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1
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 %
4 % Copyright (c) 2003-2009 by University of Queensland
5 % Earth Systems Science Computational Center (ESSCC)
6 % http://www.uq.edu.au/esscc
7 %
8 % Primary Business: Queensland, Australia
9 % Licensed under the Open Software License version 3.0
10 % http://www.opensource.org/licenses/osl-3.0.php
11 %
12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13
14
15
16 \chapter{The Module \pycad} \label{PYCAD CHAP}
17
18
19 \section{Introduction}
20
21 \pycad provides a simple way to build a mesh for your finite element
22 simulation. You begin by building what we call a \class{Design} using
23 primitive geometric objects, and then to go on to build a mesh from
24 this. The final step of generating the mesh from a \class{Design}
25 uses freely available mesh generation software, such as \gmshextern.
26
27 A \class{Design} is built by defining points, which are used to specify
28 the corners of geometric objects and the vertices of curves. Using
29 points you construct more interesting objects such as lines,
30 rectangles, and arcs. By adding many of these objects into what we
31 call a \class{Design}, you can build meshes for arbitrarily complex 2-D
32 and 3-D structures.
33
34 \section{The Unit Square}
35 So the simplest geometry is the unit square. First we generate the
36 corner points
37 \begin{python}
38 from esys.pycad import *
39 p0=Point(0.,0.,0.)
40 p1=Point(1.,0.,0.)
41 p2=Point(1.,1.,0.)
42 p3=Point(0.,1.,0.)
43 \end{python}
44 which are then linked to define the edges of the square
45 \begin{python}
46 l01=Line(p0,p1)
47 l12=Line(p1,p2)
48 l23=Line(p2,p3)
49 l30=Line(p3,p0)
50 \end{python}
51 The lines are put together to form a loop
52 \begin{python}
53 c=CurveLoop(l01,l12,l23,l30)
54 \end{python}
55 The orientation of the line defining the \class{CurveLoop} is important. It is assumed that the surrounded
56 area is to the left when moving along the lines from their starting points towards the end points. Moreover,
57 the line need to form a closed loop.
58
59 We use the \class{CurveLoop} to define a surface
60 \begin{python}
61 s=PlaneSurface(c)
62 \end{python}
63 Notice there is difference between the \class{CurveLoop} defining the boundary
64 of the surface and the actually surface \class{PlaneSurface}. This difference becomes clearer in the next example with a hole. The direction of the lines is important.
65 New we are ready to define the geometry which described by an instance of \class{Design} class:
66 \begin{python}
67 d=Design(dim=2,element_size=0.05)
68 \end{python}
69 Here we use the two dimensional domain with a local element size in the finite element mesh of $0.05$.
70 We then add the surface \code{s} to the geometry
71 \begin{python}
72 d.addItems(s)
73 \end{python}
74 This will automatically import all items used to construct \code{s} into the \class{Design} \code{d}.
75 Now we are ready to construct a \finley FEM mesh and then write it to the file \file{quad.fly}:
76 \begin{python}
77 from esys.finley import MakeDomain
78 dom=MakeDomain(d)
79 dom.write("quad.fly")
80 \end{python}
81 In some cases it is useful to access the script used to generate the geometry. You can specify a specific name
82 for the script file. In our case we use
83 \begin{python}
84 d.setScriptFileName("quad.geo")
85 \end{python}
86 If we put everything together we get the script
87 \begin{python}
88 from esys.pycad import *
89 from esys.pycad.gmsh import Design
90 from esys.finley import MakeDomain
91 p0=Point(0.,0.,0.)
92 p1=Point(1.,0.,0.)
93 p2=Point(1.,1.,0.)
94 p3=Point(0.,1.,0.)
