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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_mesh_2d_gen_boundary (d06ba)

Purpose

nag_mesh_2d_gen_boundary (d06ba) generates a boundary mesh on a closed connected subdomain ΩΩ of 22.

Syntax

[nvb, coor, nedge, edge, user, ifail] = d06ba(coorch, lined, fbnd, crus, rate, nlcomp, lcomp, nvmax, nedmx, itrace, 'nlines', nlines, 'sdcrus', sdcrus, 'ncomp', ncomp, 'user', user)
[nvb, coor, nedge, edge, user, ifail] = nag_mesh_2d_gen_boundary(coorch, lined, fbnd, crus, rate, nlcomp, lcomp, nvmax, nedmx, itrace, 'nlines', nlines, 'sdcrus', sdcrus, 'ncomp', ncomp, 'user', user)

Description

Given a closed connected subdomain ΩΩ of 22, whose boundary ΩΩ is divided by characteristic points into mm distinct line segments, nag_mesh_2d_gen_boundary (d06ba) generates a boundary mesh on ΩΩ. Each line segment may be a straight line, a curve defined by the equation f(x,y) = 0f(x,y)=0, or a polygonal curve defined by a set of given boundary mesh points.
This function is primarily designed for use with either nag_mesh_2d_gen_inc (d06aa) (a simple incremental method) or nag_mesh_2d_gen_delaunay (d06ab) (Delaunay–Voronoi method) or nag_mesh_2d_gen_front (d06ac) (Advancing Front method) to triangulate the interior of the domain ΩΩ. For more details about the boundary and interior mesh generation, consult the D06 Chapter Introduction as well as George and Borouchaki (1998).
This function is derived from material in the MODULEF package from INRIA (Institut National de Recherche en Informatique et Automatique).

References

George P L and Borouchaki H (1998) Delaunay Triangulation and Meshing: Application to Finite Elements Editions HERMES, Paris

Parameters

Compulsory Input Parameters

1:     coorch(22,nlines) – double array
coorch(1,i)coorch1i contains the xx coordinate of the iith characteristic point, for i = 1,2,,nlinesi=1,2,,nlines; while coorch(2,i)coorch2i contains the corresponding yy coordinate.
2:     lined(44,nlines) – int64int32nag_int array
The description of the lines that define the boundary domain. The line ii, for i = 1,2,,mi=1,2,,m, is defined as follows:
lined(1,i)lined1i
The number of points on the line, including two end points.
lined(2,i)lined2i
The first end point of the line. If lined(2,i) = jlined2i=j, then the coordinates of the first end point are those stored in coorch( : ,j)coorch:j.
lined(3,i)lined3i
The second end point of the line. If lined(3,i) = klined3i=k, then the coordinates of the second end point are those stored in coorch( : ,k)coorch:k.
lined(4,i)lined4i
