naginterfaces.library.mesh.dim2_​transform_​affine

naginterfaces.library.mesh.dim2_transform_affine(mode, itype, trans, coori, edgei, conni, itrace, io_manager=None)[source]

dim2_transform_affine is a utility which performs an affine transformation of a given mesh.

For full information please refer to the NAG Library document for d06da

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/d06/d06daf.html

Parameters
modeint

If , the arguments , and are overwritten on exit by the output values described in , and respectively. In this case , and are not referenced, and you can save storage space.

If , no such aliasing is assumed.

itypeint, array-like, shape

, for , indicates the type of each transformation as follows:

Identity transformation.

Translation.

Symmetric transformation with respect to a user-supplied line.

Rotation.

Scaling.

User-supplied analytic transformation.

Note that the transformations are applied in the order described in .

transfloat, array-like, shape

The arguments for each transformation. For , to contain the arguments of the th transformation.

If , elements to are not referenced.

If , the translation vector is , where and , while elements to are not referenced.

If , the user-supplied line is the curve {; such that }, where , and , while elements to are not referenced.

If , the centre of the rotation is where and , is its angle in degrees, while elements to are not referenced.

If , is the scaling coefficient in the -direction, is the scaling coefficient in the -direction, and are the scaling centre coordinates, with and ; while elements to are not referenced.

If , the user-supplied analytic affine transformation is such that and where, and with .

coorifloat, array-like, shape

contains the coordinate of the th vertex of the input mesh, for ; while contains the corresponding coordinate.

edgeiint, array-like, shape

The specification of the boundary or interface edges. and contain the vertex numbers of the two end points of the th boundary edge. is a user-supplied tag for the th boundary edge.

conniint, array-like, shape

The connectivity of the input mesh between triangles and vertices. For each triangle , gives the indices of its three vertices (in anticlockwise order), for , for .

itraceint

The level of trace information required from dim2_transform_affine.

No output is generated.

Details of each transformation, the matrix and the vector of the final transformation, which is the composition of all the transformations, are printed.

io_managerFileObjManager, optional

Manager for I/O in this routine.

Returns
coorifloat, ndarray, shape

See Further Comments.

edgeiint, ndarray, shape

If , holds the output values described in .

conniint, ndarray, shape

If , holds the output values described in .

cooroNone or float, ndarray, shape

will contain the coordinate of the th vertex of the transformed mesh, for ; while will contain the corresponding coordinate.

edgeoNone or int, ndarray, shape

The specification of the boundary or interface edges of the transformed mesh. If the number of symmetric transformations is even or zero then , for , for ; otherwise , and , for .

connoNone or int, ndarray, shape

The connectivity of the transformed mesh between triangles and vertices. If the number of symmetric transformations is even or zero then , for , for ; otherwise , and , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: , , , , or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, , , and .

Constraint: and .

(errno )

On entry, , , and .

Constraint: and .

(errno )

On entry, .

Constraint: .

(errno )

On entry, the end points of the edge have the same index : and .

(errno )

On entry, vertices and of the triangle have the same index : and .

(errno )

On entry, vertices and of the triangle have the same index : and .

(errno )

On entry, vertices and of the triangle have the same index : and .

(errno )

A serious error has occurred in an internal call to an auxiliary function. Check the input mesh especially the connectivities and the details of each transformations.

Notes

dim2_transform_affine generates a mesh (coordinates, triangle/vertex connectivities and edge/vertex connectivities) resulting from an affine transformation of a given mesh. This transformation is of the form , where

, and are in , and

is a real matrix.

Such a transformation includes a translation, a rotation, a scale reduction or increase, a symmetric transformation with respect to a user-supplied line, a user-supplied analytic transformation, or a composition of several transformations.

This function is partly derived from material in the MODULEF package from INRIA (Institut National de Recherche en Informatique et Automatique).