Any math skilled can help me? [Solved]
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Any math skilled can help me? [Solved]
I am using in a scenario this function. I have forgotten my math lessons about how interpolate a function from given points, but for calculate intermediate values and better working of code would help me a lot have a function with similar output rather than discrete values table. Can anyone do it for me?
(note that all values for f(x) x>1 are less than 1, they have a point before floating part)
f(1)=1
f(2)=.88
f(3)=.77
f(4)=.67
f(5)=.58
f(6)=.50
f(7)=.43
f(8)=.37
f(9)=.32
f(10)=.28
f(11)=.25
f(12)=.224
f(13)=.201
f(14)=.181
f(15)=.164
f(16)=.15
f(17)=.138
f(18)=.127
f(19)=.117
f(20)=.108
f(21)=.1
f(22)=.093
f(23)=.087
f(24)=.082
f(25)=.078
f(26)=.074
f(27)=.071
f(28)=.068
f(29)=.065
f(30)=.062
f(31)=.06
f(32)=.058
f(33)=.056
f(34)=.054
f(35)=.052
f(36)=.05
(note that all values for f(x) x>1 are less than 1, they have a point before floating part)
f(1)=1
f(2)=.88
f(3)=.77
f(4)=.67
f(5)=.58
f(6)=.50
f(7)=.43
f(8)=.37
f(9)=.32
f(10)=.28
f(11)=.25
f(12)=.224
f(13)=.201
f(14)=.181
f(15)=.164
f(16)=.15
f(17)=.138
f(18)=.127
f(19)=.117
f(20)=.108
f(21)=.1
f(22)=.093
f(23)=.087
f(24)=.082
f(25)=.078
f(26)=.074
f(27)=.071
f(28)=.068
f(29)=.065
f(30)=.062
f(31)=.06
f(32)=.058
f(33)=.056
f(34)=.054
f(35)=.052
f(36)=.05
Last edited by tekelili on January 18th, 2012, 6:37 am, edited 1 time in total.
Be aware English is not my first language and I could have explained bad myself using wrong or just invented words.
World Conquest II
World Conquest II

 Posts: 876
 Joined: November 28th, 2008, 6:18 pm
Re: Any math skilled can help me? (function interpolation)
There is one polynomial function of a maximal degree 35 that goes through points you listed. (http://en.wikipedia.org/wiki/Lagrange_polynomial)
You can use something like this: http://www.solvemymath.com/online_math_ ... lation.php
In case you want to calculate that function by WML/lua means: that is not a good idea, because it would be too slow. You should use rather "spline interpolation" for example.
You can use something like this: http://www.solvemymath.com/online_math_ ... lation.php
In case you want to calculate that function by WML/lua means: that is not a good idea, because it would be too slow. You should use rather "spline interpolation" for example.
I work on Conquest Minus • I use DFoolWide, Retro Terrain Package and the addon 'High Contrast Water'
I moved to Nosebane's corner (Doc Paterson's signature); I am spending my time there, so PM me if I don't answer your post in forums
I moved to Nosebane's corner (Doc Paterson's signature); I am spending my time there, so PM me if I don't answer your post in forums
Re: Any math skilled can help me? (function interpolation)
If you don't want to use an array of results such as
Then another alternative would be
For your data, it seems it would be simpler to use a lookup table than a 35th degree polynomial.
Code: Select all
[f]
value=1
[/f]
[f]
value=.88
[/f]
Code: Select all
[f]
1=1
2=.88
[/f]
http://www.wesnoth.org/wiki/User:Sapient... "Looks like your skills saved us again. Uh, well at least, they saved Soarin's apple pie."
Re: Any math skilled can help me? (function interpolation)
Thanks for help guys. I have understood I was asking for something more complicated than I expected. My final solution was interpolate a function of grade 2 for values less than 12, where I need more precision, and use table for greater ones.
for x<12 i got this one: f(x)=1+(x^227x26)/200 using the few I still remember about progressions
for x<12 i got this one: f(x)=1+(x^227x26)/200 using the few I still remember about progressions
Be aware English is not my first language and I could have explained bad myself using wrong or just invented words.
World Conquest II
World Conquest II
Re: Any math skilled can help me? (function interpolation)
I certainly wouldn't try to approximate something like this with a direct polynomial in x  you'll basically be overfitting, and it won't extrapolate nicely.
However, eyeballing it and playing with a calculator a little, it looks like away from the beginning it's doing something like (?) f(x) ~ C.x^(k), where C and k are constants (something roughly like C=5.5, k = 1.3) . You might try fiddling around with polynomials in x^(1/4) or somesuch and see if you can find something which fits well.
However, eyeballing it and playing with a calculator a little, it looks like away from the beginning it's doing something like (?) f(x) ~ C.x^(k), where C and k are constants (something roughly like C=5.5, k = 1.3) . You might try fiddling around with polynomials in x^(1/4) or somesuch and see if you can find something which fits well.
Re: Any math skilled can help me? (function interpolation)
After experiment a lot with a function drawer, I finally had a function wich curve pretty much gives me what I really wanted:
f(x)=(5/6)^((x1)/(x^(5/12)))
If neccessary, this thread can be locked.
f(x)=(5/6)^((x1)/(x^(5/12)))
If neccessary, this thread can be locked.
Be aware English is not my first language and I could have explained bad myself using wrong or just invented words.
World Conquest II
World Conquest II