NAG FL Interface
d06daf (dim2_​transform_​affine)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{nv}$ – Integer Input

On entry: the total number of vertices in the input mesh.

Constraint: $\mathbf{nv}\ge 3$.

2: $\mathbf{nedge}$ – Integer Input

On entry: the number of the boundary or interface edges in the input mesh.

Constraint: $\mathbf{nedge}\ge 1$.

3: $\mathbf{nelt}$ – Integer Input

On entry: the number of triangles in the input mesh.

Constraint: $\mathbf{nelt}\le 2\times \mathbf{nv}-1$.

4: $\mathbf{ntrans}$ – Integer Input

On entry: the number of transformations of the input mesh.

Constraint: $\mathbf{ntrans}\ge 1$.

5: $\mathbf{itype}\left(\mathbf{ntrans}\right)$ – Integer array Input

On entry: $\mathbf{itype}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{ntrans}$, indicates the type of each transformation as follows:

$\mathbf{itype}\left(i\right)=0$

Identity transformation.

$\mathbf{itype}\left(i\right)=1$

Translation.

$\mathbf{itype}\left(i\right)=2$

Symmetric transformation with respect to a user-supplied line.

$\mathbf{itype}\left(i\right)=3$

Rotation.

$\mathbf{itype}\left(i\right)=4$

Scaling.

$\mathbf{itype}\left(i\right)=10$

User-supplied analytic transformation.

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

Constraint: $\mathbf{itype}\left(\mathit{i}\right)=0$, $1$, $2$, $3$, $4$ or $10$, for $\mathit{i}=1,2,\dots ,\mathbf{ntrans}$.

6: $\mathbf{trans}\left(6,\mathbf{ntrans}\right)$ – Real (Kind=nag_wp) array Input

On entry: the arguments for each transformation. For $i=1,2,\dots ,\mathbf{ntrans}$, $\mathbf{trans}\left(1,i\right)$ to $\mathbf{trans}\left(6,i\right)$ contain the arguments of the $i$th transformation.

If $\mathbf{itype}\left(i\right)=0$, elements $\mathbf{trans}\left(1,i\right)$ to $\mathbf{trans}\left(6,i\right)$ are not referenced.

If $\mathbf{itype}\left(i\right)=1$, the translation vector is $\overrightarrow{u}=\left(\begin{array}{c}a\\ b\end{array}\right)$, where $a=\mathbf{trans}\left(1,i\right)$ and $b=\mathbf{trans}\left(2,i\right)$, while elements $\mathbf{trans}\left(3,i\right)$ to $\mathbf{trans}\left(6,i\right)$ are not referenced.

If $\mathbf{itype}\left(i\right)=2$, the user-supplied line is the curve {$\left(x,y\right)\in {ℝ}^2$; such that $ax+by+c=0$}, where $a=\mathbf{trans}\left(1,i\right)$, $b=\mathbf{trans}\left(2,i\right)$ and $c=\mathbf{trans}\left(3,i\right)$, while elements $\mathbf{trans}\left(4,i\right)$ to $\mathbf{trans}\left(6,i\right)$ are not referenced.

If $\mathbf{itype}\left(i\right)=3$, the centre of the rotation is $\left(x_0,y_0\right)$ where $x_0=\mathbf{trans}\left(1,i\right)$ and $y_0=\mathbf{trans}\left(2,i\right)$, $\theta =\mathbf{trans}\left(3,i\right)$ is its angle in degrees, while elements $\mathbf{trans}\left(4,i\right)$ to $\mathbf{trans}\left(6,i\right)$ are not referenced.

If $\mathbf{itype}\left(i\right)=4$, $a=\mathbf{trans}\left(1,i\right)$ is the scaling coefficient in the $x$-direction, $b=\mathbf{trans}\left(2,i\right)$ is the scaling coefficient in the $y$-direction, and $\left(x_0,y_0\right)$ are the scaling centre coordinates, with $x_0=\mathbf{trans}\left(3,i\right)$ and $y_0=\mathbf{trans}\left(4,i\right)$; while elements $\mathbf{trans}\left(5,i\right)$ to $\mathbf{trans}\left(6,i\right)$ are not referenced.

If $\mathbf{itype}\left(i\right)=10$, the user-supplied analytic affine transformation $Y=A\times X+B$ is such that $A={\left(a_{kl}\right)}_{1\le k,l\le 2}$ and $B={\left(b_k\right)}_{1\le k\le 2}$ where$a_{kl}=\mathbf{trans}\left(2\times \left(k-1\right)+l,i\right)$, and $b_k=\mathbf{trans}\left(4+k,i\right)$ with $k,l=1,2$.

7: $\mathbf{coori}\left(2,\mathbf{nv}\right)$ – Real (Kind=nag_wp) array Input/Output

On entry: $\mathbf{coori}\left(1,\mathit{i}\right)$ contains the $x$ coordinate of the $\mathit{i}$th vertex of the input mesh, for $\mathit{i}=1,2,\dots ,\mathbf{nv}$; while $\mathbf{coori}\left(2,i\right)$ contains the corresponding $y$ coordinate.

On exit: see Section 9.