This defines the type of line segment connecting the end points. Additional information is conveyed by the numerical value of lined(4,i)lined4i as follows:
(i) lined(4,i) > 0lined4i>0, the line is described in fbnd with lined(4,i)lined4i as the index. In this case, the line must be described in the trigonometric (anticlockwise) direction;
(ii) lined(4,i) = 0lined4i=0, the line is a straight line;
(iii) if lined(4,i) < 0lined4i<0, say (p-p), then the line is a polygonal arc joining the end points and interior points specified in crus. In this case the line contains the points whose coordinates are stored in
coorch( : ,j) ,  crus( : ,p) ,  crus( : ,p + 1) ,, crus( : ,p + r3) ,  coorch( : ,k) coorch:j , crus:p , crus:p+1 ,, crus:p+r-3 , coorch:k  ,
where z{1,2}z{1,2}, r = lined(1,i)r=lined1i, j = lined(2,i)j=lined2i and k = lined(3,i)k=lined3i.
Constraints:
For each line described by fbnd (lines with lined(4,i) > 0 lined4i > 0 , for i = 1,2,,nlinesi=1,2,,nlines) the two end points ( lined(2,i) lined2i  and lined(3,i) lined3i ) lie on the curve defined by index lined(4,i)lined4i in fbnd, i.e.,
fbnd (lined(4,i),coorch(1,lined(2,i)),coorch(2,lined(2,i)),user,user) = 0 fbnd (lined4i,coorch1lined2i,coorch2lined2i,user,user) = 0 ;
fbnd (lined(4,i),coorch(1,lined(3,i)),coorch(2,lined(3,i)),user,user) = 0 fbnd (lined4i,coorch1lined3i,coorch2lined3i,user,user) = 0 , for i = 1,2,,nlinesi=1,2,,nlines.
For all lines described as polygonal arcs (lines with lined(4,i) < 0 lined4i < 0 , for i = 1,2,,nlinesi=1,2,,nlines) the sets of intermediate points (i.e., [lined(4,i) : lined(4,i) + lined(1,i) 3 ] [-lined4i : -lined4i + lined1i - 3 ]  for all ii such that lined(4,i) < 0lined4i<0) are not overlapping. This can be expressed as:
lined(4,i) + lined(1,i)3 =  { lined(1,i) 2 }
{i,lined(4,i) < 0}
-lined4i + lined1i - 3 = {i,lined4i<0} { lined1i - 2 }
or
lined(4,i) + lined(1,i) 2 = lined(4,j) ,
-lined4i + lined1i - 2 = -lined4j ,
for a jj such that j = 1,2,,nlinesj=1,2,,nlines, jiji and lined(4,j) < 0lined4j<0.
3:     fbnd – function handle or string containing name of m-file
fbnd must be supplied to calculate the value of the function which describes the curve {(x,y)2; such that ​f(x,y) = 0} { (x,y) 2; such that ​f (x,y)=0}  on segments of the boundary for which lined(4,i) > 0lined4i>0. If there are no boundaries for which lined(4,i) > 0lined4i>0 fbnd will never be referenced by nag_mesh_2d_gen_boundary (d06ba) and fbnd may be the string 'd06bad'. (nag_mesh_2d_gen_boundary_dummy_fbnd (d06bad) is included in the NAG Toolbox.)
[result, user] = fbnd(ii, x, y, user)

