Approximating a drawing with a function

Hey Guys

Assume someone draws some arbitrary function on an x-y plane on graph paper.

Is there a way someone can create an actual mathematical function to match the drawing with a great deal of accuracy?

For example, if someone draws a parabola then it can be reasonably appoximated with a function. However, if the drawing looks more strange, then it would be difficult to easily come up with the function.

Maybe there is a way to write the function as a sum of terms. One could keep adding more terms to decrease or increase the value of the function over some specific part.

Re: Approximating a drawing with a function

Quote:

Originally Posted by **ScubaDiver**

Hey Guys

Assume someone draws some arbitrary function on an x-y plane on graph paper.

Is there a way someone can create an actual mathematical function to match the drawing with a great deal of accuracy?

For example, if someone draws a parabola then it can be reasonably appoximated with a function. However, if the drawing looks more strange, then it would be difficult to easily come up with the function.

Maybe there is a way to write the function as a sum of terms. One could keep adding more terms to decrease or increase the value of the function over some specific part.

1. The graph IS the function

2. If you mean to approximate the given function with some member of a given class of functions, there are lots of ways to do that:

a. A least squares fit of a [polynomial of given degree.

b. Splines passing through any given finite set of points on the graph.

c. Fourieer series approximations by a sum of sinusoids.

d. Approximation by sums of other orthogonal functions

and many more.

A lot depends on your specific application.