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 excluded
cyclesInArc $ 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 Arcs, 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 Arcs, 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.