coordinate_transformation_surface.py¶
Compute the coordinate transformation related variables for a
surface mapping, ,
We get an instance of class CoordinateTransformationSurface
. The
transformations are its methods.
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- class coordinate_transformation_surface.CoordinateTransformationSurface(Psi, d_Psi, iJM=None)[source]¶
The surface coordinate transformation class.
- Parameters:
Psi (function) –
The mapping
. It should be a function which returns three components of the mapping, i.e.,
d_Psi (function) –
The Jacobian matrix of
,
. It should be a function return the 6 (3*2) components of the Jacobian matrix, i.e.,
(
,
), (
,
), (
,
).
iJM – The inverse Jacobian matrix.
- Example:
>>> ctS = CoordinateTransformationSurface(Psi, d_Psi) >>> rho = np.linspace(-1,1,20) >>> tau = np.linspace(-1,1,20) >>> rho, tau = np.meshgrid(rho, tau, indexing='ij') >>> x, y, z = ctS.mapping(rho, tau) >>> J = ctS.Jacobian_matrix(rho, tau) >>> np.shape(J) (3, 2, 20, 20) >>> G = ctS.metric_matrix(rho, tau) >>> np.shape(G) (2, 2, 20, 20) >>> g = ctS.metric(rho, tau) >>> np.shape(g) (20, 20)
- Jacobian_matrix(rho, tau)[source]¶
A wrap of the input Jacobian matrix,
d_Psi
, i.e.,.
- Returns:
Return the Jacobian matrix
:
- inverse_Jacobian_matrix(rho, tau)[source]¶
Compute the inverse Jacobian matrix,
.
- Returns:
Return the inverse Jacobian matrix
:
- coordinate_transformation_surface.extract_surface_coordinate_transformations_of(ct, which_sides=None)[source]¶
We extract the six boundary coordinate transformations from a
CoordinateTransformation
instance representing a 3D mapping.
- Parameters:
ct (CoordinateTransformation) – A CoordinateTransformation instance that represents the mapping
.
which_sides – (default:
None
) We want to extract sub-mappings on which sides?
- Returns:
A tuple of 6
CoordinateTransformationSurface
instances representing the north (), south (
), west (
), east (
), back (
) and front (
) boundaries.
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