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Lazy evaluation of a continuous field of signals #600

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Lazy evaluation of a continuous field of signals #600

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Commits on Mar 24, 2023

  1. Add a "debug" visualization of signal strengths

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    Austreelis committed Mar 24, 2023
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  2. Use the same approach as tile selection to display signals 

    I'm not really pleased with the fact I had to disable the
`display_tile_overlay` system when using the signal overlay but this
can be cleanup later.

Color scheme has been updated to look better with the new terrain and
shadows, and the overlay material has been made transparent a bit.
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    Austreelis committed Mar 24, 2023
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  3. Implement lazy evaluation of a continuous field for signal diffusion 

    This only takes into account sources for now. This means that it only
reaches part of the goal set in Leafwing-Studios#511:

1. It only tracks signal emitters.
2. It does determine an equation for each emitter. The equation simply
  is the solution of the diffusion equation for that emitter:
  `1/(1+D*t) * 1/sqrt(4*pi*k*t) * exp(d^2 / (4*k*t))`
  where:
  - `D` is a decay rate constant, and `1/(1+D*t)` is a decay term.
  - `k` is a diffusivity constant.
  - `d` is the distance between the emitter and a tile.
  - `t` is the time elapsed since the signal was emitted.
3. Contributions of each emitter are then integrated to compute the
  actual field value. This works because of the linearity of this subset
  of the problem, but may not hold when tackling e.g. barriers or signal
  modifiers (I haven't yet investigated it).
4. It lazyly looks up the field value when needed, but I suspect this
  is pretty costly when displaying the signal overlay. I don't know if
  and what we'd want to do about it yet.
    @Austreelis
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  4. Move signal.rs -> signals/mod.rs

    @Austreelis
    Austreelis committed Mar 24, 2023
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  5. Fix the formula of the fundamental solution of the diffusion equation 

    Our application is in 2D. The 1D fundamental solution was used
previously.
    @Austreelis
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  6. Document maths of the diffusion equation solver

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    Austreelis committed Mar 24, 2023
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