/[escript]/trunk/doc/user/pycad.tex
ViewVC logotype

Contents of /trunk/doc/user/pycad.tex

Parent Directory Parent Directory | Revision Log Revision Log


Revision 3301 - (show annotations)
Mon Oct 25 01:27:54 2010 UTC (8 years, 10 months ago) by jfenwick
File MIME type: application/x-tex
File size: 33156 byte(s)
Modified layout of descriptions.
Fixed some overfull hboxes
1
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 %
4 % Copyright (c) 2003-2010 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 \chapter{The \pycad Module}\label{PYCAD CHAP}
15
16 \section{Introduction}
17
18 \pycad provides a simple way to build a mesh for your finite element
19 simulation. You begin by building what we call a \class{Design} using
20 primitive geometric objects, and then to go on to build a mesh from
21 this. The final step of generating the mesh from a \class{Design}
22 uses freely available mesh generation software, such as \gmshextern.
23
24 A \class{Design} is built by defining points, which are used to specify
25 the corners of geometric objects and the vertices of curves. Using
26 points you construct more interesting objects such as lines,
27 rectangles, and arcs. By adding many of these objects into what we
28 call a \class{Design}, you can build meshes for arbitrarily complex 2-D
29 and 3-D structures.
30
31 \section{The Unit Square}
32 So the simplest geometry is the unit square. First we generate the
33 corner points
34 \begin{python}
35 from esys.pycad import *
36 p0=Point(0.,0.,0.)
37 p1=Point(1.,0.,0.)
38 p2=Point(1.,1.,0.)
39 p3=Point(0.,1.,0.)
40 \end{python}
41 which are then linked to define the edges of the square
42 \begin{python}
43 l01=Line(p0,p1)
44 l12=Line(p1,p2)
45 l23=Line(p2,p3)
46 l30=Line(p3,p0)
47 \end{python}
48 The lines are put together to form a loop
49 \begin{python}
50 c=CurveLoop(l01,l12,l23,l30)
51 \end{python}
52 The orientation of the line defining the \class{CurveLoop} is important. It is assumed that the surrounded
53 area is to the left when moving along the lines from their starting points towards the end points. Moreover,
54 the line need to form a closed loop.
55
56 We use the \class{CurveLoop} to define a surface
57 \begin{python}
58 s=PlaneSurface(c)
59 \end{python}
60 Notice there is difference between the \class{CurveLoop} defining the boundary
61 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.
62 New we are ready to define the geometry which described by an instance of \class{Design} class:
63 \begin{python}
64 d=Design(dim=2,element_size=0.05)
65 \end{python}
66 Here we use the two dimensional domain with a local element size in the finite element mesh of $0.05$.
67 We then add the surface \code{s} to the geometry
68 \begin{python}
69 d.addItems(s)
70 \end{python}
71 This will automatically import all items used to construct \code{s} into the \class{Design} \code{d}.
72 Now we are ready to construct a \finley FEM mesh and then write it to the file \file{quad.fly}:
73 \begin{python}
74 from esys.finley import MakeDomain
75 dom=MakeDomain(d)
76 dom.write("quad.fly")
77 \end{python}
78 In some cases it is useful to access the script used to generate the geometry. You can specify a specific name
79 for the script file. In our case we use
80 \begin{python}
81 d.setScriptFileName("quad.geo")
82 \end{python}
83 It is also useful to check error messages generated during the mesh generation process. \gmshextern writes
84 messages to the \file{.gmsh-errors} in your home directory.
85
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.addItems(s)
104 pl1=PropertySet("sides",l01,l23)
105 pl2=PropertySet("top_and_bottom",l12,l30)
106 d.addItems(pl1, pl2)
107 dom=MakeDomain(d)
108 dom.write("quad.fly")
109 \end{python}
110 This example is included with the software in
111 \file{quad.py} in the \ExampleDirectory.
