A type representing a Transformation for d dimensional objects

Transformations and Matrices are isomorphic.

Compose transformations (right to left)

Compute the inverse transformation

>>> inverseOf $ translation (Vector2 (10.0) (5.0))
Transformation {_transformationMatrix = Matrix (Vector3 (Vector3 1.0 0.0 (-10.0)) (Vector3 0.0 1.0 (-5.0)) (Vector3 0.0 0.0 1.0))}

A class representing types that can be transformed using a transformation

Apply a transformation to a collection of objects.

>>> transformAllBy (uniformScaling 2) [Point1 1, Point1 2, Point1 3]
[Point1 2.0,Point1 4.0,Point1 6.0]

Apply transformation to a PointFunctor, ie something that contains points. Polygons, triangles, line segments, etc, are all PointFunctors.

>>> transformPointFunctor (uniformScaling 2) $ OpenLineSegment (Point1 1 :+ ()) (Point1 2 :+ ())
OpenLineSegment (Point1 2.0 :+ ()) (Point1 4.0 :+ ())

Create translation transformation from a vector.

>>> transformBy (translation $ Vector2 1 2) $ Point2 2 3
Point2 3.0 5.0

Create scaling transformation from a vector.

>>> transformBy (scaling $ Vector2 2 (-1)) $ Point2 2 3
Point2 4.0 (-3.0)

Create scaling transformation from a scalar that is applied to all dimensions.

>>> transformBy (uniformScaling 5) $ Point2 2 3
Point2 10.0 15.0
>>> uniformScaling 5 == scaling (Vector2 5 5)
True
>>> uniformScaling 5 == scaling (Vector3 5 5 5)
True

Translate a given point.

>>> translateBy (Vector2 1 2) $ Point2 2 3
Point2 3.0 5.0

Scale a given point.

>>> scaleBy (Vector2 2 (-1)) $ Point2 2 3
Point2 4.0 (-3.0)

Scale a given point uniformly in all dimensions.

>>> scaleUniformlyBy 5 $ Point2 2 3
Point2 10.0 15.0

Row in a translation matrix transRow :: forall n r. ( Arity n, Arity (n- 1), ((n - 1) + 1) ~ n , Num r) => Int -> r -> Vector n r transRow i x = set (V.element (Proxy :: Proxy (n-1))) x $ mkRow i 1

Given three new unit-length basis vectors (u,v,w) that map to (x,y,z), construct the appropriate rotation that does this.

Skew transformation that keeps the y-coordinates fixed and shifts the x coordinates.