Download the Open Source Here

Primer on Lingo Math
Provided by Colin Coupland

Maths is a subject which should really be studied all on its own. However the programming community need to know only a certain amount. However, its difficult to begin to understand the hard core elements of pure maths. Often I see signs which I don't know the meaning of.

This tutorial will try to bring together some common treads within maths.If you understand Director lingo you can go straight to downloading the files.

The example I have used for this demo is the "Lissajous.dir" curve. This is a good curve. It moves in a figure of eight type movement. It is nice and smooth. There are several curves demonstrated here though. Some more useful than others.

Maths is mainly used to move sprites. First of all you declare variables. You do this with the property commando. Then you set up the values which you want the variables to start off with - by using the beginsprite commando.

   property t,a,b,c,n

   on beginsprite me

     a=100
     b=62
     c=73
     t=0
     n=2
   end

  Then you start the core part of the program. This involves the exitframe handle. Everytime a frame finishes this source will be accessed.

  on exitframe me
    t=t+0.02
    xx = a* cos(n*t + c)
    yy = b *cos(t)
    member(3).image.setPixel(xx+200, 300+yy, rgb(255,255,255))
    member(3).image.copypixels(member(4).image,member(3).rect,member(3).rect,[#blendlevel:3])
  end

You will notice one or two things here. Firstly the T variable. All curves involve the manipulation of cosines and sines. These Trigonometry functions are usually used to calculate angles. However, they are also extremely useful for moving sprites. They give nice smooth movement. Just look at the T variable. Each frame it is increased by 0.02 That is what gives the animation. All the other variables are a contradiction - they just do not vary. You can manipulate those in other ways. But for the purposes of this simple demonstartion we will manipulate only the T variable. Also notice that the T variable is only incresed by a very small amount. With other curves the increase per frame is 1 or even two degrees. It all depend on the curve.

You will also notice the member(3).image.setpixel line. You can ignore this for the purposes of the maths. That simply draws a new white dot on the image. The next line fades the image.

So in short the main calculation is in the lines.

  xx = a* cos(n*t + c)
  yy = b *cos(t)

These two variables calculate the position along (xx) and up (yy) to draw the new dot.
You will find that Maths curves all have these several common features.

And of course all cosines and sines end up at exactly the same position so that after 360 degrees have passed the animation simply repeats itself.

The other exampamples that are included in the down load look somthing like this: