Math curve (DuplicateSprite)
The purpose is to display a mathematical function using a script..
I suppose you know well how to create objects, thus I will not insist on.
In Swish2, you might have seen a general demonstration of parametrical curves.
Creating Objects
1 - Set up movie size 400x400 (background color #999999).
Frame Rate doesn't matter.
2 - Create an horizontal line and a vertical line crossing the middle of the scene ( scene width and scene height )
3 - Now create a red circle : X = 0 Y = 0 W = 3 H = 3
Anchor point : Center
4 - Convert this circle into sprite ( name : dot , Target toggled )
Menu Modify / Convert / Convert to sprite.
5 - Use tool 
, enter the following text over 2 lines :
x = a sin t cos 2t
y = a cos t sin 2t
Choose color #FFCC00 for instance.
Script
In Outline, select Scene_1. Enter the following script :
onLoad()
{ // scene height width
H = int(_root._height);
W = int(_root._width);
a = 100;
n = 500; // number of points
}
function x( t ) { return ( a * Math.sin(t) * Math.cos(2*t) ); }
function y( t ) { return ( a * Math.cos(t) * Math.sin(2*t) ); }
/*
In scene, (0,0) is the top left corner and y-coordinates go downwards
⇒ we need to adapt mathematical relative coordinates x(i) , y(i)
to absolute coordinates of the scene.
*/
onFrame (1,afterPlacedObjectEvents)
{
T = 2 * Math.PI; // period
dt = T / n; // increment 2PI/n
for (i=1; i < n; i++)
{
duplicateSprite(dot, "dot"+i, i); // new point
("dot"+i)._X = (W / 2) + x(i*dt); // absolute x-coord
("dot"+i)._Y = (H / 2) - y(i*dt); // absolute y-coord
}
}
'Et voilà', that's it.
Of course, this is not a movie but it allows some folks to easily show a mathematical function for a few pennies.
For my own work, I use Matlab ( see my scripts in Matlab section)
But this software is quite expensive for anyone.
Otherwise, these mathematical functions could give ideas to set movement effects given in libraries as well. ( sometimes pretty tough to understand )