abstreet/docs/design/physics.md

Physics-related design notes

Floating point and units

Currently using si::Second for time, which means comparing sim state by deriving Eq is a headache. Since the timestep size is fixed anyway, this should just become ticks. Was tempted to use usize, but arch dependence is weird, and with a 0.1s timestep, 2^32 - 1 ticks is about 13.5 years, which is quite a long timescale for a traffic simulation. :) So, let's switch to u32.

Now I'm hitting all the fun FP imprecision issues. Could probably hack in epsilon and negative checks everywhere in kinematics, but why? Should research it more, but I think the better approach is to use fixed-point arithmetic for everything (aka u8 or whatever).

Problems with floats:

• they dont natively order
• they arent PartialEq
• serialization sometimes breaks
• epsilon comparison issues

Options: - just to solve epsilon comparison issues - https://crates.io/crates/float-cmp - https://crates.io/crates/approx - just to get Ord and Eq - https://crates.io/crates/decorum - https://crates.io/crates/ordered-float - use rational / fraction types - https://crates.io/crates/fraction - https://crates.io/crates/rug - this seems a bit overpowered - use my own custom wrapper type around u8 or whatever size makes sense for each thing - representing 0.1s or 0.1m or whatever - use a fixed point arithmetic crate - https://crates.io/crates/fpa - https://crates.io/crates/fixed - https://crates.io/crates/fix - would want to wrap the types anyway; only some operations make sense

• can we compare results with the prev float approach? make them store the other thing, compare results? or compare the results of a sim?

• is it possible to do this change gradually? unlikely...

  • stick all the types in geom, for now

• moment in time (tick)

  • resolution: 0.1s with u32, so about 13.5 years

• duration

  • resolution: 0.1s with u32, so about 13.5 years
  • time - time = duration

• distance (always an interval -- dist_along is relative to the start)

  • non-negative by construction!
  • say resolution is 0.3m (about 1ft), use u32, huge huge distances
  • geometry is polylines, sequences of (f64, f64) representing meters from some origin. we could keep drawing the same, but do stuff like dist_along as this new type? or change Pt2D to have more reasonable resolution?
  • still represent angles as f64 radians? for drawing, turn calculation, etc

• speed

  • meters per second, constructed from distance / duration
  • should resolution be 0.3m / 0.1s? 1 unit of distance per one timestep? or, maybe less than that?
  • can be negative

• acceleration

  • can be negative
  • what should the resolution be?

Coordinate system

Switching to something that's more easily bijective, but https://crates.io/crates/flat_projection could be a good candidate too.