-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Efficient geometric vectors and transformations.
--   
--   This Haskell library implements several small vectors types with
--   <tt>Double</tt> fields, with seperate types for each size of vector,
--   and a type class for handling vectors generally. Existing API has been
--   rearranged. Now supports 4D vectors and linear transformations.
@package AC-Vector
@version 2.0.0


-- | General function applicable to all vector types.
module Data.Vector.Class

-- | The type of vector field values.
type Scalar = Double

-- | All vector types belong to this class. Aside from <a>vpack</a> and
--   <a>vunpack</a>, these methods aren't especially useful to end-users;
--   they're used internally by the vector arithmetic implementations.
class Vector v
vmap :: (Vector v) => (Scalar -> Scalar) -> (v -> v)
vzip :: (Vector v) => (Scalar -> Scalar -> Scalar) -> (v -> v -> v)
vfold :: (Vector v) => (Scalar -> Scalar -> Scalar) -> (v -> Scalar)
vpack :: (Vector v) => [Scalar] -> Maybe v
vunpack :: (Vector v) => v -> [Scalar]

-- | Scale a vector (i.e., change its length but not its direction). This
--   operator has the same precedence as the usual <tt>(*)</tt> operator.
--   
--   The <tt>(*|)</tt> and <tt>(|*)</tt> operators are identical, but with
--   their argument flipped. Just remember that the '<tt>|</tt>' denotes
--   the scalar part.
(*|) :: (Vector v) => Scalar -> v -> v

-- | Scale a vector (i.e., change its length but not its direction). This
--   operator has the same precedence as the usual <tt>(*)</tt> operator.
--   
--   The <tt>(*|)</tt> and <tt>(|*)</tt> operators are identical, but with
--   their argument flipped. Just remember that the '<tt>|</tt>' denotes
--   the scalar part.
(|*) :: (Vector v) => v -> Scalar -> v

-- | Take the <i>dot product</i> of two vectors. This is a scalar equal to
--   the cosine of the angle between the two vectors multiplied by the
--   length of each vectors.
vdot :: (Vector v) => v -> v -> Scalar

-- | Return the length or <i>magnitude</i> of a vector. (Note that this
--   involves a slow square root operation.)
vmag :: (Vector v) => v -> Scalar

-- | Normalise a vector. In order words, return a new vector with the same
--   direction, but a length of exactly one. (If the vector's length is
--   zero or very near to zero, the vector is returned unchanged.)
vnormalise :: (Vector v) => v -> v

-- | Linearly interpolate between two points in space.
--   
--   <ul>
--   <li><pre>vlinear 0 a b = a</pre></li>
--   <li><pre>vlinear 1 a b = b</pre></li>
--   <li><tt>vlinear 0.5 a b</tt> would give a point exactly half way
--   between <tt>a</tt> and <tt>b</tt> in a straight line.</li>
--   </ul>
vlinear :: (Num v, Vector v) => Scalar -> v -> v -> v


-- | 1-dimensional vectors with vector arithmetic.
--   
--   This isn't especially useful. Usually if you want to calculate with
--   scalars, you can just use the <a>Scalar</a> type directly. However,
--   this module provides a <a>Vector1</a> newtype over <a>Scalar</a> that
--   allows a scalar to be treated as a sort of vector, which is very
--   occasionally useful.
module Data.Vector.V1

-- | The type of 1D vectors.
--   
--   Owing to its particularly simple structure, this type has more class
--   instances than 'propper' vectors have. Still, for the most part you'll
--   probably want to just use <a>Scalar</a> itself directly.
newtype Vector1
Vector1 :: Scalar -> Vector1
v1x :: Vector1 -> Scalar
instance Eq Vector1
instance Ord Vector1
instance Enum Vector1
instance Show Vector1
instance Num Vector1
instance Fractional Vector1
instance Vector Vector1


-- | 2-dimensional vectors with vector arithmetic.
module Data.Vector.V2
data Vector2
Vector2 :: !!Scalar -> !!Scalar -> Vector2
v2x :: Vector2 -> !!Scalar
v2y :: Vector2 -> !!Scalar
instance Eq Vector2
instance Show Vector2
instance Fractional Vector2
instance Num Vector2
instance Vector Vector2


-- | 3-dimensional vectors with vector arithmetic.
module Data.Vector.V3
data Vector3
Vector3 :: !!Scalar -> !!Scalar -> !!Scalar -> Vector3
v3x :: Vector3 -> !!Scalar
v3y :: Vector3 -> !!Scalar
v3z :: Vector3 -> !!Scalar

-- | Take the <i>cross product</i> of two 3D vectors. This produces a new
--   3D vector that is perpendicular to the plane of the first two vectors,
--   and who's length is equal to the sine of the angle between those
--   vectors multiplied by their lengths.
--   
--   Note that <tt>a `vcross` b = negate (b `vcross` a)</tt>.
vcross :: Vector3 -> Vector3 -> Vector3
instance Eq Vector3
instance Show Vector3
instance Fractional Vector3
instance Num Vector3
instance Vector Vector3


-- | 4-dimensional vectors with vector arithmetic.
module Data.Vector.V4
data Vector4
Vector4 :: !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> Vector4
v4x :: Vector4 -> !!Scalar
v4y :: Vector4 -> !!Scalar
v4z :: Vector4 -> !!Scalar
v4w :: Vector4 -> !!Scalar
instance Eq Vector4
instance Show Vector4
instance Fractional Vector4
instance Num Vector4
instance Vector Vector4


