Saturday, August 8, 2009

The accuracy and speed of function approximations – part 2

In part 1 we took a look at two different function approximations; Polynomials and Taylor series. We found out that Taylor series are a lot more accurate than the quadratic equation – or is it?

The quadratic equation is fine in some cases. If you want to create a swinging hammer, a wave or the movement for a platform; this approximation is fine. But we can add some extra precision to the function and get it to be even more accurate. The new function looks like this:

HighPolySineFunction

The first function f defines the sine approximation and the second function g adds some extra precision. The result will look like this:

HighPolySine

We are nearly unable to distinguish the two lines from each other. And remember from part 1, it is exact in 0, π/2 and π. So using this quadratic equation is really more accurate than Taylor series – but accuracy is not everything. We will take a look at the performance in part 3.

Update: Part 3 is here

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