Input Parameters

1:     ii – int64int32nag_int scalar
lined(4,i)lined4i, the reference index of the line (portion of the contour) ii described.
2:     x – double scalar
3:     y – double scalar
The values of xx and yy at which f(x,y)f(x,y) is to be evaluated.
4:     user – Any MATLAB object
fbnd is called from nag_mesh_2d_gen_boundary (d06ba) with the object supplied to nag_mesh_2d_gen_boundary (d06ba).

Output Parameters

1:     result – double scalar
The result of the function.
2:     user – Any MATLAB object
4:     crus(22,sdcrus) – double array
The coordinates of the intermediate points for polygonal arc lines. For a line ii defined as a polygonal arc (i.e., lined(4,i) < 0lined4i<0), if p = lined(4,i)p=-lined4i, then crus(1,k)crus1k, for k = p,,p + lined(1,i)3k=p,,p+lined1i-3, must contain the xx coordinate of the consecutive intermediate points for this line. Similarly crus(2,k)crus2k, for k = p,,p + lined(1,i)3k=p,,p+lined1i-3, must contain the corresponding yy coordinate.
5:     rate(nlines) – double array
nlines, the dimension of the array, must satisfy the constraint nlines1nlines1.
rate(i)ratei is the geometric progression ratio between the points to be generated on the line ii, for i = 1,2,,mi=1,2,,m and lined(4,i)0lined4i0.
If lined(4,i) < 0lined4i<0, rate(i)ratei is not referenced.
Constraint: if lined(4,i)0lined4i0, rate(i) > 0.0ratei>0.0, for i = 1,2,,nlinesi=1,2,,nlines.
6:     nlcomp(ncomp) – int64int32nag_int array
ncomp, the dimension of the array, must satisfy the constraint ncomp1ncomp1.
|nlcomp(k)||nlcompk| is the number of line segments in component kk of the contour. The line ii of component kk runs in the direction lined(2,i)lined2i to lined(3,i)lined3i if nlcomp(k) > 0nlcompk>0, and in the opposite direction otherwise; for k = 1,2,,nk=1,2,,n.
Constraints:
  • 1|nlcomp(k)|nlines1|nlcompk|nlines, for k = 1,2,,ncompk=1,2,,ncomp;
  • k = 1 n |nlcomp(k)| = nlines k =1 n | nlcompk | =nlines .
7:     lcomp(nlines) – int64int32nag_int array
nlines, the dimension of the array, must satisfy the constraint nlines1nlines1.
lcomp(l1 : l2) lcompl1:l2, where l2 = i = 1k |nlcomp(i)| l2 = i=1 k |nlcompi|  and l1 = l2 + 1|nlcomp(k)|l1=l2+1-|nlcompk| is the list of line numbers for the kkth components of the boundary, for k = 1,2,,ncompk=1,2,,ncomp.
Constraint: lcomplcomp must hold a valid permutation of the integers [1,nlines][1,nlines].
8:     nvmax – int64int32nag_int scalar
The maximum number of the boundary mesh vertices to be generated.
Constraint: nvmaxnlinesnvmaxnlines.
9:     nedmx – int64int32nag_int scalar
The maximum number of boundary edges in the boundary mesh to be generated.
Constraint: nedmx1nedmx1.
10:   itrace – int64int32nag_int scalar
The level of trace information required from nag_mesh_2d_gen_boundary (d06ba).
itrace = 0itrace=0 or itrace < 1itrace<-1
No output is generated.
itrace = 1itrace=1
Output from the boundary mesh generator is printed on the current advisory message unit (see nag_file_set_unit_advisory (x04ab)). This output contains the input information of each line and each connected component of the boundary.
itrace = 1itrace=-1
An analysis of the output boundary mesh is printed on the current advisory message unit. This analysis includes the orientation (clockwise or anticlockwise) of each connected component of the boundary. This information could be of interest to you, especially if an interior meshing is carried out using the output of this function, calling either nag_mesh_2d_gen_inc (d06aa), nag_mesh_2d_gen_delaunay (d06ab) or nag_mesh_2d_gen_front (d06ac).
itrace > 1itrace>1
The output is similar to that produced when itrace = 1itrace=1, but the coordinates of the generated vertices on the boundary are also output.
You are advised to set itrace = 0itrace=0, unless you are experienced with finite element mesh generation.

Optional Input Parameters

1:     nlines – int64int32nag_int scalar
Default: The dimension of the arrays coorch, lined, rate, lcomp. (An error is raised if these dimensions are not equal.)
mm, the number of lines that define the boundary of the closed connected subdomain (this equals the number of characteristic points which separate the entire boundary ΩΩ into lines).
Constraint: nlines1nlines1.
2:     sdcrus – int64int32nag_int scalar
Default: The second dimension of the array crus.
The second dimension of the array crus as declared in the (sub)program from which nag_mesh_2d_gen_boundary (d06ba) is called.
Constraint: sdcrus{i,lined(4,i) < 0} {lined(1,i)2}sdcrus{i,lined4i<0}{lined1i-2}.
3:     ncomp – int64int32nag_int scalar
Default: The dimension of the array nlcomp.
nn, the number of separately connected components of the boundary.
Constraint: ncomp1ncomp1.
4:     user – Any MATLAB object
user is not used by nag_mesh_2d_gen_boundary (d06ba), but is passed to fbnd. Note that for large objects it may be more efficient to use a global variable which is accessible from the m-files than to use user.