112
113 There are three extra statements which we have not discussed yet: By default the mesh used to subdivide
114 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
115 lines on the top and the bottom with the name ``top_and_bottom`` and the lines on the left and right hand side
116 with the name ``sides`` using \class{PropertySet} objects. The labeling is convenient
117 when using tagging \index{tagging}, see Chapter~\ref{ESCRIPT CHAP}.
118
119 \begin{figure}
120 % \centerline{\includegraphics{quad}}
121 % \centerline{\includegraphics[width=\figwidth]{quad}}
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 run-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. 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]{trap}}
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]{brick}}
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 \section{Alternative File Formats}
292 \code{pycad} supports other file formats in including
293 I-DEAS universal file, VRML, Nastran and STL. The following example shows how
294 to generate the STL file \file{brick.stl}:
295 \begin{python}
296 from esys.pycad.gmsh import Design
297
298 des=Design(dim=3, element_size = 0.1, keep_files=True)
299 des.addItems(v, top, bottom, back, front, left , right)
300
301 des.setFileFormat(des.STL)
302 des.setMeshFileName("brick.stl")
303 des.generate()
304 \end{python}
305 The example script of the cube is included with the software in
306 \file{brick_stl.py} in the \ExampleDirectory.
307
308
309 \begin{figure}
310 % \centerline{\includegraphics[width=\figwidth]{refine1}}
311 \caption{Local refinement at the origin by
312 \var{local_scale=0.01}
313 with \var{element_size=0.3} and number of elements on the top set to 10.}
314 \label{fig:PYCAD 5}
315 \end{figure}
316
317 \section{Element Sizes}
318 The element size used globally is defined by the
319 \code{element_size} argument of the \class{Design}. The mesh generator
320 will try to use this mesh size everywhere in the geometry. In some cases it can be
321 desirable to use locally a finer mesh. A local refinement can be defined at each
322 \class{Point}:
323 \begin{python}
324 p0=Point(0.,0.,0.,local_scale=0.01)
325 \end{python}
326 Here the mesh generator will create a mesh with an element size which is by the factor \code{0.01}
327 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.
328
329 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:
330 \begin{python}
331 l23=Line(p2, p3)
332 l23.setElementDistribution(20)
333 \end{python}
334 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}.
335
336 \section{\pycad Classes}
337 \declaremodule{extension}{esys.pycad}
338 \modulesynopsis{Python geometry description and meshing interface}
339
340 \subsection{Primitives}
341
342 Some of the most commonly-used objects in \pycad are listed here. For a more complete
343 list see the full API documentation.
344
345
346 \begin{classdesc}{Point}{x=0.,y=0.,z=0.\optional{,local_scale=1.}}
347 Create a point with from coordinates with local characteristic length \var{local_scale}
348 \end{classdesc}
349
350 \begin{classdesc}{CurveLoop}{list}
351 Create a closed curve from the \code{list}. of
352 \class{Line}, \class{Arc}, \class{Spline}, \class{BSpline},
353 \class{BrezierSpline}.
354 \end{classdesc}
355
356 \begin{classdesc}{SurfaceLoop}{list}
357 Create a loop of \class{PlaneSurface} or \class{RuledSurface}, which defines the shell of a volume.
358 \end{classdesc}
359
360 \subsubsection{Lines}
361 \begin{classdesc}{Line}{point1, point2}
362 Create a line with between starting and ending points.
363 \end{classdesc}
364 \begin{methoddesc}[Line]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
365 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
366 progression is applied towards the centre of the line.
367 \end{methoddesc}
368 \begin{methoddesc}[Line]{resetElementDistribution}{}
369 removes a previously set element distribution from the line.
370 \end{methoddesc}
371 \begin{methoddesc}[Line]{getElemenofDistribution}{}
372 Returns the element distribution as tuple of
373 number of elements, progression factor and bump flag. If
374 no element distribution is set None is returned.
