apply arcos to out of domain $[-1, 1]$ values, such that -1.02

113 Views Asked by At

I do apologise if the problem sounds a bit confusing, it's not a complicated question, I will make it short as possible.

I am trying to archive an ellipse parameterisation, with a reference to SVG implementation notes I met a problem using arc cos

According to the equation of compute angle between two vectors, I have two sets of vectors, which I would like to work out the angle between.

Perhaps it's due to precision loss, I had to solve a weird bug, it turns out that, sometimes, I need to work out the arc sin of for example, -1.0002, which breaks my function and return a value of NaN. I have very limited knowledge about arc sin, quickly I used demos tools, y = arccosx and it turns out arc cos has a domain [-1, 1].

Now I think I only have two ways to go:

  1. for $f(x) = arcos(x)$, if x is out of range, then assign x to the limit value, either 1 or -1;
  2. do a few Math.PI*1/2 calculation, convert x into the domain of [-1, 1], work out the arc cos.

Could someone please suggest one way to go, if you can provide me some calculations of work out

  • f(x) = arc cos(x), x ∉ [-1, 1]

I will be so grateful for your help.