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Comment by doomlaser | Hacker News Reader

atan2() is incredibly useful in game development. You can use it to determine the angle between objects, calculate the angle of a 2d vector, and other useful things.

https://ryankubik.com/blog/atan2/

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> atan2() is incredibly useful in game development

Why game development? It's useful everywhere! I have never found a genuine usage of atan(), it's always atan2() that is natural to use.

As on example, to find longitude and latitude on a sphere from stereographic projection (given as Cartesian coordinates) you need both:

[ x, y ] ↦ [ atan2(y, x), π/2 − 2 atan(√(x² + y²)) ]

But atan per se comes up all over the place if you start doing much work with angle measures.

shouldn't that be atan(1/sqrt(x^2+y^2))? In that case, I'd still use atan2 with y=1.

Yup, I felt incredibly stupid about six months ago finding out about atan2 for the first time, given the number of times I've made stupid errors using atan, and then correcting those errors by manually checking what quadrant I was in.

Same.

My favorite "looks simple but is hard" task is "given object position and angle and target position return +1 if the object should turn clockwise and -1 if the object should turn counterclockwise to face the target".

I've got it subtly wrong so many times and using atan2 only solves half the problems. Now I just copypaste it from my previous game :)

Isn’t that just the sign of the cross product of the direction vector and the vector from the object position to the target (or the orientation of the bivector in geometric algebra)? No need for trig there, I don’t think.

This is a question of whether the target is to the right or left of the line where the object is pointing. As OskarS says, you don’t need trigonometry for this at all. Just take the wedge product of the two vectors, and check the sign.

That is, if your direction is the vector (a, b), and the displacement to the target is the vector (c, d), you can compute ad – bc. If this quantity is positive turn left, else turn right.

there is also sincos(), which is useful when you need both, such as building matrices.

https://man7.org/linux/man-pages/man3/sincos.3.html

https://home.deec.uc.pt/~jlobo/tc/opcode_f.html

Thats quite cute. I imagine it is (doing something equivalent to) using the complex exponential and taking the real an imaginary parts? exp(iz) = cos(z) + i sin(z), so by working out exp you can get cos and sin for free.

In almost every context (certainly in game development) it is typically most efficient and numerically pleasant to avoid angle measures altogether and work in terms of vectors directly. To represent an angle, use a pair of numbers representing a complex number (optionally normalized to lie on the unit circle). If you want to reduce it to a single number (e.g. you have a large number of them you need to serialize to disk or send over the wire) use the stereographic projection.

Nitpick: this blog post makes an incorrect statement, namely that the domain of the inverse tangent function is -pi/2 to pi/2.

The domain of a function is the set of all possible inputs. In particular, the domain of the inverse tangent consists of all real numbers.

The author means the range.

I wish we used different words for domain and range. Like "input range" and "output range" or something. It's an endless source of confusion, especially since range can legitimately be used for the domain if you phrase it like "the range of values we can use for the input of the inverse tangent function is -infinity to infinity."

If you like, you can call it the image.

https://gowers.wordpress.com/2011/10/13/domains-codomains-ra...

In many places though it is clearer to to use vector dot product to calculate the angle than use atan2.

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