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View Full Version : More of a math question..

03-25-2004, 01:01 AM
Hey guys,

I didn't really know where else to pose this question, but...

Let's say you've got
amt inc
5000 38
10000 29

So if you have 5000, you'd use 38. If you had 10000, you'd use 29.

Now I have a table of these pairs, in ascending order on amt for every 5000. (ie. 5000, 10000, 15000, 20000, ....).

The problem I'm facing is that if I have, say, 6000, I don't have a matching 'inc'. Now I can't use 38, or 29, but I have to use something in between. But that something has to be proportionate if 'amt' is 5500 or 8900.

I hope that makes sense so far.

Now I think this has something to do with numerical analysis, but I really just can't remember what or how to do this!

Thanks,

shmoove
03-25-2004, 09:49 AM
It's called interpolation.
You can think of graphically: Your (amt,inc) pairs are points on a 2-D plane, and you connect them with a line. You go along that line until you reach the desired value on the "amt" axis, and then you see where you are on the "inc" axis.
If you did any high-school algebra or analytical geometry (I don't know if that's the name you'd use there but I mean finding the equations for lines, circles, etc.), then you should have no problem taking it from here.
If there are still problems post back.

shmoove

03-25-2004, 07:34 PM
Heh, thanks shmoove!

Funny thing, I emailed an old professor (numerical analysis prof..), and you are correct. He's told me to use Newton Interpolation.

I looked up the formula and now I'm on my way!

Thanks again,

Mhtml
03-26-2004, 11:17 AM
Newton interpolation eh, care to explain it?? I've only ever looked at linear and geometric for 3d model animation.

03-26-2004, 06:50 PM
You should probably research it, cuz I don't think I understand it all that well (like how it works..).

I just know the formula for Newton's Linear Interpolation.

INTERPOLATE - To insert a value between known values by using a procedure or algorithm specifically related to the known values.

Here's the formula:
y = y1 + (x - x1) * (y2 - y1) / (x2 - x1)

i.e.
to interpolate between:
x1 = 5000 y1 = 38
x2 = 10000 y2 = 29

y = 38 + (x - 5000) * (-9) / 5000

sample values: x = 5000 y = 38 left end
x = 10000 y = 29 right end
x = 7500 y = 33.5 middle
x = 6000 y = 36.2

Hope that helps,

shmoove
03-26-2004, 09:42 PM
Damn scientists always sticking their name everywhere....

03-26-2004, 10:59 PM
Hey you would too I'm sure! shmoove's Linear Interpolation... nice ring to it! lol

I remember in university when we were learning the different sorting algorithms, we tried to come up with our own, and we'd name them after ourselves. I had sadSort... lame, but it was funny back in the day.

Ciao,