Rotating object to face mouse pointer on mousemove

Question

I've got a mousemove cursor in my game which will make my object shoot towards my mouse cursor. I'd like my object to always rotate along to be in line with my mousecursor. How can i convert the X and Y of where the cursor is to a degree angle to rotate my object to?

I hope my fiddle will make things a little clearer of to what i mean by rotating the player(Black block): http://jsfiddle.net/3nEUv/4/

Here's my mouseMove function now; Only making sure the cursor remains in it's bounding box

function mouseMove(e) {
    if (cursor) {
        if (e.rawX && e.rawY) {
            cursorBoundingBox(e.rawX, e.rawY);
        }
    }
}

Answer 1

Basically you need to find the vector between the the point in the center of your box, and the point of the mouse cursor, then calculate the angle and convert it to degrees. Then just apply the angle via CSS:

var box=$(".box");
var boxCenter=[box.offset().left+box.width()/2, box.offset().top+box.height()/2];

var angle = Math.atan2(e.pageX - boxCenter[0], - (e.pageY - boxCenter[1]) )*(180/Math.PI);      

box.css({ "-webkit-transform": 'rotate(' + angle + 'deg)'});    
box.css({ '-moz-transform': 'rotate(' + angle + 'deg)'});

WHAT

Ok, let's take this apart. This is what we have:

The vector AB goes between the center of the box and the mouse position. We went to calculate Θ (theta), which is the angle between the X axis and AB. Since AB creates a triangle with the X and Y axes, we can use the Arctan function to calculate it. More precisely, we use the convenience function of Arctan2 which gives a positive angle when y>0 and negative angle when y<0.

atan2 returns the degrees in radians, and CSS works with degrees, so we convert between the two using 180/Math.PI. (A radian is the measure of an angle that, when drawn a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle. - Taken from here )

One last caveat - Since in the browser the Y axis is inverted (meaning, the further down you go in the page, the higher the Y value gets), we had to flip the Y axis: We did so by adding a minus sign on the Y term:

- (e.pageY - boxCenter[1])

I hope this helps clear some things...

Here's an isolated jsfiddle example

BTW, Your game is hard! :)