95 l01=Line(p0,p1)
96 l12=Line(p1,p2)
97 l23=Line(p2,p3)
98 l30=Line(p3,p0)
99 c=CurveLoop(l01,l12,l23,l30)
100 s=PlaneSurface(c)
101 d=Design(dim=2,element_size=0.05)
102 d.setScriptFileName("quad.geo")
103 d.setMeshFileName("quad.msh")
104 d.addItems(s)
105 pl1=PropertySet("sides",l01,l23)
106 pl2=PropertySet("top_and_bottom",l12,l30)
107 d.addItems(pl1, pl2)
108 dom=MakeDomain(d)
109 dom.write("quad.fly")
110 \end{python}
111 This example is included with the software in
112 \file{quad.py} in the \ExampleDirectory.
113
114 There are three extra statements which we have not discussed yet: By default the mesh used to subdivide
115 the boundary are not written into the mesh file mainly to reduce the size of the data file. One need to explicitly add the lines to the \Design which should be present in the mesh data. Here we additionally labeled the
116 lines on the top and the bottom with the name ``top_and_bottom`` and the lines on the left and right hand side
117 with the name ``sides`` using \class{PropertySet} objects. The labeling is convenient
118 when using tagging \index{tagging}, see Chapter~\ref{ESCRIPT CHAP}.
119
120 \begin{figure}
121 \centerline{\includegraphics[width=\figwidth]{figures/quad.eps}}
122 \caption{Trapozid with triangle Hole.}
123 \label{fig:PYCAD 0}
124 \end{figure}
125
126 If you have \gmshextern installed you can run the example and view the geometry and mesh with:
127 \begin{python}
128 escript quad.py
129 gmsh quad.geo
130 gmsh quad.msh
131 \end{python}
132 You can access error messages from \gmshextern in the \file{.gmsh-errors} in your home directory.
133 See Figure~\ref{fig:PYCAD 0} for a result.
134
135 In most cases it is best practice to generate the mesh and to solve the mathematical
136 model in to different scripts. In our example you can read the \finley mesh into your simulation
137 code\footnote{\gmshextern files can be directly read using the \function{ReadGmsh}, see Chapter~\ref{CHAPTER ON FINLEY}} using
138 \begin{python}
139 from finley import ReadMesh
140 mesh=ReadMesh("quad.fly")
141 \end{python}
142 Note that the underlying mesh generation software will not accept all
143 the geometries you can create with \pycad. For example, \pycad
144 will happily allow you to create a 2-D \class{Design} that is a
145 closed loop with some additional points or lines lying outside of the
146 enclosed area, but \gmshextern will fail to create a mesh for it.
147
148 \begin{figure}
149 \centerline{\includegraphics[width=\figwidth]{figures/trap.eps}}
150 \caption{Trapozid with triangle Hole.}
151 \label{fig:PYCAD 1}
152 \end{figure}
153
154
155 \section{Holes}
156 The example included below shows how to use \pycad to create a 2-D mesh
157 in the shape of a trapezoid with a cut-out area, see Figure~\ref{fig:PYCAD 1}:
158 \begin{python}
159 from esys.pycad import *
160 from esys.pycad.gmsh import Design
161 from esys.finley import MakeDomain
162
163 # A trapezoid
164 p0=Point(0.0, 0.0, 0.0)
165 p1=Point(1.0, 0.0, 0.0)
166 p2=Point(1.0, 0.5, 0.0)
167 p3=Point(0.0, 1.0, 0.0)
168 l01=Line(p0, p1)
169 l12=Line(p1, p2)
170 l23=Line(p2, p3)
171 l30=Line(p3, p0)
172 c=CurveLoop(l01, l12, l23, l30)
173
174 # A small triangular cutout
175 x0=Point(0.1, 0.1, 0.0)
176 x1=Point(0.5, 0.1, 0.0)
177 x2=Point(0.5, 0.2, 0.0)
178 x01=Line(x0, x1)
179 x12=Line(x1, x2)
180 x20=Line(x2, x0)
181 cutout=CurveLoop(x01, x12, x20)
182
183 # Create the surface with cutout
184 s=PlaneSurface(c, holes=[cutout])
185
186 # Create a Design which can make the mesh
187 d=Design(dim=2, element_size=0.05)
188
189 # Add the trapezoid with cutout
190 d.addItems(s)
191
192 # Create the geometry, mesh and Escript domain
193 d.setScriptFileName("trapezoid.geo")
194 d.setMeshFileName("trapezoid.msh")
195 domain=MakeDomain(d)
196 # write mesh to a finley file:
197 domain.write("trapezoid.fly")
198 \end{python}
199 This example is included with the software in
200 \file{trapezoid.py} in the \ExampleDirectory.
