原理:任意正多边形都是圆的内接多边形,顶点都在它的外接圆上,而且正多边形的顶点在圆上是均匀分布的。
以下先给出单位圆的任意内接正多边形的实现:
void GetRegPolygon(POINT *pHead,int n)
{
int i(0);
for (i=0;i<n;i++)
{
pHead[i].x = cos((double)(i)/(double)n*PI);
pHead[i].y = sin((double)(i)/(double)n*PI);
}
}
任意位置的正多边形可以通过设置多边形的中心点坐标和它的外接圆半径求得:
void GetRegPolygon(POINT *pHead,int n,POINT circle,double r)
{
int i(0);
for (i=0;i<n;i++)
{
pHead[i].x = circle.x + r * cos((double)(i)/(double)n);
pHead[i].y = circle.y + r * sin((double)(i)/(double)n);
}
}
这两个函数基于的POINT数据结构是
struct POINT
{
double x;
double y;
};
这是一种很简单的思路,如果需要用整形数据来表示(比如说在VC里画图的时候),只要把相应的变量类型进行修改,在运算完成的时候进行类型强制转换(或者进行四舍五入)。下面给出一个完整的程序:
#include <iostream.h>
#include <math.h>
#include <math.h>
#define PI 3.1415926
struct POINT
{
double x;
double y;
};
//做一个单位圆的内接正n边形
void GetRegPolygon(POINT *pHead,int n)
{
int i(0);
for (i=0;i<n;i++)
{
pHead[i].x = cos((double)(i)/(double)n*PI);
pHead[i].y = sin((double)(i)/(double)n*PI);
}
}
//做一个任意圆的内接正n边形
void GetRegPolygon(POINT *pHead,int n,POINT circle,double r)
{
int i(0);
for (i=0;i<n;i++)
{
pHead[i].x = circle.x + r * cos((double)(i)/(double)n);
pHead[i].y = circle.y + r * sin((double)(i)/(double)n);
}
}
int main(int argc, char* argv[])
{
int i(0);
int n;
POINT *point;
cout<<"请输入正多边形的边数n:"<<endl;
cin>>n;
point = new POINT[n];
GetRegPolygon(point,n);
cout<<"单位圆的内接正n边形各个顶点坐标依次为:"<<endl;
for (i=0;i<n;i++)
{
cout<<"x["<<i+1<<"]="<<point[i].x<<endl;
cout<<"y["<<i+1<<"]="<<point[i].y<<endl;
}
delete point;
return 0;
}
{
double x;
double y;
};
//做一个单位圆的内接正n边形
void GetRegPolygon(POINT *pHead,int n)
{
int i(0);
for (i=0;i<n;i++)
{
pHead[i].x = cos((double)(i)/(double)n*PI);
pHead[i].y = sin((double)(i)/(double)n*PI);
}
}
//做一个任意圆的内接正n边形
void GetRegPolygon(POINT *pHead,int n,POINT circle,double r)
{
int i(0);
for (i=0;i<n;i++)
{
pHead[i].x = circle.x + r * cos((double)(i)/(double)n);
pHead[i].y = circle.y + r * sin((double)(i)/(double)n);
}
}
int main(int argc, char* argv[])
{
int i(0);
int n;
POINT *point;
cout<<"请输入正多边形的边数n:"<<endl;
cin>>n;
point = new POINT[n];
GetRegPolygon(point,n);
cout<<"单位圆的内接正n边形各个顶点坐标依次为:"<<endl;
for (i=0;i<n;i++)
{
cout<<"x["<<i+1<<"]="<<point[i].x<<endl;
cout<<"y["<<i+1<<"]="<<point[i].y<<endl;
}
delete point;
return 0;
}