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


-- | Three-dimensional vectors of doubles with basic operations
--   
--   Simple three-dimensional vectors of doubles with basic vector and
--   matrix operations, supporting <a>Data.Vector.Unboxed</a> and
--   <a>Data.Vector.Storable</a>.
@package simple-vec3
@version 0.3

module Data.Vec3.Class

-- | Three-dimensional vector, with an associated matrix type.
class Vec3 v where {
    data family Matrix v;
}

-- | Origin point <tt>(0, 0, 0)</tt>.
origin :: Vec3 v => v

-- | Construct a new vector from components.
fromXYZ :: Vec3 v => (Double, Double, Double) -> v

-- | Deconstruct a vector into components.
toXYZ :: Vec3 v => v -> (Double, Double, Double)

-- | Zip two vectors elementwise.
zipWith :: Vec3 v => (Double -> Double -> Double) -> v -> v -> v

-- | Add two vectors.
(<+>) :: Vec3 v => v -> v -> v

-- | Subtract two vectors.
(<->) :: Vec3 v => v -> v -> v

-- | Cross product.
(><) :: Vec3 v => v -> v -> v

-- | Scale a vector.
(.^) :: Vec3 v => v -> Double -> v

-- | Dot product.
(.*) :: Vec3 v => v -> v -> Double

-- | Euclidean norm of a vector.
norm :: Vec3 v => v -> Double

-- | Produce unit vector with the same direction as the original one.
normalize :: Vec3 v => v -> v

-- | Distance between two points.
distance :: Vec3 v => v -> v -> Double

-- | Invert the direction of a vector.
invert :: Vec3 v => v -> v

-- | Construct a new matrix from rows.
fromRows :: Vec3 v => (v, v, v) -> Matrix v

-- | Deconstruct a matrix into rows.
toRows :: Vec3 v => Matrix v -> (v, v, v)

-- | Generic vector dot product.
--   
--   Multiply the transpose of the first vector by the given matrix, then
--   multiply the result by the second vector.
--   
--   <pre>
--                       [ a11  a12  a13 ]   [ v2x ]
--                       [               ]   [     ]
--   [ v1x  v1y  v1z ] . [ a21  a22  a23 ] . [ v2y ] = s
--                       [               ]   [     ]
--                       [ a31  a32  a33 ]   [ v2z ]
--   </pre>
dotM :: Vec3 v => v -> v -> Matrix v -> Double

-- | Multiply a matrix and a vector.
--   
--   <pre>
--   [ a11  a12  a13 ]   [ v2x ]   [ rx ]
--   [               ]   [     ]   [    ]
--   [ a21  a22  a23 ] . [ v2y ] = [ ry ]
--   [               ]   [     ]   [    ]
--   [ a31  a32  a33 ]   [ v2z ]   [ rz ]
--   </pre>
mxv :: Vec3 v => Matrix v -> v -> v

-- | Build a diagonal matrix from a number <tt>d</tt>.
--   
--   <pre>
--   [ d  0  0 ]
--   [         ]
--   [ 0  d  0 ]
--   [         ]
--   [ 0  0  d ]
--   </pre>
diag :: Vec3 v => Double -> Matrix v

-- | Transpose a vector and multiply it by another vector, producing a
--   matrix.
--   
--   <pre>
--   [ v1x ]                       [ r11  r12  r13 ]
--   [     ]                       [               ]
--   [ v1y ] . [ v2x  v2y  v2z ] = [ r21  r22  r23 ]
--   [     ]                       [               ]
--   [ v1z ]                       [ r31  r32  r33 ]
--   </pre>
vxv :: Vec3 v => v -> v -> Matrix v

-- | Add two matrices.
addM :: Vec3 v => Matrix v -> Matrix v -> Matrix v


-- | <a>Vec3</a> class and implementations.
--   
--   The package provides two different implementations for <a>Vec3</a>
--   type class, which differ in storage scheme. Benchmarks are included
--   for both. You most likely want to use <a>CVec3</a> which is based on
--   contiguous storage scheme and offers the best performance.
module Data.Vec3

-- | Three-dimensional vector, with an associated matrix type.
class Vec3 v where {
    data family Matrix v;
}

-- | Origin point <tt>(0, 0, 0)</tt>.
origin :: Vec3 v => v

-- | Construct a new vector from components.
fromXYZ :: Vec3 v => (Double, Double, Double) -> v

-- | Deconstruct a vector into components.
toXYZ :: Vec3 v => v -> (Double, Double, Double)

-- | Zip two vectors elementwise.
zipWith :: Vec3 v => (Double -> Double -> Double) -> v -> v -> v

