Wolfram: Apply Transform to Graphics

Apply Geometric Transform to Graphics

GeometricTransformation[graPrims, f]

Apply f to graPrims.

graPrims is a Graphics Primitive or a list of. It cannot be Graphics or Graphics3D.

• f is a transformation function.
• It is typically TransformationFunction[data]. 〔see Geometric Transformation Functions〕
• It can be a Transformation Matrix.
• It can have the form {matrix, vector} , where the vector is used for translation.

GeometricTransformation[angs] return itself unchanged. It display effect when it is inside Graphics or Graphics3D.

• GeometricTransformation

GeometricTransformation[graPrims, listOfTransforms]

do copy of multiple transformations.

Example: Basic

(*  GeometricTransformation first arg should be graphics primitive or list of *)

GeometricTransformation[ {Circle[], Rectangle[{0, 0}]} , RotationTransform[ 10 Degree ] ]
(* result is itself, unchanged. *)

(* has effect when it in inside Graphics or Graph3D *)
Graphics[
GeometricTransformation[
{Circle[], Rectangle[{0, 0}]} ,
RotationTransform[ 10 Degree ]
],
Axes -> True]

Example: Using a Matrix

(* rotate a rectangle *)
Graphics[
GeometricTransformation[
{Rectangle[{0, 0}]} ,
RotationMatrix[ 10 Degree ]
],
Axes -> True
]

Example: Using a Matrix and a Vector

(* transform by a matrix, and translate by a vector *)
Graphics[
GeometricTransformation[
{Rectangle[{0, 0}]} ,
{RotationMatrix[ 10 Degree ], {1,1}}
],
Axes -> True
]

Example: Error on Graphics or Graphics3D

(* if GeometricTransformation's args is Graphics[...], no transform is done. *)
result =
GeometricTransformation[
Graphics[{Rectangle[{0, 0}]}],
RotationTransform[ 10 Degree ]
]

(* if you show result inside Graphics[...], it's an error. *)
Show[ result ]