Trig and Maptools
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Re: Trig and Maptools
Someone, or perhaps a lot of someones, should develop a Lib:Math token to share.
Re: Trig and Maptools
And copy it to the wiki with the appropriate links from the Math category.

 Giant
 Posts: 249
 Joined: Mon Apr 20, 2009 9:31 pm
Re: Trig and Maptools
zEal wrote:Is there any way of having it spit out more?Akodo Makama wrote:I just copypasted what MatLab spit out at me.
1/2*Pi  x 1/6*x^3
3/40*x^5
5/112*x^7
35/1152*x^9
63/2816*x^11
231/13312*x^13
143/10240*x^15
6435/557056*x^17
12155/1245184*x^19
46189/5505024*x^21
88179/12058624*x^23
676039/104857600*x^25
1300075/226492416*x^27
5014575/973078528*x^29
9694845/2080374784*x^31
100180065/23622320128*x^33
116680311/30064771072*x^35
2268783825/635655159808*x^37
1472719325/446676598784*x^39
34461632205/11269994184704*x^41
67282234305/23639499997184*x^43
17534158031/6597069766656*x^45
514589420475/206708186021888*x^47
8061900920775/3448068464705536*x^49
5267108601573/2392537302040576*x^51
61989816618513/29836347531329536*x^53
e < 10^30 good enough (10^20 only needs up to term 37)? The recurrence formula is:
[code]N^2 * u(N) + (n^2 – 3n – 2) * u(n+2) = 0
U(0)=1/2*pi(), U(1) = 1, n>=0[code], should you require a higher order equation

 Giant
 Posts: 249
 Joined: Mon Apr 20, 2009 9:31 pm
Re: Trig and Maptools
zEal wrote:More than enough, thanks a lot.
I missed something earlier. My error values were only for values 'close' to (within 0.25 of) the origin (0 in this case).
The error at 0 is 0 after only the pi()/2 term
But the error at 0.5 needs 37 terms to drop the error to 7.8e15
To get e15 errors at 0.9, we need 131 terms
Even then (131 terms) the error at 1 would still be 5e2. That's 0.05, or 1/20.
I should have looked closer, as this is a well known problem with Taylor polynomial expansions. All the coefficients have the same sign. That's bad news for extreme input values (close to 1 or 1). There is a fix (use multiple expansions from different central points with weighted averaging or piecewise definition), but it's a bit ugly (as acos(x) is undefined at x>1), and I'll need time to figure out how what we'll need for e15 errors from [1..1]
All the other expansions likely suffer from the same problem.

 Giant
 Posts: 249
 Joined: Mon Apr 20, 2009 9:31 pm
Re: Trig and Maptools
Ok, given asin, acos is simple
acos(x) = 2 * asin( sqrt( (1x)/2 ) )
You'd think I'd remember little things like that. It was only 10 years ago I used these things on a regular basis.
acos(x) = 2 * asin( sqrt( (1x)/2 ) )
You'd think I'd remember little things like that. It was only 10 years ago I used these things on a regular basis.
Re: Trig and Maptools
I remember a proof on an exam that was worth extra credit. I didn't even know where to start:
e * i^pi + 1 = 0
I think that was calc3, IIRC. Fortunately, I don't use that kind of higher math at all on a regular basis.
e * i^pi + 1 = 0
I think that was calc3, IIRC. Fortunately, I don't use that kind of higher math at all on a regular basis.

