Unified scoring system

[Discookie]

The mod, challenge-based as it is, really needs a unified scoreboard. To achieve that, we need a unified scoring system.

My idea is a per-note based one that scales with both note difficulty, and time-distance.
(Difficulty is measured in hand acceleration, units/s²)
2 single notes 1 second apart give 100pts per difficulty the time scaling curve maxes out around 0.25 seconds, giving 200pts per difficulty.

Doublenotes multiply each hand's score by 1.25, and purples count as double notes, but with a 0.75 multiplier on each hand.

Whether it should incorporate combo-based bonus score, or calculate hits with the wrong shield, is still up in the air.

Feedback and discussion appreciated.

[Discookie]

A promising general function is

(tex) [; Accel \cdot \sin^{2a}{(\frac{\pi}{2 + 2||\Delta t| - b|^c})} ;]

This has 3 parameters:

• a controlling the ratio of scores,
• b controlling the peak note distance.
• c controlling the peak score length,

Paste this into GeoGebra and play with it:

sin(π / (2 + 2abs(abs(x)-b)^c))^(2a)

And then multiply this function with like 10000 to give human readable scores.

[Discookie]

Some values for that function that look right:

a, 
a = 2, b = 0,5, c = 1.5

b,
a = 2, b = 0.25, c = 1.25

[Discookie]

A custom scoring implementation would make artistic scorting un-retrievable. Without this, extra dance movements aren't rewarded as much. Another way of collecting such data, such as with GetHMDPositionX/Y/Z() and taking accel values between hit meteors, should be taken into consideration

[Discookie]

Initial implementation is added in dd91dea. It only takes the time between and the acceleration from the previous meteor into consideration.

I have also taken a lot faster algorithm that stays within 10% on less than 5 seconds of distance, and awards larger scores on large numbers.
2.5 for each note hit
0.75 * (accel / (1 + |time - scorePeak|^(2+scorePeak) )^(2*scoreCutoff)) for accel-based component.

I don't take combo into consideration, but combo counting is built into the mod.

Double notes were counted with an 1.5 multiplier, and a quadratic mean of the accels.
Purple notes were counted with an 1.25 multiplier, and an 1.33 multiplier on top of other notes at the same time.

Additionally, all scores are multiplied by 1000, to have an osu-like score, in terms of scale.

The How-To-Play's difficulty index needs urgent updating.

Resource impact was not measured yet, needs testers.