201
202 A \code{CurveLoop} is used to connect several lines into a single curve.
203 It is used in the example above to create the trapezoidal outline for the grid
204 and also for the triangular cutout area.
205 You can use any number of lines when creating a \class{CurveLoop}, but
206 the end of one line must be identical to the start of the next.
207
208
209 \begin{figure}
210 \centerline{\includegraphics[width=\figwidth]{figures/brick.eps}}
211 \caption{Three dimensional Block.}
212 \label{fig:PYCAD 2}
213 \end{figure}
214
215 \section{A 3D example}
216 In this section we discuss the definition of 3D geometries. The example is the unit cube, see Figure~\ref{fig:PYCAD 2}. First we generate the vertices of the cube:
217 \begin{python}
218 from esys.pycad import *
219 p0=Point(0.,0.,0.)
220 p1=Point(1.,0.,0.)
221 p2=Point(0.,1.,0.)
222 p3=Point(1.,1.,0.)
223 p4=Point(0.,0.,1.)
224 p5=Point(1.,0.,1.)
225 p6=Point(0.,1.,1.)
226 p7=Point(1.,1.,1.)
227 \end{python}
228 We connect the points to form the bottom and top surfaces of the cube:
229 \begin{python}
230 l01=Line(p0,p1)
231 l13=Line(p1,p3)
232 l32=Line(p3,p2)
233 l20=Line(p2,p0)
234 bottom=PlaneSurface(CurveLoop(l01,l13,l32,l20))
235 \end{python}
236 and
237 \begin{python}
238 l45=Line(p4,p5)
239 l57=Line(p5,p7)
240 l76=Line(p7,p6)
241 l64=Line(p6,p4)
242 top=PlaneSurface(CurveLoop(l45,l57,l76,l64))
243 \end{python}
244 To form the front face we introduce the two additional lines connecting the left and right front
245 points of the the \code{top} and \code{bottom} face:
246 \begin{python}
247 l15=Line(p1,p5)
248 l40=Line(p4,p0)
249 \end{python}
250 To form the front face we encounter the problem as the line \code{l45} used to define the
251 \code{top} face is pointing the wrong direction. In \pycad you can reversing direction of an
252 object by changing its sign. So we write \code{-l45} to indicate that the direction is to be reversed. With this notation we can write
253 \begin{python}
254 front=PlaneSurface(CurveLoop(l01,l15,-l45,l40))
255 \end{python}
256 Keep in mind that if you use \code{Line(p4,p5)} instead \code{-l45} both objects are treated as different although the connecting the same points with a straight line in the same direction. The resulting geometry would include an opening along the \code{p4}--\code{p5} connection. This will lead to an inconsistent mesh and may result in a failure of the volumetric mesh generator. Similarly we can define the other sides of the cube:
257 \begin{python}
258 l37=Line(p3,p7)
259 l62=Line(p6,p2)
260 back=PlaneSurface(CurveLoop(l32,-l62,-l76,-l37))
261 left=PlaneSurface(CurveLoop(-l40,-l64,l62,l20))
262 right=PlaneSurface(CurveLoop(-l15,l13,l37,-l57))
263 \end{python}
264 We can now put the six surfaces together to form a \class{SurfaceLoop} defining the
265 boundary of the volume of the cube:
266 \begin{python}
267 sl=SurfaceLoop(top,-bottom,front,back,left,right)
268 v=Volume(sl)
269 \end{python}
270 Similar to the definition of a \code{CurvedLoop} the orientation of the surfaces \code{SurfaceLoop} is relevant. In fact the surface normal direction defined by the the right hand rule needs to point outwards as indicated by the surface normals in
271 Figure~\ref{fig:PYCAD 2}. As the \code{bottom} face is directed upwards it is inserted with the minus sign
272 into the \code{SurfaceLoop} in order to adjust the orientation of the surface.