8: $\mathbf{edgei}\left(3,\mathbf{nedge}\right)$ – Integer array Input/Output

On entry: the specification of the boundary or interface edges. $\mathbf{edgei}\left(1,j\right)$ and $\mathbf{edgei}\left(2,j\right)$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{edgei}\left(3,j\right)$ is a user-supplied tag for the $j$th boundary edge.

Constraint: $1\le \mathbf{edgei}\left(\mathit{i},\mathit{j}\right)\le \mathbf{nv}$ and $\mathbf{edgei}\left(1,\mathit{j}\right)\ne \mathbf{edgei}\left(2,\mathit{j}\right)$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{nedge}$.

On exit: see Section 9.

9: $\mathbf{conni}\left(3,\mathbf{nelt}\right)$ – Integer array Input/Output

On entry: the connectivity of the input mesh between triangles and vertices. For each triangle $\mathit{j}$, $\mathbf{conni}\left(\mathit{i},\mathit{j}\right)$ gives the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

Constraints:

• $1\le \mathbf{conni}\left(i,j\right)\le \mathbf{nv}$;
• $\mathbf{conni}\left(1,j\right)\ne \mathbf{conni}\left(2,j\right)$;
• $\mathbf{conni}\left(1,\mathit{j}\right)\ne \mathbf{conni}\left(3,\mathit{j}\right)$ and $\mathbf{conni}\left(2,\mathit{j}\right)\ne \mathbf{conni}\left(3,\mathit{j}\right)$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

On exit: see Section 9.

10: $\mathbf{cooro}\left(2,\mathbf{nv}\right)$ – Real (Kind=nag_wp) array Output

On exit: $\mathbf{cooro}\left(1,\mathit{i}\right)$ will contain the $x$ coordinate of the $\mathit{i}$th vertex of the transformed mesh, for $\mathit{i}=1,2,\dots ,\mathbf{nv}$; while $\mathbf{cooro}\left(2,i\right)$ will contain the corresponding $y$ coordinate.

11: $\mathbf{edgeo}\left(3,\mathbf{nedge}\right)$ – Integer array Output

On exit: the specification of the boundary or interface edges of the transformed mesh. If the number of symmetric transformations is even or zero then$\mathbf{edgeo}\left(\mathit{i},\mathit{j}\right)=\mathbf{edgei}\left(\mathit{i},\mathit{j}\right)$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nedge}$; otherwise $\mathbf{edgeo}\left(1,\mathit{j}\right)=\mathbf{edgei}\left(2,\mathit{j}\right)$,$\mathbf{edgeo}\left(2,\mathit{j}\right)=\mathbf{edgei}\left(1,\mathit{j}\right)$ and $\mathbf{edgeo}\left(3,\mathit{j}\right)=\mathbf{edgei}\left(3,\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{nedge}$.

12: $\mathbf{conno}\left(3,\mathbf{nelt}\right)$ – Integer array Output

On exit: the connectivity of the transformed mesh between triangles and vertices. If the number of symmetric transformations is even or zero then$\mathbf{conno}\left(\mathit{i},\mathit{j}\right)=\mathbf{conni}\left(\mathit{i},\mathit{j}\right)$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$; otherwise $\mathbf{conno}\left(1,\mathit{j}\right)=\mathbf{conni}\left(1,\mathit{j}\right)$, $\mathbf{conno}\left(2,\mathit{j}\right)=\mathbf{conni}\left(3,\mathit{j}\right)$ and $\mathbf{conno}\left(3,\mathit{j}\right)=\mathbf{conni}\left(2,\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{nelt}$.

13: $\mathbf{itrace}$ – Integer Input

On entry: the level of trace information required from d06daf.

$\mathbf{itrace}\le 0$

No output is generated.

$\mathbf{itrace}\ge 1$

Details of each transformation, the matrix $A$ and the vector $B$ of the final transformation, which is the composition of all the ntrans transformations, are printed on the current advisory message unit (see x04abf).

14: $\mathbf{rwork}\left(\mathbf{lrwork}\right)$ – Real (Kind=nag_wp) array Workspace

15: $\mathbf{lrwork}$ – Integer Input

On entry: the dimension of the array rwork as declared in the (sub)program from which d06daf is called.

Constraint: $\mathbf{lrwork}\ge 12\times \mathbf{ntrans}$.

16: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{conni}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{conni}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{conni}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nv}$.

On entry, $\mathbf{edgei}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{edgei}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{edgei}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nv}$.

On entry, $\mathbf{itype}\left(\mathit{I}\right)=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{itype}\left(\mathit{I}\right)=0$, $1$, $2$, $3$, $4$ or $10$.

On entry, $\mathbf{lrwork}=〈\mathit{\text{value}}〉$ and $\mathrm{LRWKMN}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lrwork}\ge \mathrm{LRWKMN}$.

On entry, $\mathbf{nedge}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nedge}\ge 1$.

On entry, $\mathbf{nelt}=〈\mathit{\text{value}}〉$ and $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nelt}\le 2\times \mathbf{nv}-1$.

On entry, $\mathbf{ntrans}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ntrans}>0$.

On entry, $\mathbf{nv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nv}\ge 3$.

On entry, the end points of the edge $\mathit{J}$ have the same index $\mathit{I}$: $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $1$ and $2$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $1$ and $3$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

On entry, vertices $2$ and $3$ of the triangle $\mathit{K}$ have the same index $\mathit{I}$: $\mathit{K}=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example