Question

How can I draw a 2D crescent or moon shape in OpenGL? I have tried using sin and cos like how I did for drawing circles but because a crescent has a “cut” inside it, the sin and cos don’t look enough. I couldn’t figure out how I could do an intersection between 2 polygons either. So I’m thinking if there a mathematical formula for drawing the crescent?

Answer 1

This isn’t mathematically correct, but it may be close enough to meet your needs:

void drawCrescentLine(float step,float scale,float fullness) {
   float angle=0.0f;
   while (angle<M_PI) {
      glVertex2f(scale*sinf(angle),scale*cosf(angle));
      angle+=step;
   }
   while (angle<(2.0f*M_PI)) {
      glVertex2f(fullness*scale*sinf(angle),scale*cosf(angle));
      angle+=step;
   }
   glVertex2f(0.0f,scale);
}

or

void drawCrescentTriStrip(float step,float scale,float fullness) {
    glVertex2f(0.0f,scale);
    float angle=step;
    while (angle<M_PI) {
        float sinAngle=sinf(angle);
        float cosAngle=cosf(angle);
        glVertex2f(scale*sinAngle,scale*cosAngle);
        glVertex2f(-fullness*scale*sinAngle,scale*cosAngle);
        angle+=step;
    }
    glVertex2f(0.0f,-scale);
}

At fullness=1, it will draw a circle of size scale while at fullness=-0.99f, it will draw a very thin cresent. You could use two different fullness values, rightFullness and leftFullness, and always set one of them to 1.0f so you can change the direction of the crescent.