375 \end{methoddesc}
376
377 \subsubsection{Splines}
378 \begin{classdesc}{Spline}{point0, point1, ...}
379 A spline curve defined by a list of points \var{point0}, \var{point1},....
380 \end{classdesc}
381 \begin{methoddesc}[Spline]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
382 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
383 progression is applied towards the centre of the line.
384 \end{methoddesc}
385 \begin{methoddesc}[Spline]{resetElementDistribution}{}
386 removes a previously set element distribution from the line.
387 \end{methoddesc}
388 \begin{methoddesc}[Spline]{getElemenofDistribution}{}
389 Returns the element distribution as tuple of
390 number of elements, progression factor and bump flag. If
391 no element distribution is set None is returned.
392 \end{methoddesc}
393
394 \subsubsection{BSplines}
395 \begin{classdesc}{BSpline}{point0, point1, ...}
396 A B-spline curve defined by a list of points \var{point0}, \var{point1},....
397 \end{classdesc}
398 \begin{methoddesc}[BSpline]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
399 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
400 progression is applied towards the centre of the line.
401 \end{methoddesc}
402 \begin{methoddesc}[BSpline]{resetElementDistribution}{}
403 removes a previously set element distribution from the line.
404 \end{methoddesc}
405 \begin{methoddesc}[BSpline]{getElemenofDistribution}{}
406 Returns the element distribution as tuple of
407 number of elements, progression factor and bump flag. If
408 no element distribution is set None is returned.
409 \end{methoddesc}
410
411 \subsubsection{Brezier Curves}
412 \begin{classdesc}{BezierCurve}{point0, point1, ...}
413 A Brezier spline curve defined by a list of points \var{point0}, \var{point1},....
414 \end{classdesc}
415 \begin{methoddesc}[BezierCurve]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
416 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
417 progression is applied towards the centre of the line.
418 \end{methoddesc}
419 \begin{methoddesc}[BezierCurve]{resetElementDistribution}{}
420 removes a previously set element distribution from the line.
421 \end{methoddesc}
422 \begin{methoddesc}[BezierCurve]{getElemenofDistribution}{}
423 Returns the element distribution as tuple of
424 number of elements, progression factor and bump flag. If
425 no element distribution is set None is returned.
426 \end{methoddesc}
427
428 \subsubsection{Arcs}
429 \begin{classdesc}{Arc}{centre_point, start_point, end_point}
430 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.
431 \end{classdesc}
432 \begin{methoddesc}[Arc]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
433 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
434 progression is applied towards the centre of the line.
435 \end{methoddesc}
436 \begin{methoddesc}[Arc]{resetElementDistribution}{}
437 removes a previously set element distribution from the line.
438 \end{methoddesc}
439 \begin{methoddesc}[Arc]{getElemenofDistribution}{}
440 Returns the element distribution as tuple of
441 number of elements, progression factor and bump flag. If
442 no element distribution is set None is returned.
443 \end{methoddesc}
444
445
446
447 \subsubsection{Plain surfaces}
448 \begin{classdesc}{PlaneSurface}{loop, \optional{holes=[list]}}
449 Create a plane surface from a \class{CurveLoop}, which may have one or more holes
450 described by \var{list} of \class{CurveLoop}.
451 \end{classdesc}
452 \begin{methoddesc}[PlaneSurface]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
453 Defines the number of elements on all lines.
454 \end{methoddesc}
455
456 \begin{methoddesc}[PlaneSurface]{setRecombination}{\optional{max_deviation=45 * \var{DEG} }}
457 the mesh generator will try to recombine triangular elements
458 into quadrilateral elements. \var{max_deviation} (in radians) defines the
459 maximum deviation of any angle in the quadrilaterals from the right angle.
460 Set \var{max_deviation}=\var{None} to remove recombination.
461 \end{methoddesc}
462 \begin{methoddesc}[PlaneSurface]{setTransfiniteMeshing}{\optional{orientation="Left"}}
463 applies 2D transfinite meshing to the surface.