273
274 As in the 2D case, the \class{Design} class is used to define the geometry:
275 \begin{python}
276 from esys.pycad.gmsh import Design
277 from esys.finley import MakeDomain
278
279 des=Design(dim=3, element_size = 0.1, keep_files=True)
280 des.setScriptFileName("brick.geo")
281 des.addItems(v, top, bottom, back, front, left , right)
282
283 dom=MakeDomain(des)
284 dom.write("brick.fly")
285 \end{python}
286 Note that the \finley mesh file \file{brick.fly} will contain the
287 triangles used to define the surfaces as they are added to the \class{Design}.
288 The example script of the cube is included with the software in
289 \file{brick.py} in the \ExampleDirectory.
290
291 \begin{figure}
292 \centerline{\includegraphics[width=\figwidth]{figures/refine1.eps}}
293 \caption{Local refinement at the origin by
294 \var{local_scale=0.01}
295 with \var{element_size=0.3} and number of elements on the top set to 10.}
296 \label{fig:PYCAD 5}
297 \end{figure}
298
299 \section{Element Sizes}
300 The element size used globally is defined by the
301 \code{element_size} argument of the \class{Design}. The mesh generator
302 will try to use this mesh size everywhere in the geometry. In some cases it can be
303 desirable to use locally a finer mesh. A local refinement can be defined at each
304 \class{Point}:
305 \begin{python}
306 p0=Point(0.,0.,0.,local_scale=0.01)
307 \end{python}
308 Here the mesh generator will create a mesh with an element size which is by the factor \code{0.01}
309 times smaller than the global mesh size \code{element_size=0.3}, see Figure~\ref{fig:PYCAD 5}. The point where a refinement is defined must be a point of curve used to define the geometry.
310
311 Alternatively, one can define a mesh size along a curve by defining the number of elements to be used to subdivide the curve. For instance, to use $20$ element on line \code{l23} on uses:
312 \begin{python}
313 l23=Line(p2, p3)
314 l23.setElementDistribution(20)
315 \end{python}
316 Setting the number of elements on a curve overwrites the global mesh size \code{element_size}. The result is shown in Figure~\ref{fig:PYCAD 5}.
317
318
319
320 \section{\pycad Classes}
321 \declaremodule{extension}{esys.pycad}
322 \modulesynopsis{Python geometry description and meshing interface}
323
324 \subsection{Primitives}
325
326 Some of the most commonly-used objects in \pycad are listed here. For a more complete
327 list see the full API documentation.
328
329 \begin{classdesc}{Point}{x=0.,y=0.,z=0.\optional{,local_scale=1.}}
330 Create a point with from coordinates with local characteristic length \var{local_scale}
331 \end{classdesc}
332
333 \begin{classdesc}{Line}{point1, point2}
334 Create a line with between starting and ending points.
335 \end{classdesc}
336 \begin{methoddesc}[Line]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
337 Defines the number of elements on the line. If set it overwrites the local length setting which would be applied. The progression factor \var{progression} defines the change of element size between neighboured elements. If \var{createBump} is set
338 progression is applied towards the centre of the line.
339 \end{methoddesc}
340 \begin{methoddesc}[Line]{resetElementDistribution}{}
341 removes a previously set element distribution from the line.
342 \end{methoddesc}
343 \begin{methoddesc}[Line]{getElemenofDistribution}{}
344 Returns the element distribution as tuple of
345 number of elements, progression factor and bump flag. If
346 no element distribution is set None is returned.
347 \end{methoddesc}
348
349
350 \begin{classdesc}{Spline}{point0, point1, ...}
351 A spline curve defined by a list of points \var{point0}, \var{point1},....
352 \end{classdesc}
353 \begin{methoddesc}[Spline]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
354 Defines the number of elements on the line. If set it overwrites the local length setting which would be applied. The progression factor \var{progression} defines the change of element size between neighboured elements. If \var{createBump} is set
355 progression is applied towards the centre of the line.
