计算五星红旗上每颗小星各十个点纵横坐标的程序
写完了国际象棋棋牌和中国象棋棋牌，我又想写一个五星红旗的绘制程序。对于五星红旗，每个五角星都有十个点。大星还好办，小星的角度都是不规则的。怎么样做到“两点确定一个五角星”？于是我编写了这个程序。四个星直接有差别，不能硬搬。
//****************************************
//程序功能：输入五角星中心点和某一个角的顶点
// 坐标，输出其他各点坐标
//编制人：刘聪
//编制时间：2017年9月29日
//****************************************
#include <iostream>
#include <cmath>
using namespace std;
int main(){
float pi = 3.141592653;
int center[2] = {300,60};
int point_1[2] = {274,75};
int point_2[2] = {0};
int point_3[2] = {0};
int point_4[2] = {0};
int point_5[2] = {0};
int point_6[2] = {0};
int point_7[2] = {0};
int point_8[2] = {0};
int point_9[2] = {0};
int point_10[2] = {0};
point_2[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_2[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_3[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 2 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_3[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 2 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_4[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 3 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_4[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 3 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_5[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 4 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_5[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 4 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_6[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 5 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_6[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 5 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_7[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 6 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_7[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 6 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_8[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 7 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_8[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 7 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_9[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 8 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_9[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 8 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_10[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 9 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_10[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 9 + atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
cout << endl << "point_2[0] = " << point_2[0];
cout << \'\t\' << "point_2[1] = " << point_2[1] << endl;
cout << endl << "point_3[0] = " << point_3[0];
cout << \'\t\' << "point_3[1] = " << point_3[1] << endl;
cout << endl << "point_4[0] = " << point_4[0];
cout << \'\t\' << "point_4[1] = " << point_4[1] << endl;
cout << endl << "point_5[0] = " << point_5[0];
cout << \'\t\' << "point_5[1] = " << point_5[1] << endl;
cout << endl << "point_6[0] = " << point_6[0];
cout << \'\t\' << "point_6[1] = " << point_6[1] << endl;
cout << endl << "point_7[0] = " << point_7[0];
cout << \'\t\' << "point_7[1] = " << point_7[1] << endl;
cout << endl << "point_8[0] = " << point_8[0];
cout << \'\t\' << "point_8[1] = " << point_8[1] << endl;
cout << endl << "point_9[0] = " << point_9[0];
cout << \'\t\' << "point_9[1] = " << point_9[1] << endl;
cout << endl << "point_10[0] = " << point_10[0];
cout << \'\t\' << "point_10[1] = " << point_10[1] << endl;
return 0;
}
所求结果如下：（假定五星红旗宽为900，高为600）
第二个小星的center坐标为（360,120），point_1坐标为（330,124），代入程序计算得：
第三个小星的center坐标为（360,210），point_1坐标为（331,202），这时根据图样，两个角的加变成两个角的减，需要重写程序：
//****************************************
//程序功能：输入五角星中心点和某一个角的顶点
// 坐标，输出其他各点坐标
//编制人：刘聪
//编制时间：2017年9月29日
//****************************************
#include <iostream>
#include <cmath>
using namespace std;
int main(){
float pi = 3.141592653;
int center[2] = {360,210};
int point_1[2] = {331,202};
int point_2[2] = {0};
int point_3[2] = {0};
int point_4[2] = {0};
int point_5[2] = {0};
int point_6[2] = {0};
int point_7[2] = {0};
int point_8[2] = {0};
int point_9[2] = {0};
int point_10[2] = {0};
point_2[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_2[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_3[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 2 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_3[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 2 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_4[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 3 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_4[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 3 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_5[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 4 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_5[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 4 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_6[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 5 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_6[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 5 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_7[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 6 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_7[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 6 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_8[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 7 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_8[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 7 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_9[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 8 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_9[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 8 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_10[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 9 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_10[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 9 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
