NAG Library Routine Document

D06DAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NV – INTEGERInput

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

Constraint: NV≥3.

2:     NEDGE – INTEGERInput

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

Constraint: NEDGE≥1.

3:     NELT – INTEGERInput

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

Constraint: NELT≤2×NV-1.

4:     NTRANS – INTEGERInput

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

Constraint: NTRANS≥1.

5:     ITYPE(NTRANS) – INTEGER arrayInput

On entry: ITYPEi, for i=1,2,…,NTRANS, indicates the type of each transformation as follows:

ITYPEi=0

Identity transformation.

ITYPEi=1

Translation.

ITYPEi=2

Symmetric transformation with respect to a user-supplied line.

ITYPEi=3

Rotation.

ITYPEi=4

Scaling.

ITYPEi=10

User-supplied analytic transformation.

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

Constraint: ITYPEi=0, 1, 2, 3, 4 or 10, for i=1,2,…,NTRANS.

6:     TRANS(6,NTRANS) – double precision arrayInput

On entry: the parameters for each transformation. For i=1,2,…,NTRANS, TRANS1i to TRANS6i contain the parameters of the ith transformation.

If ITYPEi=0, elements TRANS1i to TRANS6i are not referenced.

If ITYPEi=1, the translation vector is u→= a b , where a=TRANS1i and b=TRANS2i, while elements TRANS3i to TRANS6i are not referenced.

If ITYPEi=2, the user-supplied line is the curve {x,y∈ℝ2; such that ax+by+c=0}, where a=TRANS1i, b=TRANS2i and c=TRANS3i, while elements TRANS4i to TRANS6i are not referenced.

If ITYPEi=3, the centre of the rotation is x0,y0 where x0=TRANS1i and y0=TRANS2i, θ=TRANS3i is its angle in degrees, while elements TRANS4i to TRANS6i are not referenced.

If ITYPEi=4, a=TRANS1i is the scaling coefficient in the x-direction, b=TRANS2i is the scaling coefficient in the y-direction, and x0,y0 are the scaling centre co-ordinates, with x0=TRANS3i and y0=TRANS4i; while elements TRANS5i to TRANS6i are not referenced.

If ITYPEi=10, the user-supplied analytic affine transformation Y=A×X+B is such that A=akl1≤k,l≤2 and B=bk1≤k≤2 where akl=TRANS2×k-1+li, and bk=TRANS4+ki with k,l=1,2.

7:     COORI(2,NV) – double precision arrayInput/Output

On entry: COORI1i contains the x co-ordinate of the ith vertex of the input mesh, for i=1,2,…,NV; while COORI2i contains the corresponding y co-ordinate.

On exit: see Section 8.

8:     EDGEI(3,NEDGE) – INTEGER arrayInput/Output

On entry: the specification of the boundary or interface edges. EDGEI1j and EDGEI2j contain the vertex numbers of the two end points of the jth boundary edge. EDGEI3j is a user-supplied tag for the jth boundary edge.

On exit: see Section 8.

Constraint: 1≤EDGEIij≤NV and EDGEI1j≠EDGEI2j, for i=1,2 and j=1,2,…,NEDGE.

9:     CONNI(3,NELT) – INTEGER arrayInput/Output

On entry: the connectivity of the input mesh between triangles and vertices. For each triangle j, CONNIij gives the indices of its three vertices (in anticlockwise order), for i=1,2,3 and j=1,2,…,NELT.

On exit: see Section 8.

Constraints:

• 1≤CONNIij≤NV;
• CONNI1j≠CONNI2j;
• CONNI1j≠CONNI3j and CONNI2j≠CONNI3j, for i=1,2,3 and j=1,2,…,NELT.

10:   COORO(2,NV) – double precision arrayOutput

On exit: COORO1i will contain the x co-ordinate of the ith vertex of the transformed mesh, for i=1,2,…,NV; while COORO2i will contain the corresponding y co-ordinate.

11:   EDGEO(3,NEDGE) – INTEGER arrayOutput

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 EDGEOij=EDGEIij, for i=1,2,3 and j=1,2,…,NEDGE; otherwise EDGEO1j=EDGEI2j, EDGEO2j=EDGEI1j and EDGEO3j=EDGEI3j, for j=1,2,…,NEDGE.

12:   CONNO(3,NELT) – INTEGER arrayOutput

On exit: the connectivity of the transformed mesh between triangles and vertices. If the number of symmetric transformations is even or zero then CONNOij=CONNIij, for i=1,2,3 and j=1,2,…,NELT; otherwise CONNO1j=CONNI1j, CONNO2j=CONNI3j and CONNO3j=CONNI2j, for j=1,2,…,NELT.

13:   ITRACE – INTEGERInput

On entry: the level of trace information required from D06DAF.

ITRACE≤0

No output is generated.

ITRACE≥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:   RWORK(LRWORK) – double precision arrayWorkspace

15:   LRWORK – INTEGERInput

On entry: the dimension of the array RWORK as declared in the (sub)program from which D06DAF is called.

Constraint: LRWORK≥12×NTRANS.

16:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to 0, -1​ or ​1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

On exit: IFAIL=0 unless the routine detects an error (see Section 6).

For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ or ​1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1​ or ​1 is used it is essential to test the value of IFAIL on exit.

6  Error Indicators and Warnings

IFAIL=1

On entry,	NV<3;
or	NELT>2×NV-1;
or	NEDGE<1;
or	EDGEIij<1 or EDGEIij>NV for some i=1,2 and j=1,2,…,NEDGE;
or	EDGEI1j=EDGEI2j for some j=1,2,…,NEDGE;
or	CONNIij<1 or CONNIij>NV for some i=1,2,3 and j=1,2,…,NELT;
or	CONNI1j=CONNI2j or CONNI1j=CONNI3j or CONNI2j=CONNI3j for some j=1,2,…,NELT;
or	NTRANS<1;
or	ITYPEi≠0, 1, 2, 3, 4 or 10 for some i=1,2,…,NTRANS;
or	LRWORK<12×NTRANS.

IFAIL=2

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

7  Accuracy

8  Further Comments

9  Example