Calculate the coordinates in a circle

Question

I am drawing an imaginary circle around the middle of a button.

The radius of the circle is the Height/2 if Height>Width or Width/2 if Width>Height. Now i have to calculate which coordinates (in pixels) are in this circle. The idea is that if e.g. the mouse cursor hovers over that circle, something happens.

Answer 1

Calculating each co-ordinate is overkill; just compare the distance to the center. For example:

int radius = 5; // whatever

int deltaX = originX - mouseX, deltaY = originY - mouseY;

// compare the square distance, to avoid an unnecessary square-root
if((deltaX * deltaX) + (deltaY * deltaY) <= (radius * radius)) {
    // inside the circle, or on the edge
}

To avoid a little math, you could also do a quick bounding-box check, i.e. checking the rectangular region (just addition/subtraction). This can be used in combination, i.e.

• check the bounding box
  • if it isn't in the bounding box it certainly isn't in the circle
  • if it is in the bounding box, do the math to compare the square-distance

Answer 2

You are inside the circle when this equation is satisfied:

Math.pow(mouse_pos_x-center_circle_x,2)+Math.pow(mouse_pos_y-center_circle_y,2)<Math.pow(radius,2)