ostk.mathematics.geometry.d3.Transformation

class Transformation(

self: ostk.mathematics.geometry.d3.Transformation,

matrix: numpy.ndarray[numpy.float64[4, 4]],

)

Bases: pybind11_object

Represents a 3D geometric transformation.

A Transformation can represent translation, rotation, scaling, reflection, shear, or general affine transformations.

Construct a transformation from a 4x4 matrix.

Parameters:

matrix (numpy.ndarray) -- A 4x4 transformation matrix.

Example

>>> import numpy as np
>>> matrix = numpy.eye(3)  # 3x3 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.
is_defined	Check if the transformation is defined.
rotation	Overloaded function.
rotation_around	Create a rotation transformation around a point.
string_from_type	Convert a transformation type to a string.
translation	Create a translation transformation.
type_of_matrix	Determine the type of a transformation matrix.
undefined	Create an undefined transformation.

class Type(self: ostk.mathematics.geometry.d3.Transformation.Type, value: int)

Bases: pybind11_object

Members:

Undefined

Identity

Translation

Rotation

Scaling

Reflection

Shear

Affine

property name

apply_to(*args, **kwargs)

Overloaded function.

1. apply_to(self: ostk.mathematics.geometry.d3.Transformation, point: ostk.mathematics.geometry.d3.object.Point) -> ostk.mathematics.geometry.d3.object.Point

   Apply the transformation to a point.

   Args:

   point (Point): The point to transform.

   Returns:

   Point: The transformed point.

   Example:

   >>> transformation = Transformation.identity()
   >>> point = Point(1.0, 2.0, 3.0)
   >>> transformed_point = transformation.apply_to(point)  # Point(1.0, 2.0, 3.0)
   

2. apply_to(self: ostk.mathematics.geometry.d3.Transformation, vector: numpy.ndarray[numpy.float64[3, 1]]) -> numpy.ndarray[numpy.float64[3, 1]]

   Apply the transformation to a vector.

   Args:

   vector (numpy.ndarray): The vector to transform.

   Returns:

   numpy.ndarray: The transformed vector.

   Example:

   >>> transformation = Transformation.identity()
   >>> vector = Vector3d(1.0, 2.0, 3.0)
   >>> transformed_vector = transformation.apply_to(vector)  # Vector3d(1.0, 2.0, 3.0)
   

get_inverse(

self: ostk.mathematics.geometry.d3.Transformation,

) → ostk.mathematics.geometry.d3.Transformation

Get the inverse transformation.

Returns:

The inverse transformation.

Return type:

Transformation

Example

>>> transformation = Transformation.identity()
>>> inverse = transformation.get_inverse()  # Identity transformation

get_matrix(

self: ostk.mathematics.geometry.d3.Transformation,

) → numpy.ndarray[numpy.float64[4, 4]]

Get the transformation matrix.

Returns:

The 4x4 transformation matrix.

Return type:

numpy.ndarray

Example

>>> transformation = Transformation.identity()
>>> matrix = transformation.get_matrix()  # 4x4 identity matrix

get_type(

self: ostk.mathematics.geometry.d3.Transformation,

) → ostk::mathematics::geometry::d3::Transformation::Type

Get the type of the transformation.

Returns:

The transformation type.

Return type:

Transformation.Type

Example

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

static identity() → ostk.mathematics.geometry.d3.Transformation

Create an identity transformation.

Returns:

An identity transformation.

Return type:

Transformation

Example

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

is_defined(self: ostk.mathematics.geometry.d3.Transformation) → bool

Check if the transformation is defined.

Returns:

True if the transformation is defined.

Return type:

bool

Example

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

static rotation(*args, **kwargs)

Overloaded function.

1. rotation(rotation_vector: ostk::mathematics::geometry::d3::transformation::rotation::RotationVector) -> ostk.mathematics.geometry.d3.Transformation

   Create a rotation transformation from a rotation vector.

   Args:

   rotation_vector (RotationVector): The rotation vector.

   Returns:

   Transformation: A rotation transformation.

   Example:

   >>> rotation_vector = RotationVector(1.0, 2.0, 3.0)
   >>> transformation = Transformation.rotation(rotation_vector)
   >>> transformation.is_defined()  # True
   

2. rotation(rotation_matrix: ostk::mathematics::geometry::d3::transformation::rotation::RotationMatrix) -> ostk.mathematics.geometry.d3.Transformation

   Create a rotation transformation from a rotation matrix.

   Args:

   rotation_matrix (RotationMatrix): The rotation matrix.

   Returns:

   Transformation: A rotation transformation.

   Example:

   >>> rotation_matrix = RotationMatrix(1.0, 2.0, 3.0)
   >>> transformation = Transformation.rotation(rotation_matrix)
   >>> transformation.is_defined()  # True
   

static rotation_around(

point: ostk.mathematics.geometry.d3.object.Point,

rotation_vector: ostk::mathematics::geometry::d3::transformation::rotation::RotationVector,

) → ostk.mathematics.geometry.d3.Transformation

Create a rotation transformation around a point.

Parameters:

• point (Point) -- The point to rotate around.

• rotation_vector (RotationVector) -- The rotation vector.

Returns:

A rotation transformation around the point.

Return type:

Transformation

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> rotation_vector = RotationVector(1.0, 2.0, 3.0)
>>> transformation = Transformation.rotation_around(point, rotation_vector)
>>> transformation.is_defined()  # True

static string_from_type(

type: ostk::mathematics::geometry::d3::Transformation::Type,

) → ostk.core.type.String

Convert a transformation type to a string.

Parameters:

type (Transformation.Type) -- The transformation type.

Returns:

The string representation of the type.

Return type:

str

Example

>>> transformation = Transformation.identity()
>>> transformation.string_from_type()  # "Identity"

static translation(

translation_vector: numpy.ndarray[numpy.float64[3, 1]],

) → ostk.mathematics.geometry.d3.Transformation

Create a translation transformation.

Parameters:

translation_vector (numpy.ndarray) -- The translation vector.

Returns:

A translation transformation.

Return type:

Transformation

Example

>>> translation_vector = Vector3d(1.0, 2.0, 3.0)
>>> transformation = Transformation.translation(translation_vector)
>>> transformation.is_defined()  # True

static type_of_matrix(

matrix: numpy.ndarray[numpy.float64[4, 4]],

) → ostk::mathematics::geometry::d3::Transformation::Type

Determine the type of a transformation matrix.

Parameters:

matrix (numpy.ndarray) -- The 4x4 transformation matrix.

Returns:

The type of the transformation.

Return type:

Transformation.Type

Example

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

static undefined() → ostk.mathematics.geometry.d3.Transformation

Create an undefined transformation.

Returns:

An undefined transformation.

Return type:

Transformation

Example

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