 Giant
 Posts: 249
 Joined: Mon Apr 20, 2009 9:31 pm
Re: Trig and Maptools
Azhrei wrote:I remember a proof on an exam that was worth extra credit. I didn't even know where to start:
e * i^pi + 1 = 0
I think that was calc3, IIRC. Fortunately, I don't use that kind of higher math at all on a regular basis.
You mean e^(i*pi()) +1 =0 , right?
Re: Trig and Maptools
This will pick a random angle between 1 and 90, and give you a good approximation of sine and cosine for that angle:
And to answer the previous poster's question about why you would want this: I put together a Macro for doing a scatter function for Warhammer 40K. By those rules, you get an angle and a distance to move the token. So I needed to create a macro that would determine a random angle and distance, and then move a selected token by that amount in the right direction.
Code: Select all
[h: myAngle = 1d90]
[h: myRadians = divide(myAngle, 57.2958)]
[h: sinAngle = myRadians  divide(power(myRadians, 3),6)]
[h: sinAngle = sinAngle + divide(power(myRadians, 5),120)]
[h: sinAngle = sinAngle  divide(power(myRadians, 7),5040)]
[h: cosAngle = 1  divide(power(myRadians, 2),2)]
[h: cosAngle = cosAngle + divide(power(myRadians, 4),24)]
[h: cosAngle = cosAngle  divide(power(myRadians, 6),720)]
Angle: [myAngle]<br>
SIN(Angle): [sinAngle]<br>
COS(Angle): [cosAngle]<br>
And to answer the previous poster's question about why you would want this: I put together a Macro for doing a scatter function for Warhammer 40K. By those rules, you get an angle and a distance to move the token. So I needed to create a macro that would determine a random angle and distance, and then move a selected token by that amount in the right direction.
Re: Trig and Maptools
RPTroll wrote:Someone, or perhaps a lot of someones, should develop a Lib:Math token to share.
Well, since you asked ...
I included all the trig & math functions in this thread:
 pi
 degrees
 radians
 sine
 cosine
 factorial
 modulo
 robust eval()
 my custom wrapper for number(), which returns 0 (or specified default value) if the argument is not a number.
 my custom math.list(). Requires 2 arguments: function name and a string list, or json array, of values. It lets you perform math functions like max, sum, etc. on a list of values. ex. math.list( 'sum', valueList ).
[EDIT: aliasMask has kindly posted a larger version with even more functions, without the custom 'extras' included here. His versions are probably more accurate.
Newer version (v2.1).
]
Last edited by biodude on Tue Jun 29, 2010 8:43 am, edited 1 time in total.
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Re: Trig and Maptools
great work there biodude!
Also, just while I'm typing I was wondering whether there were any functions in MT that can assess whether a number is odd or even? I can't find anything on the list of functions.
(not meaning to derail but it seems that it's a fairly good match as it may be a another useful math udf)
Mal
Also, just while I'm typing I was wondering whether there were any functions in MT that can assess whether a number is odd or even? I can't find anything on the list of functions.
(not meaning to derail but it seems that it's a fairly good match as it may be a another useful math udf)
Mal
Mal
Re: Trig and Maptools
determining if a number is even or odd is a common task, but also fairly trivial:
which is why I don't think anyone has ever written an entire UDF for it. Would such a thing be useful to people?
Code: Select all
[H: evenOrOdd = if( floor( number / 2 )==( number / 2 ) , "even", "odd" )]
which is why I don't think anyone has ever written an entire UDF for it. Would such a thing be useful to people?
"The trouble with communicating is believing you have achieved it"
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Re: Trig and Maptools
I took the lib Biodude made and added some stuff. I did remove the eval and list sum functions though. This is my own personal version, so feel free to use and modify as you will. Here's a list of functions:
Lib:Math
Lib:Math
 onCampaignLoad  Loads all the functions as UDFs in the form math.function
 angleToSlope(angle): slope  Converts the angle formed by the hypotenuse and xaxis of a right triangle to a slope value.
 cos(value): radians  Cosine
 sin(value): radians  Sine
 tan(value): radians  Tangent
 toDegrees(radians): degrees  Convert radians to degrees
 factorial(start[,end,step])  Does factors from start to end and allows skips with step parameter (defaults, end = 0, step = 1)
 toRadians(degrees): radians  Convert degrees to radians
 arcCos(value): radians  Inverse Cosine
 arcSin(value): radians  Inverse Sine
 arcTan(value): radians  Inverse Tangent
 cahAngle(adjacent,hypotenuse): degrees  Returns the angle opposite the Adjacent and Hypotenuse of a right triangle (SOACAHTOA)
 slopeToAngle(slope): degrees  Returns the arcTangent of a slope
 sohAngle(opposite,hypotenuse): degrees  Returns the angle opposite the Opposite and Hypotenuse of a right triangle (SOACAHTOA)
 toaAngle(opposite,adjacent): degrees  Returns the angle opposite the Opposite and Adjacent of a right triangle (SOACAHTOA)
 div(number,divisor): integer  Returns the integer of the number divided by the divisor
 mod(number,divisor): integer  Returns the integer of the remainder of the number divided by the divisor
 val(string): number  Forces a string value to a number where if invalid returns 0
 pi(): number  Returns the value of PI to 20 decimal places
 isOdd(integer): boolean  Returns 1 or 0 if integer is odd or even (respectively). If not an integer returns ""
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Re: Trig and Maptools
Careful, aliasmask ... you might get highschoolers taking trig stopping by RPTools and downloading that, even if they have no interest in playing actual RPGs via MapTool!
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Re: Trig and Maptools
Ha! But they'll have to learn the MACRO language first. Doing this brought back some of my highschool/college day memories.
And for any highschoolers... go to these pages:
That's where I got most of my formulas
And for any highschoolers... go to these pages:
 http://www.cc.gatech.edu/gvu/multimedia/nsfmmedia/graphics/elabor/math/mathfaq_lines.html
 http://en.wikipedia.org/wiki/Trigonometric_functions.
 http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
That's where I got most of my formulas
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