[Math] 'Jumping from one row of numbers to another'

[Ardenian]

I ran into the following problem and I would be glad if you could help me, please.
Basically, I have a certain range of numbers and a second one, imaginary linked, like this:

41	42	43	44	...	79
40	80	120	160	...	1560

Now I have only one of these two rows and I wish to 'call' the corresponding value from the second row.
How can I do this, with what mathematical expression ?

Note: I do not want to use array-based variables due to the huge amount of values I need

 

[Dr Super Good]

Assuming top row is X and bottom row is Y then...
Y = (X - 40) * 40
or
Y = X * 40 - 1600

This works for everything except 79, which it will give you 1,560 instead of 1,600 however I am guessing this value was an off-by-one mistake rather than intentional.

 

[Ardenian]

Yes exactly.

Thank you!

EDIT: Well, I did not get a solution to the following ones:

80	81	82	83	...	119
41	81	121	161	...	1521

120	121	123	124	...	160
1561	1562	1563	1564	...	1600

41	42	43	44	...	79
80	120	160	200	...	1560

I tried to learn it searching it via the Internet, but I did not find a good site to see how I can solve this.

 

[Mercious]

1.
Y = 41 + (X-80)*40

Doesnt match your last value (119) though, something is messed up there (should be 1601).

2.
Y = 1561 + (X-120)

Again, doesnt match your last value ... It should be 1601, just like above

3.
Y = 80 + (X - 41)*40

Your last value ....

Where do you even get these form and is there any connection to Wc3 Modding at all? :E

 

[Ardenian]

Thanks a lot Mercious!
Yep, I was quite tired when setting up the values so I might confuse one or another thing.

Yes, it has connection to Warcraft modding. I have a certain range of numbers and each number has a custom value. However, the Y values are not linear as the X values are, they change in certain ranges, as you can see in the tables.

However, if you don't mind, what is the easy way to get to these functions ?

 

[Dr Super Good]

However, if you don't mind, what is the easy way to get to these functions ?

They are linear functions. You should have been taught this when around 13-14 as part of your high school mathematics. Your mathematics teacher deserves a complaint letter for teaching them so badly or not teaching them at all?

To calculate you get 2 points (which you have from the table), work out the gradient between them (using (Y1-Y2) / (X1-X2)) which is the constant "a" and then work out the Y intercept which is the constant "b".

If you explain the full scope of the problem there might be an easier solution. As far as I can tell you have the following so far.
z = f(x, y) where z is discontinuous with x and y
y = g(x) where y is discontinuous with x every 40 units

If you could explain the purpose of function f(x, y) and why you need g(x) it might help solving the problem more efficiently.

 

[Ardenian]

Alright, lets try this:

X1 = 124 X2 = 248
Y1 = 456 Y2 = 1824

a = ( 456 - 1824)/( 124 - 248) = 11

f(x) = ax + b
-> 456 = 11*124 + b
b = - 908
-> Y = 11X + 908

Hm, seems this is not how it works

 

[edo494]

you magically converted the -908 to +908. It works then

 

[Ardenian]

you magically converted the -908 to +908. It works then

Huppla.. Thanks!

Thank you all guys, I am able now to do it myself!

 

[WereElf]

I made you a program for calculating these.
You just need to fill in the orange fields to get the formula, and then fill the yellow fields with other values (x) to get their y's.
I even locked the cells so you can't break it
(it's in zip, cuz Hive doesn't like excel files)

 

[Ardenian]

I made you a program for calculating these.
You just need to fill in the orange fields to get the formula, and then fill the yellow fields with other values (x) to get their y's.
I even locked the cells so you can't break it
(it's in zip, cuz Hive doesn't like excel files)

Save for dummies like me, eh

Wow, thank you! Now I realized it can easily be done this way, using an excel table.. I am surely going to make use of it!

 

[Ardenian]

Update:

Here is the visualization of my problem:

In difference to a common square, my square consists of a limited amount of points.

That being said, the border consists of 156 points

These are the X values of my value tables

The Y values we get from this one:

X	1	2	...	40
Y	1	2	...	40

-> We can ignore the Northern side

Southern Site ->

X	41	42	...	78
Y	80	120	...	1560

a = (Y1-Y2) / (X1-X2)) = ( 80 - 120)/(41-42) = 40

b = Y - a*X = -1560

Correct

-> Y = 40*X - 1560

-> Western Site

X	79	80	...	116
Y	41	81	...	1521

a = (Y1-Y2) / (X1-X2)) = ( 41 - 81)/(79-80) = 39

b = Y - a*X = -3040

-> Y = 39*X - 3040

Correct


-> Southern Site

X	117	118	...	156
Y	1561	1562	...	1600

a = (Y1-Y2) / (X1-X2)) = ( 1561 - 1562)/(117-118) = 1

b = Y - a*X = 1444

-> Y = 1*X + 1444

Correct