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Handling Angles and Sin/Cos


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#1 Moonkis   Members   -  Reputation: 273

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Posted 28 November 2012 - 04:24 AM

I'm currently trying to build an 2D ray casting engine, however I'm on the fly learning the trigonometry as well.
I'm currently working my head around angles in degrees and radians.

I'm trying to use 0-360 degrees system that when the double reaches a value of 0 or 360 it wraps around so lets say the angle is increased/decreased by 90.

Going from 360 + 90 = 90
Going from 0 - 90 = 270



This works when trying to move with cos and sin for the angular movement. But I realized that 0* and 360* is not the same value for sin ( cos 0 and 360 is equal to 0 ).

sin(0*) = 0
sin(360*) = -1 * 10^-13



While I realize that this number is incredible small and wouldn't make a noticeable difference, it's still a factor that can change the output of movement.

When checking a real time example of it ( Example Movement ):

y = 5
sin(0*(Pi/180) )*(-6) = 6*10^-13
sin(360*(Pi/1780) )*(-6) = 0



It's obvious that these are not the same, though the calculator and computer outputs the same number if it was supposed to add to y, say: 5 + 0 = 5 and 5 + 6*10^-13 = 5 ( Computer output and Ti-84+ Calculator ).



But when trying to compare these as equal each other in an if statement it did not validate as true, so there is a very small difference.

My current wrap-around code looks like this:
  if( sf::Keyboard::isKeyPressed( sf::Keyboard::A ) )
  {
   player.rot -= 5;
   if( player.rot < 0 )
   {
	player.rot = ( 360 + player.rot );
   }
  }
  if( sf::Keyboard::isKeyPressed( sf::Keyboard:<img src='http://public.gamedev.net//public/style_emoticons/<#EMO_DIR#>/biggrin.png' class='bbc_emoticon' alt=':D' /> ) )
  {
   player.rot += 5;
   if( player.rot > 360 )
   {
	player.rot = ( player.rot - 360 );
   }
  }

So, is this going to be a problem in the future or is it so small that it's negligible? After all it's only a problem on the 0 and 360 degrees.

* Converted to radians under the hood when inserted into cos or sin functions.

Edited by Moonkis, 28 November 2012 - 04:27 AM.


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#2 C0lumbo   Crossbones+   -  Reputation: 2259

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Posted 28 November 2012 - 04:32 AM

This is just something you have to learn to live with when you're using floating point numbers and you shouldn't worry about it (also, this issue is pretty much independent of trig).

You almost never should check for equality of floating point numbers, because any non-trivial calculation is going to introduce some error.

#3 J. Evola's Apprentice   Members   -  Reputation: 307

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Posted 28 November 2012 - 04:56 AM

Take a look at this page: http://floating-point-gui.de/

#4 Toothpix   Crossbones+   -  Reputation: 810

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Posted 28 November 2012 - 05:31 AM

OpenGL, if I'm not mistaken, converts angles to radians, just saying. Trigonometric ratios (sine, cosine, tangent) are not difficult to learn. One little mnemonic device American teachers use (or at least used) is the gibberish phrase "soh-cah-toa." If you remember that, you remember sine, cosine, and tangent. soh is sine which is opposite side divided by hypotenuse (soh), cosine is the adjacent side divided by hypotenuse (cah), and tangent is the opposite side divided by the adjacent side (toa).

C dominates the world of linear procedural computing, which won't advance. The future lies in MASSIVE parallelism.


#5 Serapth   Crossbones+   -  Reputation: 5450

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Posted 28 November 2012 - 08:50 AM

Ironically I just finished a couple detailed gamedev math tutorials, one on rotating to face a point and one on Angular (and non-angular) velocity, which combined cover exactly the topic you are talking about.

That said, your issue is as others have already stated, more about floating point rounding off. I simply mention it here if anyone else working with handling angles comes into the thread looking for help. :)

#6 Moonkis   Members   -  Reputation: 273

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Posted 28 November 2012 - 04:43 PM

Thanks guys! It's really helpful, I'll check the links you provided!

#7 Álvaro   Crossbones+   -  Reputation: 13308

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Posted 28 November 2012 - 05:26 PM

I'll take the opportunity to mention that you probably don't need angles. I should really write a journal entry or something of that sort to describe what I mean by that. But essentially, if instead of an angle you use a unit-length vector (effectively (cos(angle),sin(angle)), you often end up with code that is cleaner, faster and easier to get right.

#8 Toothpix   Crossbones+   -  Reputation: 810

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Posted 28 November 2012 - 06:46 PM

I should really write a journal entry or something of that sort to describe what I mean by that.

Please do, I love reading people's articles/journals as they are very interesting.

C dominates the world of linear procedural computing, which won't advance. The future lies in MASSIVE parallelism.





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