Time
Types
type Time = Rational
Time is Rational
.
data ArcF a
An arc of time, with a start time (or onset) and a stop time (or offset)
Utility functions — Time
sam
:: Time -> Time
The sam
(start of cycle) for the given time value.
Cycles have duration 1, so every integer Time value divides two cycles.
toTime
:: Real a => a -> Rational
Turns a number into a (rational) time value. An alias for toRational
.
fromTime
:: Fractional a => Time -> a
Turns a (rational) time value into another number. An alias for fromRational
.
nextSam
:: Time -> Time
The end point of the current cycle (and starting point of the next cycle)
cyclePos
:: Time -> Time
The position of a time value relative to the start of its cycle.
Utility functions — Arc
hull
:: Arc -> Arc -> Arc
convex hull union
subArc
:: Arc -> Arc -> Maybe Arc
subArc i j
is the timespan that is the intersection of i
and j
.
intersection
The definition is a bit fiddly as results might be zero-width, but
not at the end of an non-zero-width arc - e.g. (0,1) and (1,2) do
not intersect, but (1,1) (1,1) does.
subMaybeArc
:: Maybe Arc -> Maybe Arc -> Maybe (Maybe Arc)
sect
:: Arc -> Arc -> Arc
Simple intersection of two arcs
timeToCycleArc
:: Time -> Arc
The Arc returned is the cycle that the Time falls within.
Edge case: If the Time is an integer, the Arc claiming it is the one starting at that Time, not the previous one ending at that Time.
cycleArc
:: Arc -> Arc
Shifts an Arc to one of equal duration that starts within cycle zero. (Note that the output Arc probably does not start at Time 0 — that only happens when the input Arc starts at an integral Time.)
cyclesInArc
:: Integral a => Arc -> [a]
Returns the numbers of the cycles that the input Arc
overlaps
(excluding the input Arc
’s endpoint, unless it has duration 0 —
see “Edge cases” below).
(The “cycle number” of an Arc
is equal to its start value.
Thus, for instance, cyclesInArc (Arc 0 1.5) == [0,1]
.)
Edge cases:
cyclesInArc $ Arc 0 1.0001 == [0,1]cyclesInArc $ Arc 0 1 == [0] -- the endpoint is excludedcyclesInArc $ Arc 1 1 == [1] -- unless the Arc has duration 0
PITFALL: Don’t be fooled by the name. The output cycles
are not necessarily completely contained in the input Arc
,
but they definitely overlap it,
and they include every cycle that overlaps it.
cycleArcsInArc
:: Arc -> [Arc]
This provides exactly the same information as cyclesInArc
,
except that this represents its output as Arc
s,
whereas cyclesInArc
represents the same information as integral indices.
(The Arc
from 0 to 1 corresponds to the index 0,
the one from 1 to 2 has index 1, etc.)
arcCycles
:: Arc -> [Arc]
Splits the given Arc
into a list of Arc
s, at cycle boundaries.
arcCyclesZW
:: Arc -> [Arc]
Like arcCycles
, but returns zero-width arcs
mapCycle
:: (Time -> Time) -> Arc -> Arc
Similar to fmap
but time is relative to the cycle (i.e. the
sam
of the start of the arc)
isIn
:: Arc -> Time -> Bool
isIn a t
is True
if t
is inside
the arc represented by a
.