Add new utility functions for homogeneous coords

This commit is contained in:
Kiana Sheibani 2022-07-05 18:09:07 -04:00
parent ff50ebfd70
commit 97bd20d722
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
3 changed files with 84 additions and 20 deletions

View file

@ -326,6 +326,15 @@ export
arr !!.. rs = indexRange rs arr
export
indexUnsafe : Vect rk Nat -> Array {rk} s a -> a
indexUnsafe is arr = index (getLocation' (strides arr) is) (getPrim arr)
export
(!#) : Array {rk} s a -> Vect rk Nat -> a
(!#) = flip indexUnsafe
--------------------------------------------------------------------------------
-- Operations on arrays
--------------------------------------------------------------------------------
@ -338,7 +347,7 @@ arr !!.. rs = indexRange rs arr
||| @ ord The order to reinterpret the array by
export
reshape' : (s' : Vect rk' Nat) -> (ord : Order) -> Array {rk} s a ->
product s = product s' => Array s' a
(0 ok : product s = product s') => Array s' a
reshape' s' ord' arr = MkArray ord' (calcStrides ord' s') s' (getPrim arr)
||| Reshape the array into the given shape.
@ -346,7 +355,7 @@ reshape' s' ord' arr = MkArray ord' (calcStrides ord' s') s' (getPrim arr)
||| @ s' The shape to convert the array to
export
reshape : (s' : Vect rk' Nat) -> Array {rk} s a ->
product s = product s' => Array s' a
(0 ok : product s = product s') => Array s' a
reshape s' arr = reshape' s' (getOrder arr) arr

View file

@ -37,31 +37,75 @@ HVector : Nat -> Type -> Type
HVector n = Vector (S n)
export
fromVector : Num a => Vector n a -> HVector n a
fromVector v = rewrite plusCommutative 1 n in v ++ vector [1]
export
fromVectorL : Num a => Vector n a -> HVector n a
fromVectorL v = rewrite plusCommutative 1 n in v ++ vector [0]
export
toVector : HVector n a -> Vector n a
toVector = vector . init . toVect
-- TODO: Find an implementation for `toVector` that doesn't suck
--------------------------------------------------------------------------------
-- Conversion functions
--------------------------------------------------------------------------------
export
toHomogeneous : Num a => Matrix m n a -> HMatrix m n a
toHomogeneous mat with (viewShape mat)
vectorToH : Num a => Vector n a -> HVector n a
vectorToH v = rewrite plusCommutative 1 n in v ++ vector [1]
export
vectorToHLinear : Num a => Vector n a -> HVector n a
vectorToHLinear v = rewrite plusCommutative 1 n in v ++ vector [0]
export
hvector : Num a => Vect n a -> HVector n a
hvector v = rewrite plusCommutative 1 n in vector (v ++ [1])
export
hvectorLinear : Num a => Vect n a -> HVector n a
hvectorLinear v = rewrite plusCommutative 1 n in vector (v ++ [0])
export
fromHomogeneous : HVector n a -> Vector n a
fromHomogeneous = vector . init . toVect
-- TODO: Find an implementation for `fromHomogeneous` that doesn't suck
export
hmatrix : Num a => Matrix m n a -> Vector m a -> HMatrix m n a
hmatrix mat tr with (viewShape mat)
_ | Shape [m,n] = indexSet [last,last] 1 $
resize [S m, S n] 0 $
mat `hconcat` reshape
{ok = sym $ multOneRightNeutral _} [m,1] tr
export
matrixToH : Num a => Matrix m n a -> HMatrix m n a
matrixToH mat with (viewShape mat)
_ | Shape [m,n] = indexSet [last,last] 1 $ resize [S m, S n] 0 mat
export
toMatrix : HMatrix m n a -> Matrix m n a
toMatrix mat with (viewShape mat)
getMatrix : HMatrix m n a -> Matrix m n a
getMatrix mat with (viewShape mat)
_ | Shape [S m, S n] = resizeLTE [m,n] mat
{ok = [lteSuccRight reflexive,lteSuccRight reflexive]}
export
getTranslationVector : HMatrix m n a -> Vector m a
getTranslationVector mat with (viewShape mat)
_ | Shape [S m, S n] = resizeLTE [m] {ok = [lteSuccRight reflexive]} $
getColumn last mat
--------------------------------------------------------------------------------
-- Constructors of homogeneous matrices
--------------------------------------------------------------------------------
export
scalingH : Num a => {n : _} -> a -> HMatrix' n a
scalingH x = indexSet [last,last] 1 $ repeatDiag x 0
export
translationH : Num a => {n : _} -> Vector n a -> HMatrix' n a
translationH = hmatrix identity
export
rotation2DH : Double -> HMatrix' 2 Double
rotation2DH = matrixToH . rotation2D

View file

@ -65,7 +65,7 @@ identity : Num a => {n : _} -> Matrix' n a
identity = repeatDiag 1 0
||| Calculate the matrix that scales a vector by the given value.
||| Construct the matrix that scales a vector by the given value.
export
scaling : Num a => {n : _} -> a -> Matrix' n a
scaling x = repeatDiag x 0
@ -104,6 +104,17 @@ getColumn : Fin n -> Matrix m n a -> Vector m a
getColumn c mat = rewrite sym (minusZeroRight m) in indexRange [All, One c] mat
export
diagonal' : Matrix m n a -> Vector (minimum m n) a
diagonal' mat with (viewShape mat)
_ | Shape [m,n] = fromFunctionNB _ (\[i] => indexUnsafe [i,i] mat)
export
diagonal : Matrix' n a -> Vector n a
diagonal mat with (viewShape mat)
_ | Shape [n,n] = fromFunctionNB [n] (\[i] => indexUnsafe [i,i] mat)
--------------------------------------------------------------------------------
-- Operations
--------------------------------------------------------------------------------