Input Parameters Omitted from the MATLAB Interface

ruser iuser rwork lrwork iwork liwork

Output Parameters

1:     nvb – int64int32nag_int scalar
The total number of boundary mesh vertices generated.
2:     coor(22,nvmax) – double array
coor(1,i)coor1i will contain the xx coordinate of the iith boundary mesh vertex generated, for i = 1,2,,nvbi=1,2,,nvb; while coor(2,i)coor2i will contain the corresponding yy coordinate.
3:     nedge – int64int32nag_int scalar
The total number of boundary edges in the boundary mesh.
4:     edge(33,nedmx) – int64int32nag_int array
The specification of the boundary edges. edge(1,j)edge1j and edge(2,j)edge2j will contain the vertex numbers of the two end points of the jjth boundary edge. edge(3,j)edge3j is a reference number for the jjth boundary edge and
  • edge(3,j) = lined(4,i)edge3j=lined4i, where ii and jj are such that the jjth edges is part of the iith line of the boundary and lined(4,i)0lined4i0;
  • edge(3,j) = 100 + |lined(4,i)|edge3j=100+|lined4i|, where ii and jj are such that the jjth edges is part of the iith line of the boundary and lined(4,i) < 0lined4i<0.
5:     user – Any MATLAB object
6:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry,nlines < 1nlines<1;
ornvmax < nlinesnvmax<nlines;
ornedmx < 1nedmx<1;
orncomp < 1ncomp<1;
orlrwork < 2 × (nlines + sdcrus) + 2 × maxi = 1,2,,m{lined(1,i)} × nlineslrwork<2×(nlines+sdcrus)+2×maxi=1,2,,m{lined1i}×nlines;
or liwork < {i, lined(4,i) < 0 }  {lined(1,i)2} + 8 × nlines + nvmax + 3 ×   nedmx + 2 × sdcrus liwork < {i, lined4 i < 0 } { lined1 i -2 } +8 × nlines +nvmax +3 × nedmx +2 × sdcrus ;
or sdcrus < {i, lined(4,i) < 0 }  {lined(1,i)2} sdcrus < {i, lined4 i < 0 } { lined1 i -2 } ;
orrate(i) < 0.0ratei<0.0 for some i = 1,2,,nlinesi=1,2,,nlines with lined(4,i)0lined4i0;
orlined(1,i) < 2lined1i<2 for some i = 1,2,,nlinesi=1,2,,nlines;
orlined(2,i) < 1lined2i<1 or lined(2,i) > nlineslined2i>nlines for some i = 1,2,,nlinesi=1,2,,nlines;
orlined(3,i) < 1lined3i<1 or lined(3,i) > nlineslined3i>nlines for some i = 1,2,,nlinesi=1,2,,nlines;
orlined(2,i) = lined(3,i)lined2i=lined3i for some i = 1,2,,nlinesi=1,2,,nlines;
ornlcomp(k) = 0nlcompk=0, or |nlcomp(k)| > nlines|nlcompk|>nlines for a k = 1,2,,ncompk=1,2,,ncomp;
or k = 1 n |nlcomp(k)| nlines k =1 n | nlcomp k | nlines ;
orlcomp does not represent a valid permutation of the integers in [1,nlines][1,nlines];
orone of the end points for a line ii described by the user-supplied function (lines with lined(4,i) > 0lined4i>0, for i = 1,2,,nlinesi=1,2,,nlines) does not belong to the corresponding curve in fbnd;
orthe intermediate points for the lines described as polygonal arcs (lines with lined(i) < 0linedi<0, for i = 1,2,,nlinesi=1,2,,nlines) are overlapping.
  ifail = 2ifail=2
An error has occurred during the generation of the boundary mesh. It appears that nedmx is not large enough, so you are advised to increase the value of nedmx.
  ifail = 3ifail=3
An error has occurred during the generation of the boundary mesh. It appears that nvmax is not large enough, so you are advised to increase the value of nvmax.
  ifail = 4ifail=4
An error has occurred during the generation of the boundary mesh. Check the definition of each line (the parameter lined) and each connected component of the boundary (the arguments nlcomp, and lcomp, as well as the coordinates of the characteristic points. Setting itrace > 0itrace>0 may provide more details.

Accuracy

Not applicable.

Further Comments

The boundary mesh generation technique in this function has a ‘tree’ structure. The boundary should be partitioned into geometrically simple segments (straight lines or curves) delimited by characteristic points. Then, the lines should be assembled into connected components of the boundary domain.
Using this strategy, the inputs to that function can be built up, following the requirements stated in Section [Parameters]:
The example below details the use of this strategy.

