Changes to lifetime calculation in scrolling rulesets introduced in
#7367, which aimed to account for the distance between hit objects'
origin and its edge entering the scrolling area, fixed some issues with
hitobjects appearing abruptly, but also regressed some other scenarios.
Upon investigation, the regression was localised to the overlapping
scroll algorithm. The reason for this was two-fold:
* The previous code used TimeAt() to calculate the time of travel from
the hit object's edge to its origin. For other algorithms, that time
can be accurately reconstructed, because they don't have periods of
time where there are multiple hit objects scrolling at different
velocities.
That invariant does not hold for the overlapping algorithm, therefore
it is possible for different values to be technically correct for
TimeAt(). However, the only value that matters for the adjustment
is the one that's indicated by the control point that applies to the
hit object origin, which can be uniquely identified.
* Additionally, the offset returned (even if correct) was applied
externally to the hit object's start time and passed to
GetDisplayStartTime(). In the overlapping algorithm, the choice of
control point used in GetDisplayStartTime() is important, since
the value of the speed multiplier is read within.
Externally rewinding the hit object's start time meant that in some
cases the speed multiplier of the *previous* control point is applied,
which led to hit objects appearing too late if the scrolling rate
decreased.
Because of the above, modify GetDisplayStartTime() to take the offset
into account in all algorithms, and apply the adjustment correctly
inside of them. The constant and sequential algorithms needed no
adjustment from the previous logic, since:
* the constant algorithm disregarded control points, and
* the sequential algorithm would effectively rewind to time = 0,
calculate the absolute distance from time = 0 to the hit object start,
apply the origin offset *to the absolute distance*, and then convert
back to time, applying all control points in sequence. Due to this
it was impossible for control points to get mixed up while
calculating.
As for the overlapping algorithm, the high-level logic is as follows:
* The distance that the origin has to travel is the length of the scroll
plus the distance from the origin to the object edge.
* The above distance divided by the scroll length gives the relative
scroll lengths that the object has to travel.
* As one relative scroll length takes one time range, the relative
travel length multiplied by the time range gives the absolute travel
time of the object origin.
* Finally, the control point multiplier applicable at origin time is
applied to the whole travel time.
Correctness of the above is demonstrated by visual tests added before
and headless unit tests of the algorithms themselves. The sequential
scroll algorithm was not covered by unit tests, and remains uncovered
due to floating-point inaccuracies that should be addressed separately.