356 \end{methoddesc}
357 \begin{methoddesc}[Spline]{resetElementDistribution}{}
358 removes a previously set element distribution from the line.
359 \end{methoddesc}
360 \begin{methoddesc}[Spline]{getElemenofDistribution}{}
361 Returns the element distribution as tuple of
362 number of elements, progression factor and bump flag. If
363 no element distribution is set None is returned.
364 \end{methoddesc}
365
366 \begin{classdesc}{BSpline}{point0, point1, ...}
367 A B-spline curve defined by a list of points \var{point0}, \var{point1},....
368 \end{classdesc}
369 \begin{methoddesc}[BSpline]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
370 Defines the number of elements on the line. If set it overwrites the local length setting which would be applied. The progression factor \var{progression} defines the change of element size between neighboured elements. If \var{createBump} is set
371 progression is applied towards the centre of the line.
372 \end{methoddesc}
373 \begin{methoddesc}[BSpline]{resetElementDistribution}{}
374 removes a previously set element distribution from the line.
375 \end{methoddesc}
376 \begin{methoddesc}[BSpline]{getElemenofDistribution}{}
377 Returns the element distribution as tuple of
378 number of elements, progression factor and bump flag. If
379 no element distribution is set None is returned.
380 \end{methoddesc}
381
382 \begin{classdesc}{BezierCurve}{point0, point1, ...}
383 A Brezier spline curve defined by a list of points \var{point0}, \var{point1},....
384 \end{classdesc}
385 \begin{methoddesc}[BezierCurve]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
386 Defines the number of elements on the line. If set it overwrites the local length setting which would be applied. The progression factor \var{progression} defines the change of element size between neighboured elements. If \var{createBump} is set
387 progression is applied towards the centre of the line.
388 \end{methoddesc}
389 \begin{methoddesc}[BezierCurve]{resetElementDistribution}{}
390 removes a previously set element distribution from the line.
391 \end{methoddesc}
392 \begin{methoddesc}[BezierCurve]{getElemenofDistribution}{}
393 Returns the element distribution as tuple of
394 number of elements, progression factor and bump flag. If
395 no element distribution is set None is returned.
396 \end{methoddesc}
397
398 \begin{classdesc}{Arc}{centre_point, start_point, end_point}
399 Create an arc by specifying a centre for a circle and start and end points. An arc may subtend an angle of at most $\pi$ radians.
400 \end{classdesc}
401 \begin{methoddesc}[Arc]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
402 Defines the number of elements on the line. If set it overwrites the local length setting which would be applied. The progression factor \var{progression} defines the change of element size between neighboured elements. If \var{createBump} is set
403 progression is applied towards the centre of the line.
404 \end{methoddesc}
405 \begin{methoddesc}[Arc]{resetElementDistribution}{}
406 removes a previously set element distribution from the line.
407 \end{methoddesc}
408 \begin{methoddesc}[Arc]{getElemenofDistribution}{}
409 Returns the element distribution as tuple of
410 number of elements, progression factor and bump flag. If
411 no element distribution is set None is returned.
412 \end{methoddesc}
413
414 \begin{classdesc}{CurveLoop}{list}
415 Create a closed curve from the \code{list}. of
416 \class{Line}, \class{Arc}, \class{Spline}, \class{BSpline},
417 \class{BrezierSpline}.
418 \end{classdesc}
419
420 \begin{classdesc}{PlaneSurface}{loop, \optional{holes=[list]}}
421 Create a plane surface from a \class{CurveLoop}, which may have one or more holes
422 described by \var{list} of \class{CurveLoop}.
423 \end{classdesc}
424 \begin{methoddesc}[PlaneSurface]{setRecombination}{max_deviation}
425 the mesh generator will try to recombine triangular elements
426 into quadrilateral elements. \var{max_deviation} (in radians) defines the
427 maximum deviation of any angle in the quadrilaterals from the right angle.