Example

function nag_mesh_2d_gen_boundary_example
coorch = [9.5,33,9.5,-14,-4,-2,2,4,2,-2,-4,-2,2,4,7,9,13,16,9,12,7,10,...
         18,21,17,20,16,20,15.5,16,18,21,16,18,18.5811,21,17,20,20.5,23;
         -1,7.5,16,7.5,3,3,3,3,7,8,12,12,12,12,3,3,3,3,5,5,12,12,2,2,3,3,...
         5,5,6,6,6,6,6.5,6.5,10.0811,10.0811,10.7361,10.7361,12,12];
lined = [int64(15),15,15,15,4,10,10,4,15,4,10,10,4,15,4,7,4,7,4,13,5,13,4,...
         10,4,4,10,4,4,4,4,4,10,4,4,4,4,10,4,4;
         1,2,3,4,6,10,7,8,14,13,9,12,11,5,16,19,20,17,18,22,21,15,24,24,31,...
         34,34,36,40,39,38,37,37,30,29,27,28,26,25,23;
         2,3,4,1,5,6,10,7,8,14,13,9,12,11,15,16,19,20,17,18,22,21,23,32,32,...
         31,35,35,36,40,39,38,33,33,30,29,27,28,26,25;
         1,1,1,1,-1,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,...
         0,3,0,0,0,0,0,4,0,0,0,0,5,0,0];
coorus = zeros(2, 100);
coorus(1,(1:4))=[-2.6667,-3.3333,3.3333,2.6667];
coorus(2,(1:4))=[3,3,3,3];
rate = [0.95;1.05;0.95;1.05;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;
         1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1];
nlcomp = [int64(4);10;8;18];
lcomp = [int64(1);2;3;4;14;13;12;11;10;9;8;7;6;5;22;21;20;19;18;
          17;16;15;30;29;28;27;26;25;24;23;40;39;38;37;36;35;34;33;32;31];
nvmax = int64(1000);
nedmx = int64(300);
itrace = int64(-1);
user = [23.5; 8.5; 9.5; 7.5];
[nvb, coor, nedge, edge, user, ifail] = ...
     nag_mesh_2d_gen_boundary(coorch, lined, @fbnd, coorus, rate, nlcomp, lcomp, nvmax, ...
     nedmx, itrace, 'user', user);
 nvb, nedge, ifail

function [result, user] = fbnd(i, x, y, user)
      xa = user(1);
      xb = user(2);
      x0 = user(3);
      y0 = user(4);

      result = 0.d0;
      if (i == 1)
        % line 1,2,3, and 4: ellipse centred in (x0,y0) with
        % xa and xb as coefficients
         result = ((x-x0)/xa)^2 + ((y-y0)/xb)^2 - 1.d0;
      elseif (i == 2)
        % line 24, 27, 33 and 38 are a circle centred in (x0,y0)
        % with radius sqrt(radius2)
         x0 = 20.5d0;
         y0 = 4.d0;
         radius2 = 4.25d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      elseif (i == 3)
         x0 = 17.d0;
         y0 = 8.5d0;
         radius2 = 5.d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      elseif (i == 4)
         x0 = 17.d0;
         y0 = 8.5d0;
         radius2 = 5.d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      elseif (i == 5)
         x0 = 19.5d0;
         y0 = 4.d0;
         radius2 = 1.25d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      end
 
 ANALYSIS OF THE BOUNDARY CREATED:
 THE BOUNDARY MESH CONTAINS    259 VERTEX AND    259 EDGES
 THERE ARE      4 COMPONENTS CONNECTED THE BOUNDARY
 THE  1-st COMPONENT CONTAINS      4 LINES IN ANTICLOCKWISE ORIENTATION
 THE  2-nd COMPONENT CONTAINS     10 LINES IN CLOCKWISE ORIENTATION
 THE  3-rd COMPONENT CONTAINS      8 LINES IN CLOCKWISE ORIENTATION
 THE  4-th COMPONENT CONTAINS     18 LINES IN CLOCKWISE ORIENTATION