-- | 1-dimensional linear transformations.
module Data.Vector.Transform.T1

-- | The type of 1D linear transformations. Essentially, this is applying a
--   linear function to a number.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform1
Transform1 :: !!Scalar -> !!Scalar -> Transform1
t1_XX :: Transform1 -> !!Scalar
t1_1X :: Transform1 -> !!Scalar

-- | Apply a 1D transformation to a 1D point, yielding a new 1D point.
transformP1 :: Transform1 -> Vector1 -> Vector1
instance Eq Transform1
instance Show Transform1
instance Monoid Transform1


-- | 2-dimensional linear transformations.
module Data.Vector.Transform.T2

-- | The type of 2D linear transformations.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform2
Transform2 :: !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> Transform2
t2_XX :: Transform2 -> !!Scalar
t2_YX :: Transform2 -> !!Scalar
t2_1X :: Transform2 -> !!Scalar
t2_XY :: Transform2 -> !!Scalar
t2_YY :: Transform2 -> !!Scalar
t2_1Y :: Transform2 -> !!Scalar

-- | Apply a 2D transformation to a 2D point, yielding a new 2D point.
transformP2 :: Transform2 -> Vector2 -> Vector2
instance Eq Transform2
instance Show Transform2
instance Monoid Transform2


-- | 3-dimensional linear transformations.
module Data.Vector.Transform.T3

-- | The type of 3D linear transformations.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform3
Transform3 :: !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> Transform3
t3_XX :: Transform3 -> !!Scalar
t3_YX :: Transform3 -> !!Scalar
t3_ZX :: Transform3 -> !!Scalar
t3_1X :: Transform3 -> !!Scalar
t3_XY :: Transform3 -> !!Scalar
t3_YY :: Transform3 -> !!Scalar
t3_ZY :: Transform3 -> !!Scalar
t3_1Y :: Transform3 -> !!Scalar
t3_XZ :: Transform3 -> !!Scalar
t3_YZ :: Transform3 -> !!Scalar
t3_ZZ :: Transform3 -> !!Scalar
t3_1Z :: Transform3 -> !!Scalar

-- | Apply a 3D transformation to a 3D point, yielding a new 3D point.
transformP3 :: Transform3 -> Vector3 -> Vector3
instance Eq Transform3
instance Show Transform3
instance Monoid Transform3


-- | 4-dimensional linear transformations.
module Data.Vector.Transform.T4

-- | The type of 4D linear transformations.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform4
Transform4 :: !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> !!Scalar -> Transform4
t4_XX :: Transform4 -> !!Scalar
t4_YX :: Transform4 -> !!Scalar
t4_ZX :: Transform4 -> !!Scalar
t4_WX :: Transform4 -> !!Scalar
t4_1X :: Transform4 -> !!Scalar
t4_XY :: Transform4 -> !!Scalar
t4_YY :: Transform4 -> !!Scalar
t4_ZY :: Transform4 -> !!Scalar
t4_WY :: Transform4 -> !!Scalar
t4_1Y :: Transform4 -> !!Scalar
t4_XZ :: Transform4 -> !!Scalar
t4_YZ :: Transform4 -> !!Scalar
t4_ZZ :: Transform4 -> !!Scalar
t4_WZ :: Transform4 -> !!Scalar
t4_1Z :: Transform4 -> !!Scalar
t4_XW :: Transform4 -> !!Scalar
t4_YW :: Transform4 -> !!Scalar
t4_ZW :: Transform4 -> !!Scalar
t4_WW :: Transform4 -> !!Scalar
t4_1W :: Transform4 -> !!Scalar

-- | Apply a 4D transformation to a 4D point, yielding a new 4D point.
transformP4 :: Transform4 -> Vector4 -> Vector4
instance Eq Transform4
instance Show Transform4
instance Monoid Transform4


-- | Convenience module to import all sizes of transform. (This doesn't
--   include all the field names though, just the transform types and their
--   application functions.)
module Data.Vector.Transform

-- | The type of 1D linear transformations. Essentially, this is applying a
--   linear function to a number.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform1

-- | Apply a 1D transformation to a 1D point, yielding a new 1D point.
transformP1 :: Transform1 -> Vector1 -> Vector1

-- | The type of 2D linear transformations.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform2

-- | Apply a 2D transformation to a 2D point, yielding a new 2D point.
transformP2 :: Transform2 -> Vector2 -> Vector2

-- | The type of 3D linear transformations.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform3

-- | Apply a 3D transformation to a 3D point, yielding a new 3D point.
transformP3 :: Transform3 -> Vector3 -> Vector3

-- | The type of 4D linear transformations.
--   
--   Note the <tt>Monoid</tt> instance, which gives you access to the
--   identity transform (<tt>mempty</tt>) and the ability to combine a
--   series of transforms into a single transform (<tt>mappend</tt>).
data Transform4

-- | Apply a 4D transformation to a 4D point, yielding a new 4D point.
transformP4 :: Transform4 -> Vector4 -> Vector4


-- | Convenience module providing easy access to everything in this
--   package. (See individual modules for fuller details.)
module Data.Vector