4.1.1.9.1.10. pyfem.util.transformations module

getRotationMatrix(el_coords: ndarray) → ndarray[source]

Compute the 2D rotation matrix for an element.

Calculates the rotation matrix that transforms from global coordinates to element coordinates based on the element’s orientation in 2D space.

Parameters:

el_coords – Element node coordinates as (2, 2) array where rows are nodes

Returns:

2x2 rotation matrix for coordinate transformation

Raises:

NotImplementedError – If element coordinates are not 2D (shape[1] != 2)

vectorToElementCoordinates(a: ndarray, el_coords: ndarray) → ndarray[source]

Transform a vector from global to element coordinates.

Rotates a vector (or block of vectors) from the global coordinate system to the element coordinate system. Handles vectors with multiple components.

Parameters:

  • a – Vector in global coordinates with shape (n,) where n is divisible by 2

  • el_coords – Element node coordinates as (2, 2) array

Returns:

Vector in element coordinates with same shape as input

Raises:

RuntimeError – If vector length is not divisible by rotation matrix size

matrixToElementCoordinates(a: ndarray, el_coords: ndarray) → ndarray[source]

Transform a matrix from global to element coordinates.

Rotates a square matrix (or block matrix) from the global coordinate system to the element coordinate system using: a_bar = R @ a @ R^T

Parameters:

  • a – Square matrix in global coordinates with shape (m, m) where m is divisible by 2

  • el_coords – Element node coordinates as (2, 2) array

Returns:

Matrix in element coordinates with same shape as input

Raises:

RuntimeError – If matrix dimensions are not divisible by rotation matrix size

vectorToGlobalCoordinates(a_bar: ndarray, el_coords: ndarray) → ndarray[source]

Transform a vector from element to global coordinates.

Rotates a vector (or block of vectors) from the element coordinate system back to the global coordinate system. Inverse of vectorToElementCoordinates.

Parameters:

  • a_bar – Vector in element coordinates with shape (n,) where n is divisible by 2

  • el_coords – Element node coordinates as (2, 2) array

Returns:

Vector in global coordinates with same shape as input

Raises:

RuntimeError – If vector length is not divisible by rotation matrix size

matrixToGlobalCoordinates(a_bar: ndarray, el_coords: ndarray) → ndarray[source]

Transform a matrix from element to global coordinates.

Rotates a square matrix (or block matrix) from the element coordinate system back to the global coordinate system using: a = R^T @ a_bar @ R Inverse of matrixToElementCoordinates.

Parameters:

  • a_bar – Square matrix in element coordinates with shape (m, m) where m is divisible by 2

  • el_coords – Element node coordinates as (2, 2) array

Returns:

Matrix in global coordinates with same shape as input

Raises:

RuntimeError – If matrix dimensions are not divisible by rotation matrix size

toElementCoordinates(a: ndarray, el_coords: ndarray) → ndarray[source]

Transform array (vector or matrix) from global to element coordinates.

Dispatcher function that automatically detects input type (1D vector or 2D matrix) and applies the appropriate transformation. Rotates from global to element coordinate system.

Parameters:

  • a – Input vector (shape (n,)) or matrix (shape (m, m)) in global coordinates

  • el_coords – Element node coordinates as (2, 2) array

Returns:

Transformed array in element coordinates with same shape as input

Raises:

  • NotImplementedError – If input is not a 1D or 2D ndarray

  • RuntimeError – If array dimensions are incompatible with rotation matrix

toGlobalCoordinates(a: ndarray, el_coords: ndarray) → ndarray[source]

Transform array (vector or matrix) from element to global coordinates.

Dispatcher function that automatically detects input type (1D vector or 2D matrix) and applies the appropriate transformation. Rotates from element to global coordinate system. Inverse of toElementCoordinates.

Parameters:

  • a – Input vector (shape (n,)) or matrix (shape (m, m)) in element coordinates

  • el_coords – Element node coordinates as (2, 2) array

Returns:

Transformed array in global coordinates with same shape as input

Raises:

  • NotImplementedError – If input is not a 1D or 2D ndarray

  • RuntimeError – If array dimensions are incompatible with rotation matrix