Yea, I have some macros cysin and cycos that does that, I just call them cycles instead of turns, but it's the same idea.. ofc internally those are still stupid and just multiply by tau..
Turns are better than radians
31–40 of 494 posts
Re: Turns are better than radians
#32>But math never decreed that sine and cosine have to take radian arguments!
Ummm, actually it did. The Taylor-series of sine and cosine is the simplest when they work with radians. Euler's formula (e^ix = cosx + isinx) is the simplest when working with radians.
Of course you can work in other units, but you'll need to insert the appropriate scaling factors all over the place.
"Turns" don't generalize to higher dimensions either. With radians you can calculate arc length on a circle by multiplying with the radius. This extends naturally to higher dimensions: a solid angle measured in steradians lets you calculate surface area on a sphere by multiplying with the radius. How do you do the same with "turns" on a sphere? You can't in any meaningful way.
Re: Turns are better than radians
#33This is like complaining about g in F = g * m, in gravitional force formula, and redefining gravitional constant g as 1 and multiplying "gram" by 1/9.8.
Sure it simplifies things for you but you are breaking everything else that used g constant
Or we can redefine seconds perhaps and multiply it sqrt(1/9.8)
Re: Turns are better than radians
#34"math never decreed that sine and cosine have to take radian arguments!" This is at best questionable and at worst false. If you only want to use sin and cos as functions for doing trigonometry, it is true that you can choose whatever angle unit you like and stick with it and it will be fine. For most other stuff, e.g. differential equations, complex analysis, signal processing and mechanics, it's pretty much inescap…
Why do they need to be at multiple integers of pi, instead of at half turns?
Re: Turns are better than radians
#35y’’ = -y
Radians are God’s chosen angular unit. If you want to do mathematics, you have to use radians.
Re: Turns are better than radians
#36Turns sound fine. But they are turns of a circle of a given radius. So as long as everything conforms to that coordinate system, we're groovy? Radians (circle fractions) are generally preferred because we can compare, e.g. two planetary orbits, conveniently, no? Or did I miss something?
>But they are turns of a circle of a given radius.
No, a revolution is a revolution. If you turn a 1 m wheel by one revolution and a 2 m wheel also by one revolution, both will have turned one revolution, or 2 pi radians. If you roll both of them 2 pi m forward on the ground, one will have turned one revolution, or 2 pi radians, and the other will have turned half a revolution, or pi radians.
Re: Turns are better than radians
#37While I agree that "turns" are much more convenient in some applications than radians, there is no need to invent a new terminology. For a long time, including the 19th century, the plane angle measurement unit corresponding with 4 right angles, i.e. a complete rotation around a point, has been named "cycle". That is why in many old physics or engineering books one will find wave numbers measured in "cycles per meter…
https://en.m.wikipedia.org/wiki/Binary_angular_measurement
BAMS has been in use for several decades where fixed point is the norm. DSP for instance.
Re: Turns are better than radians
#38I’m surprised game engines do conversion from degrees to radian to call trigonometric functions. I would have called that bad code in an industrial context. We did everything in radians and converted to degrees only for displaying and input. It was a lot more natural from us because we are a lot more familiar with radians anyway. I don’t think I have used degrees often since starting high school twenty years ago.
> We did everything in radians and converted to degrees only for displaying and input.
This is generally how game (engine) code works as well. The example in the article is an example of performing that conversion, except with turns instead of degrees.
Re: Turns are better than radians
#39y’’ = -y Radians are God’s chosen angular unit. If you want to do mathematics, you have to use radians.
Because I didn't see it mentioned yet, this is the same feature that makes the small-angle approximation of sin elegant: sin(x) ≈ x .
Re: Turns are better than radians
#40No post body was provided.