cout << endl << "point_2[0] = " << point_2[0];
cout << \'\t\' << "point_2[1] = " << point_2[1] << endl;
cout << endl << "point_3[0] = " << point_3[0];
cout << \'\t\' << "point_3[1] = " << point_3[1] << endl;
cout << endl << "point_4[0] = " << point_4[0];
cout << \'\t\' << "point_4[1] = " << point_4[1] << endl;
cout << endl << "point_5[0] = " << point_5[0];
cout << \'\t\' << "point_5[1] = " << point_5[1] << endl;
cout << endl << "point_6[0] = " << point_6[0];
cout << \'\t\' << "point_6[1] = " << point_6[1] << endl;
cout << endl << "point_7[0] = " << point_7[0];
cout << \'\t\' << "point_7[1] = " << point_7[1] << endl;
cout << endl << "point_8[0] = " << point_8[0];
cout << \'\t\' << "point_8[1] = " << point_8[1] << endl;
cout << endl << "point_9[0] = " << point_9[0];
cout << \'\t\' << "point_9[1] = " << point_9[1] << endl;
cout << endl << "point_10[0] = " << point_10[0];
cout << \'\t\' << "point_10[1] = " << point_10[1] << endl;
return 0;
}计算结果为：
第四个小星的center坐标为（300,270），point_1坐标为（277,251），这时根据图样，point_2需要两个角相减，point_3需要36度减去之前point_2两个角的差，需要重写程序：
//****************************************
//程序功能：输入五角星中心点和某一个角的顶点
// 坐标，输出其他各点坐标
//编制人：刘聪
//编制时间：2017年9月29日
//****************************************
#include <iostream>
#include <cmath>
using namespace std;
int main(){
float pi = 3.141592653;
int center[2] = {300,270};
int point_1[2] = {277,251};
int point_2[2] = {0};
int point_3[2] = {0};
int point_4[2] = {0};
int point_5[2] = {0};
int point_6[2] = {0};
int point_7[2] = {0};
int point_8[2] = {0};
int point_9[2] = {0};
int point_10[2] = {0};
point_2[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos(atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])) - (float)36 / 360 * 2 * pi);
point_2[1] = center[1] - (float)10 / cos((float)36 / 360 * 2 * pi) *
sin(atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])) - (float)36 / 360 * 2 * pi);
point_3[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi - (atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])) - (float)36 / 360 * 2 * pi));
point_3[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi - (atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])) - (float)36 / 360 * 2 * pi));
point_4[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 3 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_4[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 3 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_5[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 4 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_5[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 4 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_6[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 5 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_6[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 5 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_7[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 6 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_7[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 6 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_8[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 7 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_8[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 7 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_9[0] = center[0] - (float)30 *
cos((float)36 / 360 * 2 * pi * 8 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_9[1] = center[1] + (float)30 *
sin((float)36 / 360 * 2 * pi * 8 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_10[0] = center[0] - (float)10 / cos((float)36 / 360 * 2 * pi) *
cos((float)36 / 360 * 2 * pi * 9 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
point_10[1] = center[1] + (float)10 / cos((float)36 / 360 * 2 * pi) *
sin((float)36 / 360 * 2 * pi * 9 - atan((float)fabs(point_1[1] - center[1])
/ (float)fabs(point_1[0] - center[0])));
cout << endl << "point_2[0] = " << point_2[0];
cout << \'\t\' << "point_2[1] = " << point_2[1] << endl;
cout << endl << "point_3[0] = " << point_3[0];
cout << \'\t\' << "point_3[1] = " << point_3[1] << endl;
cout << endl << "point_4[0] = " << point_4[0];
cout << \'\t\' << "point_4[1] = " << point_4[1] << endl;
cout << endl << "point_5[0] = " << point_5[0];
cout << \'\t\' << "point_5[1] = " << point_5[1] << endl;
cout << endl << "point_6[0] = " << point_6[0];
cout << \'\t\' << "point_6[1] = " << point_6[1] << endl;
cout << endl << "point_7[0] = " << point_7[0];
cout << \'\t\' << "point_7[1] = " << point_7[1] << endl;
cout << endl << "point_8[0] = " << point_8[0];
cout << \'\t\' << "point_8[1] = " << point_8[1] << endl;
cout << endl << "point_9[0] = " << point_9[0];
cout << \'\t\' << "point_9[1] = " << point_9[1] << endl;
cout << endl << "point_10[0] = " << point_10[0];
cout << \'\t\' << "point_10[1] = " << point_10[1] << endl;
return 0;
}
计算结果为：