151–160 of 225 posts
Let's do a full circle. It all began with replacing frequent occurrence of 2π in calls of sin and cos functions with τ. This post suggests an optimisation by getting rid of τ by getting rid of radians. That way one can get rid of frequent and adjacent radians to degrees conversions and back. I say, let's get rid of sin and cos itself ! Of course I am being over the top here. However, if you represent angle not as a s…
Having read over this entire conversation I feel that people are almost uniformly missing the practical impact of this, which is simply that you can write your own math in terms of "turns" as much as you like. Nothing stops you right now. Defining a sinT function that takes turns is trivial. And so on for all the functions. I haven't done much graphics programming, but what I did I did with tau rather than pi. You al…
One would reap the most benefit if libraries were compiled late for the compiler to optimize away adjacent conversions and back. With C++ template libraries one can do that but compile times can become a hell.
Earlier quoted context omitted.
Euler angles have nothing to do with e^ix = cos x + i sin x. They are a completely different concept.
Yes and no. The x in e^ix is to SO(2) what Euler angles are to SO(3).
Let's do a full circle. It all began with replacing frequent occurrence of 2π in calls of sin and cos functions with τ. This post suggests an optimisation by getting rid of τ by getting rid of radians. That way one can get rid of frequent and adjacent radians to degrees conversions and back. I say, let's get rid of sin and cos itself ! Of course I am being over the top here. However, if you represent angle not as a s…
HN has clumsy filtering, but you're allowed to write π and τ.
Note to readers who maybe confused by the parent comment. I was using \pi and \tau.
I just noticed now that my default mobile keyboard has π.
Earlier quoted context omitted.
> all angles are without a unit. Dimensionless, sure, but what do you mean here? Radians and degrees are units, are they not?
In a very awkward way: rad is m/m, which is 1...
Pi is a naturally-emerging concept: it's the ratio of a circle's circumference to its diameter. It just so happens that a lot of useful stuff we do in math operate on that ratio, not on either on the individual values (at least, not those alone).
- 0000_0000 = 0 or tau
- 1000_0000 = pi
- 1100_0000 = 3*pi/4
And the addition and multiplication by integer scalars all apply and the overflows work naturally. I wrote a little library in rust [0] to help with this as you can define the operations */+-% etc.
Earlier quoted context omitted.
In another comment, I asked why people chose to use the symbol τ over just writing turn or " rev (olution)" (defined to be the constant ≈ 6.28318530718 ) given how unambiguous the latter is as a name for 2π. And why not just write sinrev() or sinturn(), and leave the symbols sin() and rev (defined to be ≈ 6.28318530718) alone?
I think it's Tau[0]. [0] https://en.wikipedia.org/wiki/Tau_(mathematics)
First sentence of the Wikipedia link:
> The number τ (spelled as tau)
The nice thing about turns is that they can be represented by an unsigned integer. For example with an 8 bit unsigned integer: - 0000_0000 = 0 or tau - 1000_0000 = pi - 1100_0000 = 3*pi/4 And the addition and multiplication by integer scalars all apply and the overflows work naturally. I wrote a little library in rust [0] to help with this as you can define the operations */+-% etc. [0] https://docs.rs/turns/latest/t…
Of course, gut instinct can be wrong, so I checked in godbolt and was surprised to find out that even if I try to force lto, it still doesn't get inlined and remains a call.