active-0.1.0.19: Abstractions for animation

Data.Active

Description

Inspired by the work of Kevin Matlage and Andy Gill (Every Animation Should Have a Beginning, a Middle, and an End, Trends in Functional Programming, 2010. http://ittc.ku.edu/csdl/fpg/node/46), this module defines a simple abstraction for working with time-varying values. A value of type `Active a` is either a constant value of type `a`, or a time-varying value of type `a` (i.e. a function from time to `a`) with specific start and end times. Since active values have start and end times, they can be aligned, sequenced, stretched, or reversed.

In a sense, this is sort of like a stripped-down version of functional reactive programming (FRP), without the reactivity.

The original motivating use for this library is to support making animations with the diagrams framework (http://projects.haskell.org/diagrams), but the hope is that it may find more general utility.

There are two basic ways to create an `Active` value. The first is to use `mkActive` to create one directly, by specifying a start and end time and a function of time. More indirectly, one can use the `Applicative` instance together with the unit interval `ui`, which takes on values from the unit interval from time 0 to time 1, or `interval`, which creates an active over an arbitrary interval.

For example, to create a value of type `Active Double` which represents one period of a sine wave starting at time 0 and ending at time 1, we could write

`mkActive 0 1 (\t -> sin (fromTime t * tau))`

or

`(sin . (*tau)) <\$> ui`

`pure` can also be used to create `Active` values which are constant and have no start or end time. For example,

`mod <\$> (floor <\$> interval 0 100) <*> pure 7`

cycles repeatedly through the numbers 0-6.