nvb =

                  259


nedge =

                  259


ifail =

                    0


function d06ba_example
coorch = [9.5,33,9.5,-14,-4,-2,2,4,2,-2,-4,-2,2,4,7,9,13,16,9,12,7,10,...
         18,21,17,20,16,20,15.5,16,18,21,16,18,18.5811,21,17,20,20.5,23;
         -1,7.5,16,7.5,3,3,3,3,7,8,12,12,12,12,3,3,3,3,5,5,12,12,2,2,3,3,...
         5,5,6,6,6,6,6.5,6.5,10.0811,10.0811,10.7361,10.7361,12,12];
lined = [int64(15),15,15,15,4,10,10,4,15,4,10,10,4,15,4,7,4,7,4,13,5,13,4,...
         10,4,4,10,4,4,4,4,4,10,4,4,4,4,10,4,4;
         1,2,3,4,6,10,7,8,14,13,9,12,11,5,16,19,20,17,18,22,21,15,24,24,31,...
         34,34,36,40,39,38,37,37,30,29,27,28,26,25,23;
         2,3,4,1,5,6,10,7,8,14,13,9,12,11,15,16,19,20,17,18,22,21,23,32,32,...
         31,35,35,36,40,39,38,33,33,30,29,27,28,26,25;
         1,1,1,1,-1,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,...
         0,3,0,0,0,0,0,4,0,0,0,0,5,0,0];
coorus = zeros(2, 100);
coorus(1,(1:4))=[-2.6667,-3.3333,3.3333,2.6667];
coorus(2,(1:4))=[3,3,3,3];
rate = [0.95;1.05;0.95;1.05;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;
         1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1];
nlcomp = [int64(4);10;8;18];
lcomp = [int64(1);2;3;4;14;13;12;11;10;9;8;7;6;5;22;21;20;19;18;
          17;16;15;30;29;28;27;26;25;24;23;40;39;38;37;36;35;34;33;32;31];
nvmax = int64(1000);
nedmx = int64(300);
itrace = int64(-1);
user = [23.5; 8.5; 9.5; 7.5];
[nvb, coor, nedge, edge, user, ifail] = ...
     d06ba(coorch, lined, @fbnd, coorus, rate, nlcomp, lcomp, nvmax, ...
     nedmx, itrace, 'user', user);
 nvb, nedge, ifail

function [result, user] = fbnd(i, x, y, user)
      xa = user(1);
      xb = user(2);
      x0 = user(3);
      y0 = user(4);

      result = 0.d0;
      if (i == 1)
        % line 1,2,3, and 4: ellipse centred in (x0,y0) with
        % xa and xb as coefficients
         result = ((x-x0)/xa)^2 + ((y-y0)/xb)^2 - 1.d0;
      elseif (i == 2)
        % line 24, 27, 33 and 38 are a circle centred in (x0,y0)
        % with radius sqrt(radius2)
         x0 = 20.5d0;
         y0 = 4.d0;
         radius2 = 4.25d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      elseif (i == 3)
         x0 = 17.d0;
         y0 = 8.5d0;
         radius2 = 5.d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      elseif (i == 4)
         x0 = 17.d0;
         y0 = 8.5d0;
         radius2 = 5.d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      elseif (i == 5)
         x0 = 19.5d0;
         y0 = 4.d0;
         radius2 = 1.25d0;
         result = (x-x0)^2 + (y-y0)^2 - radius2;
      end
 
 ANALYSIS OF THE BOUNDARY CREATED:
 THE BOUNDARY MESH CONTAINS    259 VERTEX AND    259 EDGES
 THERE ARE      4 COMPONENTS CONNECTED THE BOUNDARY
 THE  1-st COMPONENT CONTAINS      4 LINES IN ANTICLOCKWISE ORIENTATION
 THE  2-nd COMPONENT CONTAINS     10 LINES IN CLOCKWISE ORIENTATION
 THE  3-rd COMPONENT CONTAINS      8 LINES IN CLOCKWISE ORIENTATION
 THE  4-th COMPONENT CONTAINS     18 LINES IN CLOCKWISE ORIENTATION

nvb =

                  259


nedge =

                  259


ifail =

                    0



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