OpenGL画正五角星

先计算出各顶点（外顶点和内顶点），可以确定每个三角形和中间的正五边形，分别涂色即可。

代码：

#include <windows.h>
#ifdef __APPLE__
#include <GLUT/glut.h>
#else
#include <GL/glut.h>
#endif
#include <bits/stdc++.h>
#include <stdlib.h>
using namespace std;
const double PI = acos(-1.0);

struct Point{
    GLfloat x, y;
    Point operator - (const Point &b) const {
        return Point{x-b.x, y-b.y};
    }
    Point rot(Point p, double angle){
        Point v = (*this)-p;
        double c = cos(angle), s = sin(angle);
        return Point{p.x+v.x*c-v.y*s, p.y+v.x*s+v.y*c};
    }
};

void init(){
    glClearColor(0.0, 0.0, 0.0, 0.0);
    glColor3f(1.0, 1.0, 1.0);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(-1.0, 1.0, -1.0, 1.0);
}

double a = 0.8;
Point p[5] = {
    Point{0, a},
    Point{-a*cos(18*PI/180), a*sin(18*PI/180)},
    Point{-a*cos(54*PI/180), -a*sin(54*PI/180)},
    Point{a*cos(54*PI/180), -a*sin(54*PI/180)},
    Point{a*cos(18*PI/180), a*sin(18*PI/180)}
};
void Star(int n){
    glColor3f(1, 0, 1);
    Point pp[5];
    for(int i=0; i<n; i++){
        Point p0 = Point{(p[i].x+p[(i+1)%5].x)/2, (p[i].y+p[(i+1)%5].y)/2};
        double rato = sin(36*PI/180)/cos(36*PI/180);
        rato = 1 - rato*rato;
        pp[i] = Point{p0.x*rato, p0.y*rato};
    }

    for(int i=0; i<5; i++){
        switch(i){
        case (0): glColor3f(1, 1, 0); break;
        case (1): glColor3f(1, 0, 0); break;
        case (2): glColor3f(0, 0, 1); break;
        case (3): glColor3f(0, 1, 0.75); break;
        case (4): glColor3f(1, 0, 1); break;
        }
        glBegin(GL_POLYGON);
            glVertex2f(p[i].x, p[i].y);
            glVertex2f(pp[(i+4)%5].x, pp[(i+4)%5].y);
            glVertex2f(pp[i].x, pp[i].y);
        glEnd();
    }
    glColor3f(0.5, 0.9, 1);
    glBegin(GL_POLYGON);
        for(int i=0; i<5; i++)
            glVertex2f(pp[i].x, pp[i].y);
    glEnd();
}

void display(){
    glClear(GL_COLOR_BUFFER_BIT);
    Star(5);
    glFlush();
}
int main(int argc, char **argv){
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
    glutInitWindowSize(500, 500);
    glutInitWindowPosition(0, 0);
    glutCreateWindow("STAR");

    glutDisplayFunc(display);

    init();
    glutMainLoop();
}

效果