Download source file: fallingleaves.fla
Parametric equations are particularly amenable to applications in Flash that call for dynamic animation along complex paths. The file above uses a simple equation to model the leaves' motion.
One can use this approach to describe 2D and even 3D motion paths. For example, consider the vector-valued function that describes a the helix (spiraling) curve: g(t)= (R1cos(t), R2sin(t), h/2pi*t)
R1 and R2 are the horizontal and vertical radiuses. they describe the shape
of the helix if you looked at it from top-down--so if R1=R2, the top down view would be a circle.
'h' is the change in z during one revolution--it's called the pitch of thehelix. if you think of the helix curve as a spring coil, h determines how "squeezed" the coil is.
t is the angle that acts as the parameter which "animates" the curve. We use it as a counter that runs from 1 to 360 and then repeats. when you calculate the values for x and y, you'll need to
turn t into its corresponding value in radians. the code for this is "Math.PI/180*t".
In Flash, we make a function with the following code and call it from an enterFrame clip event:
1. Increase variable t by some constant increment--say, 8. If it reaches 360, reset t to one.
2.
Calculate values for the three variables (x, y, and z) according to the
function above--set x = R1*cosine of t, y = R2* sine of t, and z = 2 times "pi" divided by t times some constant, h.
3. modify a movie clip's _x and _y properties through some code that takes into
account the x, y and z values. This might consist in some kind of scheme that modifies the
_x and _y one pixel to the left and one pixel down for a one unit increase
in z, and, conversely, right and up for one unit decrease in z.
© David Gillis, 2004