Does atan2 required normalized vectors? Which is better to use acos or atan for angles between vectors?

Question

When calculating the angle between two vectors, I have traditionally used acos, but this requires the two vectors to be normalised. atan2 can be used to accomplish the same (specifically atan2(b.y_, b.x_) - atan2(a.y_, a.x_)), does this require normalised vectors?

If atan2 doesn't require normalised vectors, would this be better to use since normalisation can be costly and 'more' error prone since it requires a sqrt operation?

Then I read that atan2 itself can be more costly than acos, but more accurate? And then I also read other interwebs suggesting the opposite :( lots of conflicting information, unsure what the deal is with using acos or atan for calculating the angle between two vectors.

Which is recommeneded? and what are the benefits/issues for each usage?

Any help would be appreciated, thanks!

Aurelioaurelius

atan2 does not require normalised vectors – Prudence

No, atan2() does not required any scaling/normalising of inputs, as long as at least one argument is non-zero. Recommended usage depends on how the input values are supplied. Simple minded advice like "never use acos()" is simply dumb - the skill is picking an appropriate option based on how input data is supplied/calculated, and the form of output required. Sometimes more than one alternative may be appropriate. – Hemitrope

Answer 1

No, atan2 does not require normalized vectors, and if your vectors are not already normalized you shouldn't pre-normalize them as that may slightly reduce precision. The function works correctly for any inputs other than (0,0).

You should never use acos for anything.

Spout

Thankyou. atan2 certainly would be more useful in a number of situations for me due to not having to normalise ;) – Aurelioaurelius

You may add that atan2 provides a result modulo 2-pi, on the contrary of acos or atan. – Prudence