428 Set \var{max_deviation}=\var{None} to remove recombination.
429 \end{methoddesc}
430 \begin{methoddesc}[PlaneSurface]{setTransfiniteMeshing}{\optional{orientation="Left"}}
431 applies 2D transfinite meshing to the surface.
432 \var{orientation} defines the orientation of triangles. Allowed values
433 are \var{``Left''}, \var{``Right''} or \var{``Alternate''}. The
434 boundary of the surface must be defined by three or four lines where an
435 element distribution must be defined on all faces where opposite
436 faces uses the same element distribution. No holes must be present.
437 \end{methoddesc}
438
439
440
441 \begin{classdesc}{RuledSurface}{list}
442 Create a surface that can be interpolated using transfinite interpolation.
443 \var{list} gives a list of three or four lines defining the boundary of the
444 surface.
445 \end{classdesc}
446 \begin{methoddesc}[RuledSurface]{setRecombination}{max_deviation}
447 the mesh generator will try to recombine triangular elements
448 into quadrilateral elements. \var{max_deviation} (in radians) defines the
449 maximum deviation of any angle in the quadrilaterals from the right angle.
450 Set \var{max_deviation}=\var{None} to remove recombination.
451 \end{methoddesc}
452 \begin{methoddesc}[RuledSurface]{setTransfiniteMeshing}{\optional{orientation="Left"}}
453 applies 2D transfinite meshing to the surface.
454 \var{orientation} defines the orientation of triangles. Allowed values
455 are \var{``Left''}, \var{``Right''} or \var{``Alternate''}. The
456 boundary of the surface must be defined by three or four lines where an
457 element distribution must be defined on all faces where opposite
458 faces uses the same element distribution. No holes must be present.
459 \end{methoddesc}
460
461
462 \begin{classdesc}{SurfaceLoop}{list}
463 Create a loop of \class{PlaneSurface} or \class{RuledSurface}, which defines the shell of a volume.
464 \end{classdesc}
465
466 \begin{classdesc}{Volume}{loop, \optional{holes=[list]}}
467 Create a volume given a \class{SurfaceLoop}, which may have one or more holes
468 define by the list of \class{SurfaceLoop}.
469 \end{classdesc}
470
471 \begin{classdesc}{PropertySet}{list}
472 Create a PropertySet given a list of 1-D, 2-D or 3-D items. See the section on Properties below for more information.
473 \end{classdesc}
474
475 %============================================================================================================
476 \subsection{Transformations}
477
478 Sometimes it's convenient to create an object and then make copies at
479 different orientations and in different sizes. Transformations are
480 used to move geometrical objects in the 3-dimensional space and to
481 resize them.
482
483 \begin{classdesc}{Translation}{\optional{b=[0,0,0]}}
484 defines a translation $x \to x+b$. \var{b} can be any object that can be converted
485 into a \numpy object of shape $(3,)$.
486 \end{classdesc}
487
488 \begin{classdesc}{Rotatation}{\optional{axis=[1,1,1], \optional{ point = [0,0,0], \optional{angle=0*RAD} } } }
489 defines a rotation by \var{angle} around axis through point \var{point} and direction \var{axis}.
490 \var{axis} and \var{point} can be any object that can be converted
491 into a \numpy object of shape $(3,)$.
492 \var{axis} does not have to be normalised but must have positive length. The right hand rule~\cite{RIGHTHANDRULE}
493 applies.
494 \end{classdesc}
495
496
497 \begin{classdesc}{Dilation}{\optional{factor=1., \optional{centre=[0,0,0]}}}
498 defines a dilation by the expansion/contraction \var{factor} with
499 \var{centre} as the dilation centre.
500 \var{centre} can be any object that can be converted
501 into a \numpy object of shape $(3,)$.
502 \end{classdesc}
503
504 \begin{classdesc}{Reflection}{\optional{normal=[1,1,1], \optional{offset=0}}}
505 defines a reflection on a plane defined in normal form $n^t x = d$
506 where $n$ is the surface normal \var{normal} and $d$ is the plane \var{offset}.
507 \var{normal} can be any object that can be converted
508 into a \numpy object of shape $(3,)$.
