fastest way to compute angle with x-axis

Question

What is the fastest way to calculate angle between a line and the x-axis?

I need to define a function, which is Injective at the PI:2PI interval (I have to angle between point which is the uppermost point and any point below).

PointType * top = UPPERMOST_POINT;
PointType * targ = TARGET_POINT;

double targetVectorX = targ->x - top->x;
double targetVectorY = targ->y - top->y;

first try

//#1
double magnitudeTarVec = sqrt(targetVectorX*targetVectorX + targetVectorY*targetVectorY);
angle = tarX / magTar;

second try

//#2 slower
angle = atan2(targetVectorY, targetVectorX);

I do not need the angle directly (radians or degrees), just any value is fine as far as by comparing these values of this kind from 2 points I can tell which angle is bigger. (for example angle in example one is between -1 and 1 (it is cosine argument))

@Mooing SO on phone? where do you get a free data plan like that? — Captain Giraffe, Oct 23 '11 at 18:27
how can this be what I need? Imagine my top point is Origin. Other points are for example a=[-10,-10] b=[-3,-5] and c=[-8,-5]. Sorted by angles: c,a,b Sorted by your method: b,c,a... — relaxxx, Oct 23 '11 at 18:28
My phone has unlimited data, and the SO site is great on phones, except I can't delete comments, and a few other minor things. — Mooing Duck, Oct 23 '11 at 18:30
I have 0.5 Gigs for about 7 dollars, I am extremely wary of extras =) — Captain Giraffe, Oct 23 '11 at 18:31
I also just noticed all those sample angles are in the range (PI, 2PI), instead of (0,PI) like I interpreted from the question. @relaxxx, can you clarify the range? — Mooing Duck, Oct 23 '11 at 18:35

score 2 · Answer 1 · edited May 23 '17 at 11:43

I just wrote Fastest way to sort vectors by angle without actually computing that angle about the general question of finding functions monotonic in the angle, without any code or connections to C++ or the likes. Based on the currently accepted answer there I'd now suggest

double angle = copysign( // magnitude of first argument with sign of second
  1. - targetVectorX/(fabs(targetVectorX) + fabs(targetVectorY)),
  targetVectorY);

The great benefit compared to the currently accepted answer here is the fact that you won't have to worry about infinite values, since all non-zero vectors (i.e. targetVectorX and targetVectorY are not both equal to zero at the same time) will result in finite pseudoangle values. The resulting pseudoangles will be in the range [−2 … 2] for real angles [−π … π], so the signs and the discontinuity are just like you'd get them from atan2.

score 2 · Accepted Answer · answered Oct 23 '11 at 18:25

2

Check for y being zero as atan2 does; then The quotient x/y will be plenty fine. (assuming I understand you correctly).

answered Oct 23 '11 at 18:25

Captain Giraffe

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-x/(y+.0001) may be faster, then you don't have to check for zero – Mooing Duck Oct 23 '11 at 18:31
It is doubles, put another 7-11 zeroes in there =) – Captain Giraffe Oct 23 '11 at 18:38
I just realized you might not have to do anything special at all on machines with +inf and -inf. They should sort correctly, right? Maybe? – Mooing Duck Oct 23 '11 at 18:43
Division by zero is always messy regardless of arch. – Captain Giraffe Oct 23 '11 at 18:44
In which case the amount added to the y should be a fraction of y, probably making the check for zero the faster option then. – Mooing Duck Oct 23 '11 at 19:53

fastest way to compute angle with x-axis

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