Note that the "idiom bracket" notation supported by the SHE preprocessor (http://personal.cis.strath.ac.uk/~conor/pub/she/, http://hackage.haskell.org/package/she) can make for somewhat more readable `Applicative` code. For example, the above example can be rewritten using SHE as

```{-# OPTIONS_GHC -F -pgmF she #-}

... (| mod (| floor (interval 0 100) |) ~7 |)```

There are many functions for transforming and composing active values; see the documentation below for more details.

Synopsis

# Representing time

## Time and duration

data Time Source

An abstract type for representing points in time. Note that literal numeric values may be used as `Time`s, thanks to the the `Num` and `Fractional` instances. `toTime` and `fromTime` are also provided for convenience in converting between `Time` and other numeric types.

Instances

 Enum Time Eq Time Fractional Time Num Time Ord Time Read Time Real Time RealFrac Time Show Time AffineSpace Time VectorSpace Time InnerSpace Time AdditiveGroup Time Newtype Time Rational type Diff Time = Duration type Scalar Time = Rational

toTime :: Real a => a -> Time Source

Convert any value of a `Real` type (including `Int`, `Integer`, `Rational`, `Float`, and `Double`) to a `Time`.

fromTime :: Fractional a => Time -> a Source

Convert a `Time` to a value of any `Fractional` type (such as `Rational`, `Float`, or `Double`).

data Duration Source

An abstract type representing elapsed time between two points in time. Note that durations can be negative. Literal numeric values may be used as `Duration`s thanks to the `Num` and `Fractional` instances. `toDuration` and `fromDuration` are also provided for convenience in converting between `Duration`s and other numeric types.

toDuration :: Real a => a -> Duration Source

Convert any value of a `Real` type (including `Int`, `Integer`, `Rational`, `Float`, and `Double`) to a `Duration`.

fromDuration :: Fractional a => Duration -> a Source

Convert a `Duration` to any other `Fractional` type (such as `Rational`, `Float`, or `Double`).

## Eras

data Era Source

An `Era` is a concrete span of time, that is, a pair of times representing the start and end of the era. `Era`s form a semigroup: the combination of two `Era`s is the smallest `Era` which contains both. They do not form a `Monoid`, since there is no `Era` which acts as the identity with respect to this combining operation.

`Era` is abstract. To construct `Era` values, use `mkEra`; to deconstruct, use `start` and `end`.

Instances

 Show Era Semigroup Era

mkEra :: Time -> Time -> Era Source

Create an `Era` by specifying start and end `Time`s.

Get the start `Time` of an `Era`.

end :: Era -> Time Source

Get the end `Time` of an `Era`.

Compute the `Duration` of an `Era`.

# Dynamic values

data Dynamic a Source

A `Dynamic a` can be thought of as an `a` value that changes over the course of a particular `Era`. It's envisioned that `Dynamic` will be mostly an internal implementation detail and that `Active` will be most commonly used. But you never know what uses people might find for things.

Constructors

 Dynamic Fieldsera :: Era runDynamic :: Time -> a

Instances

 Functor Dynamic Apply Dynamic `Dynamic` is an instance of `Apply` (i.e. `Applicative` without `pure`): a time-varying function is applied to a time-varying value pointwise; the era of the result is the combination of the function and value eras. Note, however, that `Dynamic` is not an instance of `Applicative` since there is no way to implement `pure`: the era would have to be empty, but there is no such thing as an empty era (that is, `Era` is not an instance of `Monoid`). Semigroup a => Semigroup (Dynamic a) `Dynamic a` is a `Semigroup` whenever `a` is: the eras are combined according to their semigroup structure, and the values of type `a` are combined pointwise. Note that `Dynamic a` cannot be an instance of `Monoid` since `Era` is not. Newtype (Active a) (MaybeApply Dynamic a)

mkDynamic :: Time -> Time -> (Time -> a) -> Dynamic a Source

Create a `Dynamic` from a start time, an end time, and a time-varying value.

onDynamic :: (Time -> Time -> (Time -> a) -> b) -> Dynamic a -> b Source

Fold for `Dynamic`.

Shift a `Dynamic` value by a certain duration.

# Active values

For working with time-varying values, it is convenient to have an `Applicative` instance: `<*>` lets us apply time-varying functions to time-varying values; `pure` allows treating constants as time-varying values which do not vary. However, as explained in its documentation, `Dynamic` cannot be made an instance of `Applicative` since there is no way to implement `pure`. The problem is that all `Dynamic` values must have a finite start and end time. The solution is to adjoin a special constructor for pure/constant values with no start or end time, giving us `Active`.

data Active a Source

There are two types of `Active` values:

• An `Active` can simply be a `Dynamic`, that is, a time-varying value with start and end times.
• An `Active` value can also be a constant: a single value, constant across time, with no start and end times.

The addition of constant values enable `Monoid` and `Applicative` instances for `Active`.

Instances

 Functor Active Applicative Active Apply Active (Monoid a, Semigroup a) => Monoid (Active a) Semigroup a => Semigroup (Active a) Active values over a type with a `Semigroup` instance are also an instance of `Semigroup`. Two active values are combined pointwise; the resulting value is constant iff both inputs are. Newtype (Active a) (MaybeApply Dynamic a)

mkActive :: Time -> Time -> (Time -> a) -> Active a Source

Create a dynamic `Active` from a start time, an end time, and a time-varying value.

Create an `Active` value from a `Dynamic`.

Test whether an `Active` value is constant.

Test whether an `Active` value is `Dynamic`.

onActive :: (a -> b) -> (Dynamic a -> b) -> Active a -> b Source

Fold for `Active`s. Process an 'Active a', given a function to apply if it is a pure (constant) value, and a function to apply if it is a `Dynamic`.

modActive :: (a -> b) -> (Dynamic a -> Dynamic b) -> Active a -> Active b Source

Modify an `Active` value using a case analysis to see whether it is constant or dynamic.

runActive :: Active a -> Time -> a Source

Interpret an `Active` value as a function from time.

Get the `Era` of an `Active` value (or `Nothing` if it is a constant/pure value).

setEra :: Era -> Active a -> Active a Source

