before I go further I want you to know that I'm developing a collision detection system in a programming language (Javascript).
I'm not used to math terms (it was like 10 years ago when I was in school), but I think this should be simple:
I need the formula to find this angle.
In the picture you can see I need the angle of the first vertex, but I also need the formula to find the other angles to the bottom right vertex, the bottom left vertex and so on.
Although the rectangle size is variable, I have access to its width and height, and also the X,Y coordinate of its center point.
Thank you beforehand!
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$\begingroup$To find the "bearings" (angles) to the rectangle's vertices, all that is needed are the height (the vertical, Y direction: let's call it $h$) and the width (the horizontal, X direction: let's call it $w$). The coordinates of the center are not needed.
The upper-right vertex has bearing $\tan^{-1}\frac wh$ where $\tan^{-1}$ is the arctangent function, sometimes called $\operatorname{atan}$ or $\arctan$. I believe in javascript you would write
$$\operatorname{Math.atan}(w/h)$$
and the answer would be an angle in radians.
The lower-right vertex has bearing
$$\operatorname{Math.PI}-\operatorname{Math.atan}(w/h)$$
The lower-left vertex has bearing
$$\operatorname{Math.PI}+\operatorname{Math.atan}(w/h)$$
and the upper-left vertex has bearing
$$2*\operatorname{Math.PI}-\operatorname{Math.atan}(w/h)$$
Do you need further explanation of these formulas?
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