After I got married, I was sitting home one afternoon alone. I was trying to figure out how to cook my husband the perfect dinner by surprise. With my current cooking abilities, this was really not possible. I decided to get my shoes on and get ready to head to town to the local grocery store to buy a frozen lasagna dinner for the two of us. I thought to myself to not forget to turn off the television, as it was still on in the other room. With my keys and purse at hand, I went to the living room to turn off the TV, and noticed a popular cooking show was on. They were in the process of showing step by step directions on how to make the perfect lasagna. This was very odd considering I was off to the store to pick up the same exact dinner, but frozen. I decided to grab a pen and paper and take some notes; how hard could this possibly be?

45 minutes went by and the cook on TV has the most amazing lasagna already prepared. I decided to run to the grocery store and grab the listed ingredients. I carefully followed every step as the professional on television had instructed. I decided to go watch more of the cooking shows while my first homemade dinner bakes. Forty-five minutes later, I pulled the most beautiful lasagna I have ever seen, well ever cooked, out of my oven. To my surprise, it tasted just as good as it looked. My husband was impressed, needless to say.

After that, I continued to watch daily food shows on the food network and some of my satellite tv indian channels. I now am a chef at a popular restaurant in town. I owe all credit to my television set, and good timing. Watching cooking shows on TV can be very exciting!

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When two objects rebound after colliding with each other, it is due to a spring force, even though it may not look like it. When two billiard balls collide, the compression of the ball is limited to a miniscule fraction of its width but it still happens.

Using a spring force requires higher model rates to realistically collide faster, harder objects. The fps display in the demo shows the actual frame rate. The movie itself is set to 999 fps. On a 1.3 GHz P3 it averages about 980 actual fps.

Collision using spring force – source movie

repeat with s = 1 to 4
if s <> me.spritenum then
spOther = sprite(s)

–distance components
distX = (spOther.x) – x
distY = (spOther.y) – y

–pythagorean theorem to get distance
dist = sqrt(power(distX,2) + power(distY,2))

–spring force
xSpring = 0
ySpring = 0
minDist = (sp.width + spOther.width) / 2.0 - 10
if dist < minDist then
springF = (minDist – dist) * .02
xSpring = springF * -(distX/dist)
ySpring = springF * -(distY/dist)
end if

xTotalForce = xTotalForce + xSpring
yTotalForce = yTotalForce + ySpring
end if
end repeat

The algorithm is almost identical to general gravity, so only the repeat loop is shown. Instead of calculating gravity, it calculates spring force. Spring force only acts when the objects are within a certain distance of each other, expressed as dist < minDist.

The magnitude of the spring force is given by minDist – dist. This is the restPosition – position equation from the Spring Forces section. Scaling by .02 puts the force into proportion with other values in the animation. It can be considered the stiffness of the object, the higher it is the stiffer the object.

This demo gives each object a mass, and uses the mass in the
accel = force / mass equation. The behavior of the large object shows how mass affects acceleration. When two objects collide, each experiences the same amount of force, acting in opposite directions. This force translates into a smaller acceleration for more massive objects.

Mass can be set however you’d like. In this demo it is set to the cube of the sprite width, which would roughly correspond to its mass if it was a
3-dimensional sphere.

The type of collision modelled in this demo is for round objects with no friction between them. Friction or non-round shape would cause part of the energy in the collision to go into rotational velocity, making the objects spin.

For comments on the rest of the script, see General Gravity.

The recording of the animation may be done as part of the program, or done beforehand. If it is done beforehand, the data needs to be saved, most conveniently in a field or text cast member, and then retrieved at run-time. For saving lists in text form, see the Lingo functions string() and value().

Playback of recorded motion is essentially a parametric animation, with the parameter driving an index into the list of recorded values.

This demo allows the user to record a piece of incremental animation, and then play it back with a slider driver. The animation is a combination of collision and general gravity.

