2D sprite 360 degrees rotation according to the mouse

Question

I am trying to make my top down character rotate according to degrees between its position and the mouse. I'm using this code:

float xDiff = mouseState.X - (graphics.PreferredBackBufferWidth / 2);
            float yDiff = mouseState.Y - (graphics.PreferredBackBufferHeight / 2);

float angle = (float)(Math.Atan2(yDiff, xDiff)) * 180 / Math.PI); 

But it's not working. At the place where I should get somewhere about 0 degrees - I get about -75.

Answer 1

If you look at a circle with the angles marked you will see that 270 degrees corresponds with (0,-1) i.e. straight down.

By convention degrees are marked as acceding in a counter-clockwise direction. They do however form a loop and as such 270 degrees (purple arrow) can also be expressed as -90 degrees (orange arrow) i.e. a quarter turn in the opposite direction.

The coordinates that you provided (-2, -145) correspond with both 269.21 and -90.79 degrees depending on how you choose to express this angle..

The documentation for Atan2() for .Net 4.5 states that it will return value is the range -π <= θ <= π, after converting to degrees this is -180 <= θ <= 180.

To further explain the expected results here is a table with the results of the following formula with the corresponding values of x and y.

angle = Math.Atan2(y, x) * 180 / Math.PI;

         x    -1       0       1
   y   +------------------------
   1   |     135      90      45
   0   |     180       0       0
  -1   |    -135     -90     -45

If you prefer to have your angles expressed in the range 0 <= θ <= 360 they are easy to convert:

while (angle > 360) {
    angle -= 360;
}
while (angle < 0) {
    angle += 360;
}