[Snippet] A nice math function...

[AceHart]

Well, "nice"... no idea what to call this.
or if there even is any kind of need...

Anyway, ever wanted something like
do 5 damage on level 1,
do 8 damage on level 2,
do 12 damage on level 3,
do 17 damage on level 4,
...

Only to sit there and try to come up with a formula instead of "if level == 1 then ..."?

So,
5, 8, 12, 17, 23
take the differences from one to the next:
3, 4, 5, 6
take the differences from one to the next:
1, 1, 1
The line is constant!
Given it was the second, the most common case,
our damage can be calculated with this formula:
damage = a * level * level + b * level + c

But... what are a, b and c?

That's where this function comes to the rescue:

function solve takes real y1,real y2,real y3 returns nothing
    local real a = 0.5 * (y3 - 2 * y2 + y1)
    local real b = y2 - y1 - 3 * a
    local real c = y1 - a - b
    local string s1 = "+"
    local string s2 = "+"
    if b < 0 then
        set s1 = "-"
        set b = -b
    endif
    if c < 0 then
        set s2 = "-"
        set c = -c
    endif
    call DisplayTextToPlayer(GetLocalPlayer(), 0, 0, R2S(a) + " * level * level " + s1 + " " + R2S(b) + " * level " + s2 + " " + R2S(c))
endfunction

Examples:
call solve(5, 8, 12) (always call with the expected values on levels 1 to 3)
Which will say
0.5 * level * level + 1.5 * level + 3

Or,
call solve(10, 18, 34):
4 * level * level - 4 * level + 10


Of course, this could be improved by telling it to simplify
4 * level * level - 4 * level + 10
to
4 * level * (level - 1) + 10
but, then again, that would be the famous "exercise for the interested reader"


Just because it's fun, here's an online version that runs in your browser:
Formula finder

[Flare]

Pretty cool idea (even though having to test the map just to get the values would be annoying )

[SerraAvenger]

Originally Posted by Flare

Pretty cool idea (even though having to test the map just to get the values would be annoying )

Exactly. Doing this in JASS is like trying to teach a squirrel fly.

Also, wouldn't this require to have the graph of the damage increase have a certain shape?

The line is constant!

Don't make it too easy for yourself. That was just "randomly" true ( actually I believe you designed the sequence like that ).
You can't draw a 3rd degree polynomial through ALL sets of points.


So, why not ( Damien will hate me for this :evilgrin: ) do an executable of it with something easy like Python2Exe ^.-
Python comes here quite handy; You don't need no call for MAXXXXEFFICIENCYY!!!!, so you also needn't call for Perl ( oO ).
Anyway, just choose a language that
+ knows regex ( for an input like a;b;c;d )
+ can handle higher degree polynomials
+ has a lightweight + nice GUI toolkit ( like PythonQT for python )
+ dynamically allocates arrays

And code a similiar function there. Perhaps I'll do it some sleepless weekend
Best regards, Davey

[DrEvil]

If i was to use this system ( which i probably wont )

How would i get [ real y1 , real y2 and real y3 ] ?

function solve takes real y1,real y2,real y3 returns nothing

Sorry to ask im just trying to get used to using JASS functions taking stuff in [ Somehow , i dont know ]

Thanks for answering {[( In future post's )]}

[Flare]

Let's say you wanted to get a formula for
Level 1: 5
Level 2: 6
Level 3: 8

call solve (5, 6, 8)

y1/2/3 are the particular values you have for the associated level of the ability

[DrEvil]

So

call solve (5, 6, 8)

Would call the function solve giving ?
real y1 = 5
real y2 = 6
real y3 = 8

EDIT : call solve ( 5, 6, 8) { Would be a gui custom script ? Calling frm a spell cast maybe ? }

[Flare]

Ye (assuming I understand what you're asking) - you want to know how/where you get the values you pass to the function (y1, y2, y3), right?

[DrEvil]

Nice system you got there Ace

Yes , Thanks for helping me understand Flare .

Offtopic

And for other functions i could use like getting x,y coordinates and returning for a spell ?

[Darthfett]

Basic Derivatives, or algebra, depending on how you look at it :

damage = a * level * level + b * level + c

ax² + bx + c is the basic quadratic equation.

You basically wrote a guide on how to get a formula when you already know the intervals. Basically, it's finding the derivative of an equation you don't know.

The reverse derivative (being able to find the output from any level):

X is the level.
Y is the damage amount.
Y' is the difference of damage between one level and the next.
Y'' is how much Y' changes every level.

Y'' = c __ c is a constant number. Since Acehart solved the difference in difference in damage (Y'') to being 1, we can just plug in 1 for c.

Y' = cx + d __ d is an unknown constant. In this case, you can substitute 3, 4, 5, 6 for difference in damage (Y'), making d become 2.

Y = c x²/2 + dx + e __ e is an unknown constant. in this case, we can plug in 5, 8, 12, 17, 23 for damage (Y) and solve for e.

c = 1 :
Y'' = 1
Y' = x + d
Y = X²/2 + dx + e

(1) + d = 3

c = 1, d = 2:

Y'' = 1
Y' = x + 2
Y = X²/2 + 2x + e

(1)²/2 + 2(1) + e = 5

c = 1, d = 2, e = 2.5

Y'' = 1
Y' = x + 2
Y = X²/2 + 2x + 2.5

Now you can calculate the amount of damage dealt to any level using Y = X²/2 + 2x + 3

*Work in Progress Post, the formula is not quite working out as I intended. Sorry to post it incomplete, but I have a class to be at. :S*

See? Calculus is useful!

[Strilanc]

Solution for arbitrary degree polynomials:
http://en.wikipedia.org/wiki/Polynomial_interpolation

[AceHart]

Formula Finder

[Uberplayer]

(The title of the thread fights against all those title writing rules.)

Why did you let this drop? It's awesome!

(you should return to the chat, so I could bomb you at my random questions)

[AceHart]

Drop?
I wrote "The Amazing Formula Finder by AceHart"(tm) and put it online... what more can you ask for?

Link:
Formula Finder

[UndeadDragon]

Wow, that formula finder is useful

[Siretu]

You just made my homework LOTS easier. Thanks!