Drawing a crescent shape in OpenGL

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 cresc开发者_高级运维ent?

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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.

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You can draw two perpendicular ellipses that intersect each other. A crescent is formed with the space that is cut out from one of the eclipses. The intersection can be removed by using a bitwise NAND logical operator when drawing.

glEnable(GL_COLOR_LOGIC_OP);
drawEllipse1(); 
glLogicOp(GL_NAND);
drawEllipse2();

The long way of doing it is to specify a bunch of vertices that form a skeleton for the shape that you want. You can then 'connect the dots' with GL_LINES to draw your shape. If you want a smoother shape, you can use the vertices as control points for a Bezier/Catmull-Rom spline that would draw a smooth curve joining all your vertices.

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You can try this:

Vertex outside [N+1]; // Fill in N with the precision you want
Vertex  inside [N+1]; // Fill in N with the precision you want

double neg_size = sqrt (1 + NEG_DIST); // Size of intescting circle.
                                       // NEG_DIST is the distance between their centers
                                       //  Greater NEG_DIST => wider crecent

double start_angle = atan (1 / NEG_DIST); // Start angle for the inside edge
double arc = M_PI - (2 * start_angle);    // Arc of the inside edge

for (int i = 0; i <= N; i++)
{
  // Outside edge
  outside [i].x = cos ((M_PI / N) * i) * SIZE;
  outside [i].y = sin ((M_PI / N) * i) * SIZE;

  // Inside edge
  inside [i].x = (cos (start_angle + ((arc / N) * i)) * neg_size) * SIZE;
  inside [i].y = (sin (start_angle + ((arc / N) * i)) * neg_size - NEG_DIST) * SIZE;
}

This produces the intersected polys version of a crescent. It will give you an array of coordinates for an inside and outside arc for a crescent. Then you can feed these through your favorite draw method.

NOTE: The endpoints of inside and outside overlap (I did this so that I wouldn't have +/- 1's all over the place). I'm pretty sure a GL program will be fine with it, but if you have a fence post error with this, that may be where it came from