Swingpant's Game Lab

So you’re in Flash and want to move an item on the stage, rotate a camera or dynamically change a volume depending on another value. You could use the curves available in various Maths libraries, but you can spend a lot of time matching and applying constants.

A quicker – more accurate way can be to come up with your own formulae.

What!!? It is easy – you really don’t have to understand the mathematics, you can get Excel and Flash to do the heavy lifting for you.

Let me explain this by means of an example:
I was building a 3D application. I had a camera and needed it’s X rotation to be close to certain values depending on the camera’s position on the Z axis. I manually moved the camera into position and noted down samples of the values I required and placed them into Excel: One column for the z value and one for the required angle. – I only need a handful of samples to allow me to plot a regression trend line.

I now select the values on the spreadsheet and create an XY scatter chart. Great, my points are on the graph. I can see it makes a curve. In the ‘Chart’ drop down menu I now ‘Add Trendline…’. If I choose ‘Linear’ I get a straight line, but I want a curve so I can choose from a number of different methods. In this case ‘Exponential’ seems good. Select that and a look at the Options tab allows me to select ‘Display Equation on Chart’.

Now as soon as I press OK, I get my equation. Simple.

Regression Curve Formula in Excel from sample data

How do I represent this formula in Actionscript? Basically it is saying 202.62 times the exponential of 0.0014 times the chart’s x value. So in AS:

The final formula in Actionscript

As required, I have calculated the formula using the camera.z value and applied it to camera.rotationX. Now whenever the z value changes I have a smooth curve applied to rotationX.

Nice!

2nd Oct 2010:
A quick addition to this post. If a more complex curve is needed then a polynomial should be chosen. A polynomial can have multiple ‘orders’. This more orders you have the more compelx the curve can be. (Excel allows up to 6). A great thing about polynomials is speed. It is merely a series of multiplications which are very light on the processor.

So a polynomial trend gives you (for example) the formula:
109.13×4 – 265.48×3 + 125.34×2 + 40.012x + 2

To represent this in Actionscript I’d need to replace x4 (x to the power of 4) with the x value paramter – say delta – so x4 becomes delta * delta * delta * delta (or indeed Math.pow(delta,4)), and so on. The final formula would be:
109.13 * Math.pow(delta,4) – 265.48 * Math.pow(delta,3) + 125.34 * Math.pow(delta,2) + 40.012 * delta + 2