ostk.mathematics.geometry.d2.Transformation¶

class Transformation( self: ostk.mathematics.geometry.d2.Transformation, matrix: numpy.ndarray[numpy.float64[3, 3]], )¶

Bases: pybind11_object

Create a 2D transformation from a 3x3 transformation matrix.

Parameters:: matrix (Matrix3d) -- The 3x3 transformation matrix in homogeneous coordinates.

Example

>>> import numpy as np
>>> matrix = numpy.eye(3)  # Identity matrix
>>> transformation = Transformation(matrix)

Methods

`apply_to`	Overloaded function.
`get_inverse`	Get the inverse transformation.
`get_matrix`	Get the transformation matrix.
`get_type`	Get the type of the transformation.
`identity`	Create an identity transformation (no change).
`is_defined`	Check if the transformation is defined.
`rotation`	Create a rotation transformation around the origin.
`rotation_around`	Create a rotation transformation around a specific point.
`string_from_type`	Get the string representation of a transformation type.
`translation`	Create a translation transformation.
`type_of_matrix`	Determine the transformation type from a matrix.
`undefined`	Create an undefined transformation.

class Type(self: ostk.mathematics.geometry.d2.Transformation.Type, value: int)¶

Bases: pybind11_object

Members:

Undefined

Identity

Translation

Rotation

Scaling

Reflection

Shear

Affine

property name¶

apply_to(*args, **kwargs)¶

Overloaded function.

apply_to(self: ostk.mathematics.geometry.d2.Transformation, point: ostk.mathematics.geometry.d2.object.Point) -> ostk.mathematics.geometry.d2.object.Point
Apply the transformation to a point.
Args:
point (Point): The point to transform.

Returns:
Point: The transformed point.

Example:
>>> point = Point(1.0, 2.0) >>> translation = Transformation.translation([1.0, 1.0]) >>> transformed = translation.apply_to(point) # Point(2.0, 3.0)
apply_to(self: ostk.mathematics.geometry.d2.Transformation, vector: numpy.ndarray[numpy.float64[2, 1]]) -> numpy.ndarray[numpy.float64[2, 1]]
Apply the transformation to a vector.
Args:
vector (Vector2d): The vector to transform.

Returns:
Vector2d: The transformed vector.

Example:
>>> vector = numpy.array([1.0, 0.0]) >>> rotation = Transformation.rotation(Angle.degrees(90.0)) >>> transformed = rotation.apply_to(vector) # [0.0, 1.0]

get_inverse( self: ostk.mathematics.geometry.d2.Transformation, ) → ostk.mathematics.geometry.d2.Transformation¶

Get the inverse transformation.

Returns:: The inverse transformation.
Return type:: Transformation

Example

>>> translation = Transformation.translation([1.0, 2.0])
>>> inverse = translation.get_inverse()  # Translation by [-1.0, -2.0]

get_matrix( self: ostk.mathematics.geometry.d2.Transformation, ) → numpy.ndarray[numpy.float64[3, 3]]¶

Get the transformation matrix.

Returns:: The 3x3 transformation matrix in homogeneous coordinates.
Return type:: Matrix3d

Example

>>> transformation = Transformation.identity()
>>> matrix = transformation.get_matrix()  # 3x3 identity matrix

get_type( self: ostk.mathematics.geometry.d2.Transformation, ) → ostk::mathematics::geometry::d2::Transformation::Type¶

Get the type of the transformation.

Returns:: The transformation type (Identity, Translation, Rotation, etc.).
Return type:: Transformation.Type

Example

>>> transformation = Transformation.identity()
>>> transformation.get_type()  # Transformation.Type.Identity

static identity() → ostk.mathematics.geometry.d2.Transformation¶

Create an identity transformation (no change).

Returns:: The identity transformation.
Return type:: Transformation

Example

>>> identity = Transformation.identity()
>>> point = Point(1.0, 2.0)
>>> identity.apply_to(point)  # Point(1.0, 2.0) - unchanged

is_defined(self: ostk.mathematics.geometry.d2.Transformation) → bool¶

Check if the transformation is defined.

Returns:: True if the transformation is defined, False otherwise.
Return type:: bool

Example

>>> transformation = Transformation.identity()
>>> transformation.is_defined()  # True

static rotation( rotation_angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d2.Transformation¶

Create a rotation transformation around the origin.

Parameters:: rotation_angle (Angle) -- The rotation angle.
Returns:: The rotation transformation.
Return type:: Transformation

Example

>>> rotation = Transformation.rotation(Angle.degrees(90.0))
>>> point = Point(1.0, 0.0)
>>> rotation.apply_to(point)  # Point(0.0, 1.0)

static rotation_around( point: ostk.mathematics.geometry.d2.object.Point, rotation_angle: ostk::mathematics::geometry::Angle, ) → ostk.mathematics.geometry.d2.Transformation¶

Create a rotation transformation around a specific point.

Parameters:

point (Point) -- The center point of rotation.
rotation_angle (Angle) -- The rotation angle.

Returns:

The rotation transformation around the specified point.

Return type:

Transformation

Example

>>> center = Point(1.0, 1.0)
>>> rotation = Transformation.rotation_around(center, Angle.degrees(90.0))
>>> point = Point(2.0, 1.0)
>>> rotation.apply_to(point)  # Point(1.0, 2.0)

static string_from_type( type: ostk::mathematics::geometry::d2::Transformation::Type, ) → ostk.core.type.String¶

Get the string representation of a transformation type.

Parameters:: type (Transformation.Type) -- The transformation type.
Returns:: String representation of the type.
Return type:: str

Example

>>> Transformation.string_from_type(Transformation.Type.Translation)  # "Translation"

static translation( translation_vector: numpy.ndarray[numpy.float64[2, 1]], ) → ostk.mathematics.geometry.d2.Transformation¶

Create a translation transformation.

Parameters:: translation_vector (Vector2d) -- The translation vector.
Returns:: The translation transformation.
Return type:: Transformation

Example

>>> translation = Transformation.translation([1.0, 2.0])
>>> point = Point(0.0, 0.0)
>>> translation.apply_to(point)  # Point(1.0, 2.0)

static type_of_matrix( matrix: numpy.ndarray[numpy.float64[3, 3]], ) → ostk::mathematics::geometry::d2::Transformation::Type¶

Determine the transformation type from a matrix.

Parameters:: matrix (Matrix3d) -- The transformation matrix to analyze.
Returns:: The detected transformation type.
Return type:: Transformation.Type

Example

>>> import numpy as np
>>> matrix = numpy.eye(3)
>>> Transformation.type_of_matrix(matrix)  # Transformation.Type.Identity

static undefined() → ostk.mathematics.geometry.d2.Transformation¶

Create an undefined transformation.

Returns:: An undefined transformation.
Return type:: Transformation

Example

>>> undefined_transform = Transformation.undefined()
>>> undefined_transform.is_defined()  # False