Muscat.LinAlg.Transform module

CheckIntegrity(GUI: bool = False)

class Transform(offset: ArrayLike | None = None, first: ArrayLike | None = None, second: ArrayLike | None = None)

Bases: object

ApplyInvTransform(point: ArrayLike) → np.ndarray

we apply inverse of the transformation

#p = M^-1*point+self.offset

Parameters:

point (ArrayLike) – List of points to apply the transformation

Returns:

the position of the point on the new reference system

Return type:

np.ndarray

ApplyInvTransformDirection(point: ArrayLike) → np.ndarray

we apply inverse of the transformation (only the direction, no offset)

p = M^-1*(point)

Parameters:

point (ArrayLike) – List of points to apply the transformation

Returns:

the position of the point on the new reference system

Return type:

np.ndarray

ApplyInvTransformTensor(tensor: ArrayLike) → np.ndarray

Apply the inverse of the transformation on a tensor

Parameters:

tensor (ArrayLike) – np array of size (3,3)

Returns:

the tensor on the (old) base

Return type:

np.ndarray

ApplyTransform(point: ArrayLike) → np.ndarray

p = M*(point-self.offset)

Parameters:

point (ArrayLike) – List of points to apply the transformation

Returns:

the position of the point on the new reference system

Return type:

np.ndarray

ApplyTransformDirection(point: ArrayLike) → np.ndarray

Apply only the direction transformation (not the offset)

p = M*(point)

Parameters:

point (ArrayLike) – List of points to apply the transformation

Returns:

the position of the point on the new reference system

Return type:

np.ndarray

ApplyTransformTensor(tensor: ArrayLike) → np.ndarray

Apply rotation on a tensor

Parameters:

tensor (ArrayLike) – np array of size (3,3)

Returns:

the tensor on the new base

Return type:

np.ndarray

GetDirection(i: MuscatIndex, pos: ArrayLike | None = None, direction: ArrayLike | None = None) → np.ndarray

Return the direction of the i component of the coordinate system. for linear transformation pos is not used

Parameters:

• i (MuscatIndex) – must be in [0,2]

• pos (Optional[ArrayLike], optional) – _description_, by default None

• direction (Optional[ArrayLike], optional) – _description_, by default None

Returns:

the i vector of the base

Return type:

np.ndarray

GetOrthoNormalBase() → Transform

Return a new transform but with orthogonal base

Returns:

_description_

Return type:

Transform

SetAsRotationAroundAxis(vector: ArrayLike, angle: float64, center: ArrayLike | None = None) → None

Setter method for setting the transform as a rotation around a vector with a given angle the transformation matrix and offset are computed from the center and the angle :param vector: must be 1D of size 3, vector around which the rotation is performed :type vector: ArrayLike :param angle: angle (in rad) for the rotation :type angle: MuscatFloat :param center: center point for the rotation of size 3, by default None :type center: Optional[ArrayLike], optional

SetFirst(data: ArrayLike) → None

define the x coordinate (direction) with respect to the new origin

Parameters:

data (ArrayLike) – the first direction of the coordinate system

SetOffset(data: ArrayLike) → None

Set the origin of the new coordinate system

Parameters:

data (ArrayLike) – offset

SetOpUsingThird(third: ArrayLike) → None

SetOperator(first: ArrayLike | None = None, second: ArrayLike | None = None, third: ArrayLike | None = None, op=None) → None

SetSecond(data: ArrayLike | None = None) → None

Define the y coordinate (direction) with respect to the new origin # the z direction is calculated with a cross product

Parameters:

data (ArrayLike, optional) – if non the second vector of the internal rotation matrix is used , by default None

Raises:

ValueError – RuntimeError if the incoming vector is colinear to the first vector

SetThird(data: ArrayLike | None = None) → None

Define the z coordinate (direction) with respect to the new origin # the z direction is calculated with a cross product of x, y

Parameters:

data (ArrayLike, optional) – _description_, by default None

Raises:

ValueError – if the incoming vector is colinear to x, y

class Transform2D(offset: ArrayLike | None = None, first: ArrayLike | None = None, second: ArrayLike | None = None)

Bases: object

This class is a wrapper around the Transform class to work on points in 2D. Please refer to the documentation of Transform for all the functions

ApplyInvTransform(points: np.ndarray)

ApplyInvTransformDirection(point: np.ndarray)

ApplyTransform(points: np.ndarray)

ApplyTransformDirection(direction: np.ndarray)

EnsureIn2D(data)

EnsureIn3D(data: np.ndarray | None) → np.ndarray

GetDirection(i: MuscatIndex, pos: np.ndarray | None = None, direction: np.ndarray | None = None)

GetOrthoNormalBase()

SetFirst(data)

SetOffset(data)

property keepNormalized

property keepOrthogonal