to share.

//Couch曲线的画法
void　Couch(CDC　*pDC,int　x1,int　y1,int　x2,int　y2,int　n)
{
//pDC是画图的设备上下文的指针
//x1,y1,x2,y2是起始的两点
//其中参数n是递归的层数
int　x3,y3,x4,y4,x5,y5;
//以下是根据空间几何计算出来的坐标
x3=x1+(x2-x1)/3;
y3=y1+(y2-y1)/3;
x4=x1+(x2-x1)*2/3;
y4=y1+(y2-y1)*2/3;
x5=x3+(x4-x3)/2+int(sqrt(3)*(y4-y3)/2);
y5=y3-int(sqrt(3)*(x4-x3)/2)+(y4-y3)/2;
//递归最后一层,递归的出口
if(n==1)
{
pDC->MoveTo(x1,y1);
pDC->LineTo(x3,y3);
pDC->LineTo(x5,y5);
pDC->LineTo(x4,y4);
pDC->LineTo(x2,y2);
}
else
{
//递归画图
Couch(pDC,x1,y1,x3,y3,n-1);
Couch(pDC,x3,y3,x5,y5,n-1);
Couch(pDC,x5,y5,x4,y4,n-1);
Couch(pDC,x4,y4,x2,y2,n-1);
}
}

//斯宾斯基篓垫的画法
void　Floor(CDC　*pDC,int　x1,　int　y1,int　x2,int　y2,int　x3,int　y3,int　n)
{
//pDC是画图的设备上下文的指针
//x1,y1,x2,y2,x3,y3是起始的三角形的三点坐标
//其中参数n是递归的层数
int　x11,x22,x33,y11,y22,y33;
//以下是根据空间几何计算出来的坐标
x11=(x2+x3)/2;
y11=(y2+y3)/2;
x22=(x1+x3)/2;
y22=(y1+y3)/2;
x33=(x1+x2)/2;
y33=(y1+y2)/2;

pDC->MoveTo(x11,y11);
pDC->LineTo(x22,y22);
pDC->MoveTo(x11,y11);
pDC->LineTo(x33,y33);
pDC->MoveTo(x22,y22);
pDC->LineTo(x33,y33);
//递归最后一层,递归的出口
if(n==1)
{
pDC->MoveTo(x11,y11);
pDC->LineTo(x22,y22);
pDC->LineTo(x33,y33);
pDC->LineTo(x11,y11);
}
else
{
//递归画图
Floor(pDC,x1,y1,x33,y33,x22,y22,n-1);
Floor(pDC,x33,y33,x2,y2,x11,y11,n-1);
Floor(pDC,x22,y22,x11,y11,x3,y3,n-1);
}
}