floating point precision

[PJani]

Hy.
If i have scale 1 unit = 1 meter and float type in newton, how "big"(1000m?) numbers would start to damage newton balance without any scaling involved?

[Julio Jerez]

I believe 32 float precision wok fine with up to around 8000 units witch requires 14 bits of the 24 bit mantissa, leaving 10 for fraction.

[JernejL]

If i give you a example, GTA san andreas engine uses -3000..3000 X and -3000 3000 Y floating point range giving it 9000000 square "meters" of surface for the game world. That game's world HUGE, but i think you could go up to -4000..4000 or -5000..5000 to each direction without any noticeable precision issues, just remember to use the negative range aswell.

[PJani]

@Delfi: GTA SA uses smaller scale. if i remember right 1unit in GTASA is not 1m

With 14bit for whole number(including sign bit) [-8196..8196]x[-8196..8196] => 16384x16384m that results in 270 square km!

[JernejL]

@Delfi: GTA SA uses smaller scale. if i remember right 1unit in GTASA is not 1m

You are mistaken. 1 unit in gtasa is very close to 1 meter.
The game was made in scotland and they use meteric system, and i modded gta3/vs/sa gta games to death, even made a map viewer for it.. The scale is definetly very close to 1 meter and the used world area is 3000 units from 0,0,0 points in each direction.

[PJani]

Hmm u are right, probably i mixed something up.
I was modding GTA VC like crazy back in days when GTAVC was popular , with GTA SA i wasn't playing much.

i am thinking how to solve unstable buoyancy because of floating point precision problem.
Later today i was looking newton source and i was thinking which part actually makes buoyancy very unstable?

[JernejL]

You probably used some of my editors then, i wrote a dozen of tools for the gta3-sa era of GTAs

[PJani]

Its very possible i did use some of your tools back then because i tried every single tool i found!

[Julio Jerez]

what makes buoyancy very unstable in that the code only calculates the force on the fluid, using the volume ratios immersed under the fluid plane,
but it does not consider the viscosity of the fluid to calculate friction of drag. you can read about the drag here.
http://en.wikipedia.org/wiki/Drag_%28physics%29

Instead the code apply a cheesy fixed drag that makes it either very unrealistic or very unstable.
A step up for newer newton version could be to actually calculate the current surface area of the volume under the liquid and calculate a better approximation of the drag.
one way may be to divide the volume into beams beams of equal area and for each beam determine the speed of the front face hit the liquid, them integrate over the the differential torque and force contribution of each beam.
I like this idea because in extend to more than just a flat liquid plane and generalize to any kind of volume.

It can be an interesting feature, but I have not put too much thought on it

[PJani]

I would never guess the damping is problem!
Hmm thats an excellent idea!

[JernejL]

Maybe using convex cast against the water plane, & simulating drag based on the projected shape would work.

[Julio Jerez]

I would never guess the damping is problem!

Oh yes bouyancy forces using the alchymedes principle fall into the cathegory of "Conservatives forces".
Conservatives forces is a force that when they act on a particle, the net work excuted by the motion of the particle is zero. that is there is not lost of energy as the particle moves.
example of Consertive forces are: Spring Mass, Gravity and kenetic / pontencial energy (a rollercoster), Gravitational orbits, the electric and Magnetic field, the Bouyancy, many some others I do not remember now.

Since the action of those forces alone do not lose energy, when they are simulated numerically, the simulation should last for ever (like a spring with not damping force)
however because numercial methods are only aproximation of diferencial equations, they can not reproduce the exact path the particle should follows.
I am not refering to float acuracy, I am talking about the fact that there is not known numerical method that can integrates a secund order differencial equation exactly, not even using exact arithmetic,
and only very few first order differencial equations can be integrated exactly using numerical methods.
they can only reproduce an aproximation of the path, therefore the discrepancy between the ideal path, and the simulated path is translated to a net gain of lost of energy in the simulation.

what makes the simulation stable is if there is a processs that drain an amount of energy that is equal and larger than the energy gained by the integration process.
Friction, Drag and Viscosity are non consevative forces that always lose energy, they can be used to mak a system stable.