Misc. changes

This commit is contained in:
Kiana Sheibani 2022-11-30 12:54:01 -05:00
parent 0a54f607b0
commit 524486bb58
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
5 changed files with 51 additions and 3 deletions

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@ -27,7 +27,7 @@ public export
HMatrix' : Nat -> Type -> Type
HMatrix' n = HMatrix n n
||| An `n`-dimensional homogeneous vector type.
||| An homogeneous vector type.
|||
||| Homogeneous vectors are vectors intended to be multiplied with homogeneous
||| matrices (see `HMatrix`). They have an extra dimension compared to regular
@ -129,6 +129,7 @@ translationH : Num a => Vector n a -> HMatrix' n a
translationH {n} v with (viewShape v)
_ | Shape [n] = hmatrix identity v
||| Construct a 2D homogeneous matrix that rotates by the given angle (in radians).
export
rotate2DH : Double -> HMatrix' 2 Double
@ -148,3 +149,20 @@ rotate3DYH = matrixToH . rotate3DY
export
rotate3DZH : Double -> HMatrix' 3 Double
rotate3DZH = matrixToH . rotate3DZ
export
reflectH : {n : _} -> Neg a => Fin n -> HMatrix' n a
reflectH i = indexSet [weaken i,weaken i] (-1) identity
export
reflectXH : {n : _} -> Neg a => HMatrix' (1 + n) a
reflectXH = reflectH 0
export
reflectYH : {n : _} -> Neg a => HMatrix' (2 + n) a
reflectYH = reflectH 0
export
reflectZH : {n : _} -> Neg a => HMatrix' (3 + n) a
reflectZH = reflectH 0

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@ -31,7 +31,6 @@ export
FieldCmp Double where
abslt = (<) `on` abs
-- Alternative implementations of `Eq` and `FieldCmp` that compare floating
-- point numbers approximately, useful when working with transforms
namespace Eq

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@ -96,6 +96,23 @@ rotate3DZ : Double -> Matrix' 3 Double
rotate3DZ a = matrix [[cos a, - sin a, 0], [sin a, cos a, 0], [0,0,1]]
export
reflect : {n : _} -> Neg a => Fin n -> Matrix' n a
reflect i = indexSet [i, i] (-1) (repeatDiag 1 0)
export
reflectX : {n : _} -> Neg a => Matrix' (1 + n) a
reflectX = reflect 0
export
reflectY : {n : _} -> Neg a => Matrix' (2 + n) a
reflectY = reflect 1
export
reflectZ : {n : _} -> Neg a => Matrix' (3 + n) a
reflectZ = reflect 2
--------------------------------------------------------------------------------
-- Indexing
--------------------------------------------------------------------------------
@ -225,6 +242,14 @@ trace : Num a => Matrix m n a -> a
trace = sum . diagonal'
||| Construct a matrix that reflects a vector along a hyperplane of the
||| given normal vector. The input does not have to be a unit vector.
export
reflectNormal : (Neg a, Fractional a) => Vector n a -> Matrix' n a
reflectNormal {n} v with (viewShape v)
_ | Shape [n] = repeatDiag 1 0 - (2 / normSq v) *. outer v v
--------------------------------------------------------------------------------
-- Matrix multiplication
--------------------------------------------------------------------------------

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@ -40,7 +40,7 @@ fromMatrix mat = if isOrthonormal' mat then Just (unsafeMkTrans (matrixToH mat))
||| Construct an orthonormal transform that reflects a particular coordinate.
export
reflect : {n : _} -> Neg a => Fin n -> Orthonormal n a
reflect i = unsafeMkTrans $ indexSet [weaken i,weaken i] (-1) identity
reflect = unsafeMkTrans . reflectH
||| The orthonormal transform that reflects on the x-coordinate (first coordinate).
export

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@ -25,6 +25,7 @@ isRotation' : FieldCmp a => Matrix' n a -> Bool
isRotation' mat = isOrthonormal' mat && det mat == 1
||| Try to constuct a rotation from a matrix.
export
fromMatrix : FieldCmp a => Matrix' n a -> Maybe (Rotation n a)
fromMatrix mat = if isRotation' mat then Just (unsafeMkTrans $ matrixToH mat)
else Nothing
@ -35,6 +36,11 @@ isRotation : FieldCmp a => HMatrix' n a -> Bool
isRotation {n} mat with (viewShape mat)
_ | Shape [S n, S n] = isHMatrix mat && all (==0) (mat !!.. [EndBound last, One last])
export
fromHMatrix : FieldCmp a => HMatrix' n a -> Maybe (Rotation n a)
fromHMatrix mat = if isRotation mat then Just (unsafeMkTrans mat)
else Nothing
||| Construct a 2D rotation that rotates by the given angle (in radians).
export
rotate2D : Num a => Double -> Rotation 2 Double