Set the era of an `Active` value. Note that this will change a constant `Active` into a dynamic one which happens to have the same value at all times.

atTime :: Time -> Active a -> Active a Source

`atTime t a` is an active value with the same behavior as `a`, shifted so that it starts at time `t`. If `a` is constant it is returned unchanged.

activeStart :: Active a -> a Source

Get the value of an `Active a` at the beginning of its era.

activeEnd :: Active a -> a Source

Get the value of an `Active a` at the end of its era.

# Combinators

## Special active values

ui :: Fractional a => Active a Source

`ui` represents the unit interval, which takes on the value `t` at time `t`, and has as its era `[0,1]`. It is equivalent to `interval 0 1`, and can be visualized as follows:

On the x-axis is time, and the value that `ui` takes on is on the y-axis. The shaded portion represents the era. Note that the value of `ui` (as with any active) is still defined outside its era, and this can make a difference when it is combined with other active values with different eras. Applying a function with `fmap` affects all values, both inside and outside the era. To manipulate values outside the era specifically, see `clamp` and `trim`.

To alter the values that `ui` takes on without altering its era, use its `Functor` and `Applicative` instances. For example, `(*2) <\$> ui` varies from `0` to `2` over the era `[0,1]`. To alter the era, you can use `stretch` or `shift`.

interval :: Fractional a => Time -> Time -> Active a Source

`interval a b` is an active value starting at time `a`, ending at time `b`, and taking the value `t` at time `t`.

## Transforming active values

stretch :: Rational -> Active a -> Active a Source

`stretch s act` "stretches" the active `act` so that it takes `s` times as long (retaining the same start time).

stretchTo :: Duration -> Active a -> Active a Source

`stretchTo d` `stretch`es an `Active` so it has duration `d`. Has no effect if (1) `d` is non-positive, or (2) the `Active` value is constant, or (3) the `Active` value has zero duration.

during :: Active a -> Active a -> Active a Source

`a1 `during` a2` `stretch`es and `shift`s `a1` so that it has the same era as `a2`. Has no effect if either of `a1` or `a2` are constant.

shift :: Duration -> Active a -> Active a Source

`shift d act` shifts the start time of `act` by duration `d`. Has no effect on constant values.

backwards :: Active a -> Active a Source

Reverse an active value so the start of its era gets mapped to the end and vice versa. For example, `backwards ui` can be visualized as

snapshot :: Time -> Active a -> Active a Source

Take a "snapshot" of an active value at a particular time, resulting in a constant value.

## Working with values outside the era

clamp :: Active a -> Active a Source

"Clamp" an active value so that it is constant before and after its era. Before the era, `clamp a` takes on the value of `a` at the start of the era. Likewise, after the era, `clamp a` takes on the value of `a` at the end of the era. `clamp` has no effect on constant values.

For example, `clamp ui` can be visualized as

See also `clampBefore` and `clampAfter`, which clamp only before or after the era, respectively.

"Clamp" an active value so that it is constant before the start of its era. For example, `clampBefore ui` can be visualized as

See the documentation of `clamp` for more information.

clampAfter :: Active a -> Active a Source

"Clamp" an active value so that it is constant after the end of its era. For example, `clampBefore ui` can be visualized as

See the documentation of `clamp` for more information.

trim :: Monoid a => Active a -> Active a Source

"Trim" an active value so that it is empty outside its era. `trim` has no effect on constant values.

For example, `trim ui` can be visualized as

Actually, `trim ui` is not well-typed, since it is not guaranteed that `ui`'s values will be monoidal (and usually they won't be)! But the above image still provides a good intuitive idea of what `trim` is doing. To make this precise we could consider something like `trim (First . Just \$ ui)`.

See also `trimBefore` and `trimActive`, which trim only before or after the era, respectively.

trimBefore :: Monoid a => Active a -> Active a Source

"Trim" an active value so that it is empty before the start of its era. For example, `trimBefore ui` can be visualized as

See the documentation of `trim` for more details.

trimAfter :: Monoid a => Active a -> Active a Source

"Trim" an active value so that it is empty after the end of its era. For example, `trimAfter ui` can be visualized as

See the documentation of `trim` for more details.

## Composing active values

after :: Active a -> Active a -> Active a Source

`a1 `after` a2` produces an active that behaves like `a1` but is shifted to start at the end time of `a2`. If either `a1` or `a2` are constant, `a1` is returned unchanged.

(->>) :: Semigroup a => Active a -> Active a -> Active a infixr 5 Source

Sequence/overlay two `Active` values: shift the second to start immediately after the first (using `after`), then compose them (using `<>`).

(|>>) :: Active a -> Active a -> Active a Source

"Splice" two `Active` values together: shift the second to start immediately after the first (using `after`), and produce the value which acts like the first up to the common end/start point, then like the second after that. If both are constant, return the first.

movie :: [Active a] -> Active a Source

Splice together a list of active values using `|>>`. The list must be nonempty.

# Discretization

discrete :: [a] -> Active a Source

Create an `Active` which takes on each value in the given list in turn during the time `[0,1]`, with each value getting an equal amount of time. In other words, `discrete` creates a "slide show" that starts at time 0 and ends at time 1. The first element is used prior to time 0, and the last element is used after time 1.

It is an error to call `discrete` on the empty list.

simulate :: Rational -> Active a -> [a] Source

`simulate r act` simulates the `Active` value `act`, returning a list of "snapshots" taken at regular intervals from the start time to the end time. The interval used is determined by the rate `r`, which denotes the "frame rate", that is, the number of snapshots per unit time.

If the `Active` value is constant (and thus has no start or end times), a list of length 1 is returned, containing the constant value.