I’m working on designing a HTML5 canvas test that needs to have two circles at a fixed distance apart but the locations are randomized on each completion of the test. My plan is to keep one of the circles at pre-set locations and find random locations for the other circle.
I’d like to find a list of points a given distance away from a given point as a possible location of center of the other circle. Basically the points on the circumference of a circle with the given point as the center and given distance as radius. Is there any jquery or javascript math function that already does this or will I have to figure out a way to solve the distance formula equation below ?
Given the centre of a fixed circle (x0,y0), a formula for a uniformly distributed random circle centre of distance r from (x0,y0) is simply:
(x0 + r * cosθ,y0 + r * sinθ)
where θ is uniformly distributed over [0,2π). That takes one line of code to create the random angle, and one line to perform those calculations. That’s a whopping two lines of code… Of course you’ll realise immediately that this formula doesn’t require (x0,y0) to be fixed, so you can just as easily add a third line of code randomising its position at every iteration, and then calculate the random point.
When generalising to higher dimensions (a uniform point on an N-sphere), polar co-ordinates are no longer very useful. There are simple methods that take only 5 lines of code to implement, see http://mathworld.wolfram.com/SpherePointPicking.html.