Zoing! Another fine Canadian product.

Alonzo Gariepy
620 Christie St.
Toronto, Ontario
CANADA  M6G 3E5


Here's something I have been thinking about for several weeks.
This program simulates a system of rebounding balls.  Zoing!
I hope you enjoy playing with it as much as I did designing
and tuning it.

Please include this file in any distribution of the source code!

Usage: zoing  [ BALLS [ GRAVITY [ LEVITY ] ] ]

where
    1 <=  BALLS  <= 7,  default 7
    0 <= GRAVITY <= 9,  default 0
    0 <= LEVITY  <= 5,  default 0

You can run it from the workbench, but you can only get the
defaults.  Some explanation is necessary.

General Description
===================

    The bouncing balls are all perfectly elastic.
    This means they don't lose energy when they collide.

    When the Zoing! window is active the cursor becomes a ball.
    This ball is infinitely massive and fairly inelastic.  This
    means that other balls cannot impart velocity to the cursor
    and that collisions with it entail a loss of energy.  The
    window comes up inactive so that the balls do not start to
    lose energy through cursor collisions.

    The cursor is inelastic as a convenient means of removing
    excess energy from the system.  The balls can be slowed by
    performing a "catching" operation with the cursor, but this
    is difficult especially at high speeds.  You may slide the
    cursor into a ball to create a collison and speed it up.

    You may vary the number of balls by giving a number between
    1 and 7 as the first parameter on the command line. Gravity
    may be added to the system in the same way.  I suggest you
    try all the values.  Gravity of one or two is very pleasing
    to watch.  You will find that the energy of the system will
    slowly decline under the influence of gravity.  Stir it up.

    Levity is just like gravity except that the system slowly
    gains energy over time. A levity of one is probably all you
    will want.  The gravitational effect will be the sum of the
    gravity and levity.  With gravitation, there is a higher
    density of balls toward the bottom of the screen.  If you
    add some levity and park the cursor in the middle of the
    screen, the energizing of the levity and de-energizing of
    the cursor will reach an equilibrium based on how high the
    cursor is from the bottom of the screen.  This produces a
    very nice effect as balls occasionally roll over the top of
    the cursor or soar way above.  If you are clever you can
    make a ledge with the cursor and the side of the screen to
    trap balls.  You can raise them slowly using the amiga and
    cursor keys.

Suggested Values
================

    zoing
    zoing 3
    zoing 7 1 1
    zoing 7 2
    zoing 4 3
    zoing 1

About The Program
=================

    The best part is that Zoing! uses no floating point variables
    or calculations.  The positions and velocities are represented
    internally using an integer coordinate system.  The collision
    calculations require no trig functions or square roots and are
    only limited by the accuracy of the coordinate representation.

    Accurately including gravity would require the extraction of
    square roots.  I chose a simple fudge.  The gravitational field
    is made up of the gravity and levity parameters.  Gravity is
    applied to the velocity before calculating wall collisions and
    levity is applied afterwards.  The name levity comes from the
    observation that this post-application tends to slowly increase
    the energy in the system.  I could explain why, but I won't.

    I was going to add sound effects but I couldn't get a recording
    of Schostakowitsch's 5th symphony, that was as good as the live
    performance by the Toronto Symphony last year.  I will remember
    the first movement all my life (and I'm not a flake).  It would
    be nice to add some sound effects.  Collisions with the walls
    should be silent and those with the cursor lower pitched than
    the ones between balls.  The velocity should also modify the
    pitch and volume.  It is truly not worth the work.

    The accuracy of the simulation should be proportional to the
    number of simulation steps per frame.  You could probably make
    this greater than 2, but since the number of fraction bits has
    to stay at 6 (with more than that you get overflow on some of
    the calculations), you would increase your minimum gravity and
    lose some nice effects.