This gem is about how you can approximate a quadratic/quadratic like curve with just adds. And this might come in handy some day. It is fast, and easy to set up.

To fully utilise this gem, we need a formula, so you can precalculate the needed add values. So imagine the standard quadratic equation:

        f(x)=ax^2+bx+c=0

Now, to calculate the two vaules we need for our addition, we need three points, with both X and Y coordinates. Then we need to apply some mathematics to it (this is an example, approximating sin x):

        0=a*0^2+b*0+c
	1=a*(pi/2)^2+b*pi/2+c
        0=a*pi^2+b*pi+c

This system can easily be solved using some kind of elemination. In my example these are the values I get:

        c=0
	b=4/pi
        a=4/pi^2

Now, we can easily apply them in our formula:

        add     ax,bx           ; where ax=c, bx=a
	add     bx,cx           ; where cx=b

If you do more additions in your loop, you may "save" some additions by using the ADC-gem mentioned earlier.
The approximation you will get is quite good.

Gem writer: Stefan Ohrhallinger
last updated: 1999-08-09