## Posts Tagged ‘exponential

18
Dec
09

### Creating Mathematical Formulae from sample data using Excel

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.

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:

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

18
Nov
09

### Ranged Numbers. Non-Linear response curves for Sliders and TouchPads.

I’ve been building a few apps recently and have found that a linear response over a range of numbers has been a poor solution. I needed to be able to apply different response curves to user interface components (knobs, sliders, touchpads) as well as on screen display objects, characters, etc.

I needed a good name for the class, but instead came up with the pretty poor moniker ‘RangedNumbers’. I’ll change it when I come up with a better one.

So the idea is, a ‘ranged number’ is instantiated, initialised for the required range then a simple call with a value in that range will result with a percentage that can be applied to the intended recipient accordingly. I realised that an inverted curve would be handy too, so have added that functionality.

I have included exponential and powered curves as well as linear.

So to use the ranged number system:

//Instantiate and Initialise
var ranged_num:RangedNumber=new RangedNumber(min,max)
//Where min is the minumum number in the range and max is the maximum

//In use:
trace ( ranged_num.calculatedRangeNumber(value, curve_type, inverted) )
//Where:
// value is the value within the range to be calculated
// curve_type is the type of response curve.
// Curve types: RangedNumber.LINEAR, RangedNumber.EXPONENTIAL, RangedNumber.POWERED
// inverted is a boolean flag. True if the inverted response is required

I have put together two demos to show the RangedNumber class in action:

Firstly using a Slider component. Grab the slider and watch how the markers are represented on all the displayed response curves.

Now here is the same demo but this time using a TouchPad. Click on the touchpad to engage. In this demo horizontal movement controls the standard curves and vertical the inverted.

The source for these demos and the Ranged Number class can be found here: Ranged Number ZIP

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