Recorded animation - source movie

Methods from script “modelManager”

In this demo the recording is done by a script adapted from the modelRate script in Independent Model Rate, and renamed modelManager. The three methods above show how it does recording and playback.

Notice that the variables recorded are the animation model variables, not the sprite properties. This is generally the best way to go, for several reasons:

• less information to record. For example, in 3D the x, y, and z coordinates are used to set more than three sprite properties. Of course, this means that during playback a rendering algorithm will still be needed.
• more importantly, at playback you still have control over rendering.

The variables are recorded once each movie frame in this demo, rather than once each model frame. In this demo the model rate is about 20 times the movie rate. If you wanted to do “super slo-mo” playback, you could record the variables based on model frames, and at slow playback you’ll get a smoother motion.

To record the movement of the mouse, use a script that keeps its x and y animation model variables at the mouse location, and pass the script instance to modelManager’s addInstance() method.

Miscellaneous Points
recordList
This is the property list used by modelManager to record the x and y variables of each recorded object. The unusual thing about it is that the keys in the list are object references. recordList associates each object reference with the linear list of recorded position settings for that object.

Usually in sample code the keys are symbols, but the property list can be used to associate values of any data type with each other. This is generally called a hash table, and most likely property lists are implemented in Director using a hash table of some sort.

If recordList is saved in a text cast member, retrieving the list using value() will not recreate object references. To save recordList, use something like sprite numbers for the keys instead of references.

Animation Anomalies
If you watch the animation long enough you’ll notice some interesting anomalies in the behavior of the objects. When I have time I’ll try to pinpoint what is happening. There may or may not be a perfect fix.

Things To Try
Make the playback “instant replay” style by using a time driver instead of a slider to control the playback. You might use a slider to control the speed of the replay.

When two objects rebound after colliding with each other, it is due to a spring force, even though it may not look like it. When two billiard balls collide, the compression of the ball is limited to a miniscule fraction of its width but it still happens.

Using a spring force requires higher model rates to realistically collide faster, harder objects. The fps display in the demo shows the actual frame rate. The movie itself is set to 999 fps. On a 1.3 GHz P3 it averages about 980 actual fps.

Collision using spring force – source movie

repeat with s = 1 to 4
if s <> me.spritenum then
spOther = sprite(s)

–distance components
distX = (spOther.x) – x
distY = (spOther.y) – y

–pythagorean theorem to get distance
dist = sqrt(power(distX,2) + power(distY,2))

–spring force
xSpring = 0
ySpring = 0
minDist = (sp.width + spOther.width) / 2.0 - 10
if dist < minDist then
springF = (minDist – dist) * .02
xSpring = springF * -(distX/dist)
ySpring = springF * -(distY/dist)
end if

xTotalForce = xTotalForce + xSpring
yTotalForce = yTotalForce + ySpring
end if
end repeat

The algorithm is almost identical to general gravity, so only the repeat loop is shown. Instead of calculating gravity, it calculates spring force. Spring force only acts when the objects are within a certain distance of each other, expressed as dist < minDist.

The magnitude of the spring force is given by minDist – dist. This is the restPosition – position equation from the Spring Forces section. Scaling by .02 puts the force into proportion with other values in the animation. It can be considered the stiffness of the object, the higher it is the stiffer the object.

This demo gives each object a mass, and uses the mass in the
accel = force / mass equation. The behavior of the large object shows how mass affects acceleration. When two objects collide, each experiences the same amount of force, acting in opposite directions. This force translates into a smaller acceleration for more massive objects.

Mass can be set however you’d like. In this demo it is set to the cube of the sprite width, which would roughly correspond to its mass if it was a
3-dimensional sphere.

The type of collision modelled in this demo is for round objects with no friction between them. Friction or non-round shape would cause part of the energy in the collision to go into rotational velocity, making the objects spin.

For comments on the rest of the script, see General Gravity.

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