Check if a point is within a "gluPartialDisk" (OpenGL and C++) - c++

Question

I'm making a pie chart program and I'm creating the pie segments with "gluPartialDisks". However, I also want to check if a point is within the area of one of the disks (The point in question being my mouse cursor). I know how to find the position of a mouse cursor, but how can I check if it is within the area of a disk?
Quick snippet of code:
glTranslatef(-0.3, 0, 0);
gluPartialDisk(gluNewQuadric(), 0, 0.65, 10, 1,
((2 * 3.141592654 * 0.65) * (/*Specific angle*/) - (/*Specific angle*/ * 5),
/*Different angle*/ * 360);

Answer 1

As long as your partial disks are parallel to the screen, and rendered with a parallel projection, it's easiest to do the math without getting OpenGL involved at all.
Say you were drawing a partial disk with:
glTranslatef(xPos, yPos, 0.0f);
gluPartialDisk(quadric, innerRad, outerRad, slices, loops, startAng, sweepAng);
Now if you want to test point (x0, y0), you subtract the translation vector, and then calculate the polar coordinates:
x0 -= xPos;
y0 -= yPos;
float dist = sqrt(xPos * xPos + yPos * yPos);
float ang = atan2(yPos, xPos);
To be inside the partial disk, the distance to the center would have to be within the range of radii:
if (dist < innerRad || dist > outerRad) {
// it's outside!
}
The angle is slightly trickier because it wraps around. Also, the result of atan2() is in radians, measured counter-clockwise from the x-axis in a range [-PI, PI] while the arguments to gluPartialDisk() are in degrees, and measured clockwise from the y-axis. With startAng and sweepAng in the range [0.0, 360.0] degrees, the interval test logic could look like this (untested):
ang *= 180.0f / PI; // convert to degrees
ang = 90.0f - ang; // make clockwise, relative to y-axis
if (ang < 0.0f) {
ang += 360.0f; // wrap into range [0.0, 360.0]
}
ang -= startAng; // make relative to startAng
if (ang < 0.0f) {
ang += 360.0f; // ... and back into range [0.0, 360.0]
}
if (ang > sweepAng) {
// it's outside!
} else {
// it's inside!
}

Answer 2

OpenGL is not going to do this for you, unfortunately.
You can either compute a bounding area for your disk and then do some point vs. bounding area intersection testing (which would be complicated for a shape like this) or you can implement color picking.
Since this is for a charting program, it may be very useful to go with the latter approach. The idea there is to assign each object in your scene a unique color code, draw the scene and then read back the color at the cursor's position. This approach is pixel-perfect and much too slow for most applications, but for a simple charting program it is perfect.