509 \var{normal} does not have to be normalised but must have positive length.
510 \end{classdesc}
511
512 \begin{datadesc}{DEG}
513 A constant to convert from degrees to an internal angle representation in radians. For instance use \code{90*DEG} for $90$ degrees.
514 \end{datadesc}
515
516 \subsection{Properties}
517
518 If you are building a larger geometry you may find it convenient to
519 create it in smaller pieces and then assemble them into the whole.
520 Property sets make this easy, and they allow you to name the smaller
521 pieces for convenience.
522
523 Property sets are used to bundle a set of geometrical objects in a
524 group. The group is identified by a name. Typically a property set
525 is used to mark subregions with share the same material properties or
526 to mark portions of the boundary. For efficiency, the \Design class
527 object assigns a integer to each of its property sets, a so-called tag
528 \index{tag}. The appropriate tag is attached to the elements at
529 generation time.
530
531 See the file \code{pycad/examples/quad.py} for an example using a {\it PropertySet}.
532
533
534 \begin{classdesc}{PropertySet}{name,*items}
535 defines a group geometrical objects which can be accessed through a \var{name}
536 The objects in the tuple \var{items} mast all be \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD objects.
537 \end{classdesc}
538
539
540 \begin{methoddesc}[PropertySet]{getManifoldClass}{}
541 returns the manifold class \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD expected from the items
542 in the property set.
543 \end{methoddesc}
544
545 \begin{methoddesc}[PropertySet]{getDim}{}
546 returns the spatial dimension of the items
547 in the property set.
548 \end{methoddesc}
549
550 \begin{methoddesc}[PropertySet]{getName}{}
551 returns the name of the set
552 \end{methoddesc}
553
554 \begin{methoddesc}[PropertySet]{setName}{name}
555 sets the name. This name should be unique within a \Design.
556 \end{methoddesc}
557
558 \begin{methoddesc}[PropertySet]{addItem}{*items}
559 adds a tuple of items. They need to be objects of class \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD.
560 \end{methoddesc}
561
562 \begin{methoddesc}[PropertySet]{getItems}{}
563 returns the list of items
564 \end{methoddesc}
565
566 \begin{methoddesc}[PropertySet]{clearItems}{}
567 clears the list of items
568 \end{methoddesc}
569
570 \begin{methoddesc}[PropertySet]{getTag}{}
571 returns the tag used for this property set
572 \end{methoddesc}
573
574 \section{Interface to the mesh generation software}
575 \declaremodule{extension}{esys.pycad.gmsh}
576 \modulesynopsis{Python geometry description and meshing interface}
577
578 The class and methods described here provide an interface to the mesh
579 generation software, which is currently \gmshextern. This interface could be
580 adopted to triangle or another mesh generation package if this is
581 deemed to be desirable in the future.
582
583 \begin{classdesc}{Design}{
584 \optional{dim=3, \optional{element_size=1., \optional{order=1, \optional{keep_files=False}}}}}
585 The \class{Design} describes the geometry defined by primitives to be meshed.
586 The \var{dim} specifies the spatial dimension. The argument \var{element_size} defines the global
587 element size which is multiplied by the local scale to set the element size at each \Point.
588 The argument \var{order} defines the element order to be used. If \var{keep_files} is set to
589 \True temporary files a kept otherwise they are removed when the instance of the class is deleted.
590 \end{classdesc}
591
592
593 \begin{methoddesc}[Design]{setDim}{\optional{dim=3}}
594 sets the spatial dimension which needs to be $1$, $2$ or $3$.
595 \end{methoddesc}
596
597 \begin{methoddesc}[Design]{getDim}{}
598 returns the spatial dimension.
599 \end{methoddesc}
600
601 \begin{methoddesc}[Design]{setElementOrder}{\optional{order=1}}
602 sets the element order which needs to be $1$ or $2$.
603 \end{methoddesc}
604
605 \begin{methoddesc}[Design]{getElementOrder}{}
606 returns the element order.
