Getting a formula/function out of a finite pair of numbers

Hi everybody.

I use a machine which is able to move in 3 dimensions( x , y , z ).I define the way how it should move with a finite pair of numbers. Almost always z( height ) is fixed, so only x and y are changing.

How can i get a formula/function f(x,y,z) out of this

for example: i give him a vector [x,y]=[(0,0) (0,4) (1,5) .... ]

how do i get this then:

f(x,y,z) = Ax^n +By^m +....

Answer 1

[Star Strider]

It looks to me that you have a matrix of (x,y) pairs, and that it is actually:

xy = [0 0;  0 4;  1 5];

A = ...
B = ...
n = ...
m = ...

f = @(xy) A.*xy(:,1).^n + B.*xy(:,2).^m + ...

That is how I would do it.

[samir]

But how do i know how big is my n and m.I found a similar question

My question is about trying to find a formula between numbers. For example, suppose I have 10 numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 It is obvious that the first number plus 2 will yield the second number, 4; 4 plus 2 will yield the number 6, and so on. So the formula for this group of numbers is x + 2.

Say I have another set of numbers: 2, 6, 14, 30, 62..... If the first number is multiplied by 2 and 2 is then added, you will get 6. 6*2 + 2 will yield 14. 14*2 + 2 will be 30.. So the formula is x*2 + 2.

[Star Strider]

I have no idea what m and n are. I got the impression that you defined A, B, m and n, and that you wanted to know how to separate the elements of your matrix into x and y values in your function.

If you’re solving for m and n, you must already know the trajectory of the robot. Then this becomes a curve-fitting (parameter estimation) problem.

The illustration you described in your comment is exactly a parameter estimation problem, although in that situation using linear least squares. Yours appears to be a nonlinear system, so probably fminsearch would be the best way for you to determine n and m.

What is it you want to do?