GRAVITY.DOC

					GRAVITY SIMULATION IN SCI

Standard gravitational acceleration is 9.8 m/s/s.  To convert this to the
SCI simulation units of pixels/cycle/cycle, we use the following formula


	g = 9.8 * h/(f ** 2)

where

	h	is the height, in pixels, of a one meter tall object

	f	is the frequency, in cycles/second, of the animation cycles


Normal animation speed is 10 animation cycles/second, so in general this
reduces to

	g = .098 * h


A standard sized actor is about 33 pixels tall.  Assuming that the actor is
a meter tall, we get a default g of

	g = 3.23
	  = 3




							JumpTo

The JumpTo motion class is designed to allow an actor to jump to a certain
point on the screen.  This is done by assuming that, in the Jump class, the
horizontal and vertical speeds are related by the scale factor n.  We then
solve for the magnitude which gets us where we want to go.

The x coordinate of the endpoint is given by

	x1 = x0 + v * t

so that

	t = (x1 - x0)/v

The y coordinate is given by

	y1	= y0 + n * v * t + g * t**2/2

		= y0 + n * v * (x1 - x0)/v + g * (x1 - x0)**2/(2 * v**2)


writing

	dx = x1 - x0
	dy = y1 - y0

we have

	dy - n * dx = g * dx**2/(2 * v**2)

so that

	v = sqrt(g * dx**2/(2 * (dy - dx)))