Program: InterpX2
By: Ben Axelrod   


     What is interpolation?  2D interpolation takes two points and 
draws a line through them.  Then it takes the X value you gave it 
(which is usually between these points but does not have to be) and 
uses this imaginary line to find the Y value there.  You could also 
give it Y to get X.  It doesnt mater.  What usually happens when you 
have problems with 3 variables, one is usually constant.  This way 
you can just do a normal 2D interpolation holding the other constant. 
 However, you might have to work in the (x,z) or another weird plane. 
 But the numbers will work out, and you will get the right answer. 

     3Dimensional interpolation is just three, 2D interpolations.  Of 
course, the 4 points that you give it have to be squared to the X and 
Y axes.  (They have to make a rectangle, not a diamond)  That was the 
reason I wrote this program.  What if the information you had wasnt 
so nice?  This program really only does two interpolations and a 
little trigonometry.  Here is a bad picture of what you should have.  
The *s are the two (x,y,z) points you have projected on the (x,y) 
plane.  The line on the x axis is the value that you have.  The 
program does a simple interpolation to first get the y value of the 
point you have.  Then uses the Pythagorean theorem to sort of make a 
rotated axis that it interpolates on to get the final Z value.  


y |
  |               *2
  | 
  |                
  |
  |
  |    *1         
  |
--|---------|---------
  |                  x


It is fun to check this program with the normal 3D interpolation 
program.  Just give it the corner points and depending on what kind 
of values you entered, it is usually pretty close!  I have 3 other 
interpolation programs that you should take a look at.  If you have
any questions or comments, please email me at: bmaxelro@syr.edu
