Tribes 1 Physics, Part Four: Explosions

Explosions (or more accurately, knockback), the final piece to the physics puzzle! If you implement all of the previous articles, make a disc launcher, plug in the apparently simple knockback force and radius from baseProjData.cs, and finally attempt to disc jump, you will be greeted with… a nice and wimpy boost. Playing around with the knockback force will only break explosions in new ways. Argh, you were so close! How could Tribes possibly screw this one up?

Basic Knockback

The basic idea for knockbacks from explosions is you want to take the position of the explosion and the object, scale the explosion force, and apply an impulse to the object in the appropriate direction. Generally this is implemented something like so:

Player.onExplosion( Vector3 explosion, float radius, float knockback, float damage ) {
    Vector3 distance = ( hitbox.center - explosion ), direction = distance.Normalize
    if ( distance.Length > radius )
        return

    float power = 1 - ( distance.Length / radius )
    ApplyDamage( power * damage )
    ApplyImpulse( knockback * ( power * direction ) / armor.Mass )   
}

power is where the magic happens and while it should be an exponential falloff, it is common to do linear because there is not much of a noticeable difference. It is also where Tribes deviates from the norm in a fairly big way.

Tribes Knockback

What is obvious when you implement the basic knockback is that it packs a much smaller punch than Tribes. What you might not notice is that the Tribes knockback up close, e.g. at your feet from a standstill, is actually weaker than from a bit of a distance, e.g. at your feet while you’re in the air after jumping. Whether this was intended as an aid to disc jumping or an accident of a botched formula is impossible to say, but it doubtless would have been harder to gain speed from disc jumps without this odd feature.

If you work out exactly what the Tribes knockback function does (not fun) and re-factor the formula (not fun and also confusing), you come out with a somewhat familiar power calculation. Instead of the basic ( 1 – ( d / r ) ), Tribes uses ( ( d / Max( d – minHitboxDimension, 1 ) ) – ( d / r ) ), i.e. instead of using a constant ( 100% – linear falloff ) for the power, Tribes does some weird calculations which I can only guess are trying to account for the hitbox in some way. This image illustrates the power falloff for Tribes, the power falloff for the basic formula, and the power falloff for the basic formula if it were boosted so players were able to disc jump properly:

This shows why the linear falloff formula cannot be fixed by boosting the knockback force without getting wildly inaccurate up close. Here is the proper formula:

Player.onExplosion( Vector3 explosion, float radius, float knockback, float damage ) {
    Vector3 distance = ( hitbox.Center - explosion ), direction = distance.Normalize
    float minbox = Min( Min( hitbox.Width.x, hitbox.Width.y ), hitbox.Width.z )
    float d = Max( distance.Length - minbox, MetersToUnits( 1 ) )
    if ( d > radius )
        return

    float power = ( distance.Length / d ) - ( distance.Length / radius )
    ApplyDamage( damage * ( 1 - d / radius ) )
    ApplyImpulse( knockback * ( power * direction ) / armor.Mass )   
}

For the Light Armor with a BOX_WIDTH of 0.5, BOX_DEPTH of 0.5, and BOX_HEIGHT of 2.3, minbox equates to Min( Min( BOX_WIDTH * 2, BOX_DEPTH * 2 ), BOX_HEIGHT ), or 1.0. The player origin is at the center of the player’s feet and the hitbox dimensions extend out from that, so the width and depth extend out in either direction and need to be doubled while the height goes from the feet to the head. Note that if you increase the smallest hitbox dimension, e.g. increase BOX_WIDTH and BOX_DEPTH to have a value of 2.3 when doubled, the linear ramp leading up to the downward falloff of the power will grow, presumably to account for greater surface contact area with the explosion.

You’re Done!

You should have all you need to get authentic Tribes 1 Physics going in your engine of choice! After this you should only need to create some dummy weapons, scale their velocities to whatever units you are using, add two flags, and you can get an honest game of LT going.

What? You don’t believe me that it works and you don’t want to waste your time implementing the physics only to find out that I lied? Hmmm, here’s something that should convince you. This is the full T1 physics running on Raindance in ET:QW. I did this for the ET:QW Tribes mod that was in the works, but unfortunately things kind of fizzled out. The map is authentic Raindance (every crevasse and triangle is there) with an 8192×8192 command map texture overlaid on top with Arcanox’s bases and bridge. This is currently the closest thing to Tribes you will ever see in another engine.

You can also download the hi-res version (15mb), although the burps are more apparent since my computer wasn’t quite up to spec to run QW. How I got the terrain in and textured will have to wait for another day.

Tribes 1 Physics Series

• Part One: Overview
• Part Two: Movement
• Part Three: Collision
• Part Four: Explosions