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.

enter image description here

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!

  • 1
    $\begingroup$ @JuanBonnet: Is that point at the exact center? $\endgroup$ – Moo Jan 1 '16 at 20:55
  • $\begingroup$ Not in my drawing, but IT IS in the software hehe $\endgroup$ – Juan Bonnett Jan 1 '16 at 20:56
  • $\begingroup$ Let's say I'm developing a videogame, and that rectangle is just a box that can be anywhere in a X,Y space, the center is variable relative to the whole 2D space, but not variable inside the rectangle itself. $\endgroup$ – Juan Bonnett Jan 1 '16 at 20:58

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


and the answer would be an angle in radians.

The lower-right vertex has bearing


The lower-left vertex has bearing


and the upper-left vertex has bearing


Do you need further explanation of these formulas?

  • $\begingroup$ It works perfect, plus you used the native Javacript functions, thank you very much sir, I hope we can meet again when I have more questions now that I'm diving into complex computing stuff! Much respect and happy new year! $\endgroup$ – Juan Bonnett Jan 1 '16 at 21:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.