-- | Add two vectors.
(<+>) :: Vec3 v => v -> v -> v

-- | Subtract two vectors.
(<->) :: Vec3 v => v -> v -> v

-- | Cross product.
(><) :: Vec3 v => v -> v -> v

-- | Scale a vector.
(.^) :: Vec3 v => v -> Double -> v

-- | Dot product.
(.*) :: Vec3 v => v -> v -> Double

-- | Euclidean norm of a vector.
norm :: Vec3 v => v -> Double

-- | Produce unit vector with the same direction as the original one.
normalize :: Vec3 v => v -> v

-- | Distance between two points.
distance :: Vec3 v => v -> v -> Double

-- | Invert the direction of a vector.
invert :: Vec3 v => v -> v

-- | Construct a new matrix from rows.
fromRows :: Vec3 v => (v, v, v) -> Matrix v

-- | Deconstruct a matrix into rows.
toRows :: Vec3 v => Matrix v -> (v, v, v)

-- | Generic vector dot product.
--   
--   Multiply the transpose of the first vector by the given matrix, then
--   multiply the result by the second vector.
--   
--   <pre>
--                       [ a11  a12  a13 ]   [ v2x ]
--                       [               ]   [     ]
--   [ v1x  v1y  v1z ] . [ a21  a22  a23 ] . [ v2y ] = s
--                       [               ]   [     ]
--                       [ a31  a32  a33 ]   [ v2z ]
--   </pre>
dotM :: Vec3 v => v -> v -> Matrix v -> Double

-- | Multiply a matrix and a vector.
--   
--   <pre>
--   [ a11  a12  a13 ]   [ v2x ]   [ rx ]
--   [               ]   [     ]   [    ]
--   [ a21  a22  a23 ] . [ v2y ] = [ ry ]
--   [               ]   [     ]   [    ]
--   [ a31  a32  a33 ]   [ v2z ]   [ rz ]
--   </pre>
mxv :: Vec3 v => Matrix v -> v -> v

-- | Build a diagonal matrix from a number <tt>d</tt>.
--   
--   <pre>
--   [ d  0  0 ]
--   [         ]
--   [ 0  d  0 ]
--   [         ]
--   [ 0  0  d ]
--   </pre>
diag :: Vec3 v => Double -> Matrix v

-- | Transpose a vector and multiply it by another vector, producing a
--   matrix.
--   
--   <pre>
--   [ v1x ]                       [ r11  r12  r13 ]
--   [     ]                       [               ]
--   [ v1y ] . [ v2x  v2y  v2z ] = [ r21  r22  r23 ]
--   [     ]                       [               ]
--   [ v1z ]                       [ r31  r32  r33 ]
--   </pre>
vxv :: Vec3 v => v -> v -> Matrix v

-- | Add two matrices.
addM :: Vec3 v => Matrix v -> Matrix v -> Matrix v

-- | <a>Vec3</a> implementation with <a>Unbox</a> and <a>Storable</a>
--   instances based on a single contiguous array storage scheme, suitable
--   for use with <a>Data.Vector.Unboxed</a> and
--   <a>Data.Vector.Storable</a>.
--   
--   <pre>
--   interface: [v1 x   y   z  ; v2 x   y   z  ...], length = N = M / 3
--                  |   |   |       |   |   |
--   storage:   [  v1x v2y v2z ;   v2x v2y v2z ...], length = M
--   </pre>
--   
--   This implementation has the best performance.
data CVec3
CVec3 :: !Double -> !Double -> !Double -> CVec3

-- | <a>Vec3</a> implementation with <a>Unbox</a> instance based on default
--   Unbox instance for tuples of arrays, which wraps a vector of tuples as
--   a tuple of vectors.
--   
--   <pre>
--   interface:  [v1 (x, y, z); v2 (x, y, z) ...], length = N
--                    |  |  |       |  |  |
--   storage(x): [v1x-+  |  | ; v2x-+  |  |  ...], length = N
--   storage(y): [v1y----+  | ; v2y----+  |  ...], length = N
--   storage(z): [v1z-------+ ; v2z-------+  ...], length = N
--   </pre>
--   
--   You almost definitely want to use <tt>CVec3</tt> instead as it has
--   better performance.
newtype TVec3
TVec3 :: (Double, Double, Double) -> TVec3
instance GHC.Show.Show Data.Vec3.CVec3
instance GHC.Classes.Eq Data.Vec3.CVec3
instance Data.Vec3.Class.Vec3 Data.Vec3.CVec3
instance Data.Vector.Generic.Mutable.Base.MVector Data.Vector.Unboxed.Base.MVector Data.Vec3.CVec3
instance Data.Vector.Generic.Base.Vector Data.Vector.Unboxed.Base.Vector Data.Vec3.CVec3
instance Data.Vector.Unboxed.Base.Unbox Data.Vec3.CVec3
instance Foreign.Storable.Storable Data.Vec3.CVec3
instance Test.QuickCheck.Arbitrary.Arbitrary Data.Vec3.CVec3