607 \end{methoddesc}
608
609
610 \begin{methoddesc}[Design]{setElementSize}{\optional{element_size=1}}
611 set the global element size. The local element size at a point is defined as
612 the global element size multiplied by the local scale. The element size must be positive.
613 \end{methoddesc}
614
615
616 \begin{methoddesc}[Design]{getElementSize}{}
617 returns the global element size.
618 \end{methoddesc}
619
620 \begin{memberdesc}[Design]{DELAUNAY}
621 the gmsh Delauny triangulator.
622 \end{memberdesc}
623
624 \begin{memberdesc}[Design]{TETGEN}
625 the TetGen~\cite{TETGEN} triangulator.
626 \end{memberdesc}
627
628 \begin{memberdesc}[Design]{NETGEN}
629 the NETGEN~\cite{NETGEN} triangulator.
630 \end{memberdesc}
631
632 \begin{methoddesc}[Design]{setKeepFilesOn}{}
633 work files are kept at the end of the generation.
634 \end{methoddesc}
635
636 \begin{methoddesc}[Design]{setKeepFilesOff}{}
637 work files are deleted at the end of the generation.
638 \end{methoddesc}
639
640 \begin{methoddesc}[Design]{keepFiles}{}
641 returns \True if work files are kept. Otherwise \False is returned.
642 \end{methoddesc}
643
644 \begin{methoddesc}[Design]{setScriptFileName}{\optional{name=None}}
645 set the file name for the gmsh input script. if no name is given a name with extension "geo" is generated.
646 \end{methoddesc}
647
648 \begin{methoddesc}[Design]{getScriptFileName}{}
649 returns the name of the file for the gmsh script.
650 \end{methoddesc}
651
652
653 \begin{methoddesc}[Design]{setMeshFileName}{\optional{name=None}}
654 sets the name for the gmsh mesh file. if no name is given a name with extension "msh" is generated.
655 \end{methoddesc}
656
657 \begin{methoddesc}[Design]{getMeshFileName}{}
658 returns the name of the file for the gmsh msh
659 \end{methoddesc}
660
661
662 \begin{methoddesc}[Design]{addItems}{*items}
663 adds the tuple of var{items}. An item can be any primitive or a \class{PropertySet}.
664 \warning{If a \PropertySet is added as an item added object that are not
665 part of a \PropertySet are not considered in the messing.
666 }
667
668 \end{methoddesc}
669
670 \begin{methoddesc}[Design]{getItems}{}
671 returns a list of the items
672 \end{methoddesc}
673
674 \begin{methoddesc}[Design]{clearItems}{}
675 resets the items in design
676 \end{methoddesc}
677
678 \begin{methoddesc}[Design]{getMeshHandler}{}
679 returns a handle to the mesh. The call of this method generates the mesh from the geometry and
680 returns a mechanism to access the mesh data. In the current implementation this
681 method returns a file name for a gmsh file containing the mesh data.
682 \end{methoddesc}
683
684 \begin{methoddesc}[Design]{getScriptString}{}
685 returns the gmsh script to generate the mesh as a string.
686 \end{methoddesc}
687
688 \begin{methoddesc}[Design]{getCommandString}{}
689 returns the gmsh command used to generate the mesh as string.
690 \end{methoddesc}
691
692 \begin{methoddesc}[Design]{setOptions}{\optional{algorithm=None, \optional{ optimize_quality=True,\optional{ smoothing=1}}}}
693 sets options for the mesh generator. \var{algorithm} sets the algorithm to be used.
694 The algorithm needs to be \var{Design.DELAUNAY}
695 \var{Design.TETGEN}
696 or \var{Design.NETGEN}. By default \var{Design.DELAUNAY} is used. \var{optimize_quality}=\True invokes an optimization of the mesh quality. \var{smoothing} sets the number of smoothing steps to be applied to the mesh.
697 \end{methoddesc}
698
699 \begin{methoddesc}[Design]{getTagMap}{}
700 returns a \class{TagMap} to map the name \class{PropertySet} in the class to tag numbers generated by gmsh.
701 \end{methoddesc}

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