Algorithm of the joystick on the touchable screen

Question

I would like to simulate an analog joystick on the touchable screen like this picture.

When the center of the stick area is set to (cx, cy), how should I calculate X-direction ratio and Y-direction ratio(-1.0～1.0) from the touched position(tx, ty)?

Answer 1

The x direction ratio is (tx-cx)/r, where r is the radius magnitude of the circle. Similarly, the y direction ratio is (ty-cy)/r.

I am assuming a right-handed cartesian coordinate with x axis in the direction of the right of the picture. Otherwise, you may need to multiply a (-1) to adjust the direction.