464 \var{orientation} defines the orientation of triangles. Allowed values
465 are \var{``Left''}, \var{``Right''} or \var{``Alternate''}. The
466 boundary of the surface must be defined by three or four lines where an
467 element distribution must be defined on all faces where opposite
468 faces uses the same element distribution. No holes must be present.
469 \end{methoddesc}
470
471
472
473 \subsubsection{Ruled Surfaces}
474 \begin{classdesc}{RuledSurface}{list}
475 Create a surface that can be interpolated using transfinite interpolation.
476 \var{list} gives a list of three or four lines defining the boundary of the
477 surface.
478 \end{classdesc}
479
480 \begin{methoddesc}[RuledSurface]{setRecombination}{\optional{max_deviation=45 * \var{DEG} }}
481 the mesh generator will try to recombine triangular elements
482 into quadrilateral elements. \var{max_deviation} (in radians) defines the
483 maximum deviation of any angle in the quadrilaterals from the right angle.
484 Set \var{max_deviation}=\var{None} to remove recombination.
485 \end{methoddesc}
486
487 \begin{methoddesc}[RuledSurface]{setTransfiniteMeshing}{\optional{orientation="Left"}}
488 applies 2D transfinite meshing to the surface.
489 \var{orientation} defines the orientation of triangles. Allowed values
490 are \var{``Left''}, \var{``Right''} or \var{``Alternate''}. The
491 boundary of the surface must be defined by three or four lines where an
492 element distribution must be defined on all faces where opposite
493 faces uses the same element distribution. No holes must be present.
494 \end{methoddesc}
495
496 \begin{methoddesc}[RuledSurface]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
497 Defines the number of elements on all lines.
498 \end{methoddesc}
499
500 \subsubsection{Volumes}
501
502 \begin{classdesc}{Volume}{loop, \optional{holes=[list]}}
503 Create a volume given a \class{SurfaceLoop}, which may have one or more holes
504 define by the list of \class{SurfaceLoop}.
505 \end{classdesc}
506
507 \begin{methoddesc}[Volume]{setElementDistribution}{n\optional{,progression=1\optional{,createBump=\False}}}
508 Defines the number of elements on all lines.
509 \end{methoddesc}
510
511 \begin{methoddesc}[Volume]{setRecombination}{\optional{max_deviation=45 * \var{DEG} }}
512 the mesh generator will try to recombine triangular elements
513 into quadrilateral elements. These meshes are then used to generate the volume mesh if possible.
514 Together with transfinite meshing one can construct rectanglar meshes.
515 \var{max_deviation} (in radians) defines the maximum deviation of any angle in the quadrilaterals from the right angle.
516 Set \var{max_deviation}=\var{None} to remove recombination.
517 \end{methoddesc}
518
519 \begin{methoddesc}[Volume]{setTransfiniteMeshing}{\optional{orientation="Left"}}
520 applies transfinite meshing to the volume and all surfaces (if \var{orientation} is not equal to \var{None})
521 \var{orientation} defines the orientation of triangles. Allowed values
522 are \var{``Left''}, \var{``Right''} or \var{``Alternate''}. The
523 boundary of the surface must be defined by three or four lines where an
524 element distribution must be defined on all faces where opposite
525 faces uses the same element distribution.
526 If \var{orientation} is equal to \var{None} transfinite meshing is not switched on for the surfaces but needs
527 to be set by the user. No holes must be present.
528 \textbf{Warning: The functionality of transfinite meshing without recombination is not entirely clear in \gmshextern.
529 So please apply this method with care.}
530 \end{methoddesc}
531
532
533 %============================================================================================================
534 \subsection{Transformations}
535
536 Sometimes it's convenient to create an object and then make copies at
537 different orientations and in different sizes. Transformations are
538 used to move geometrical objects in the 3-dimensional space and to
539 resize them.
540
541 \begin{classdesc}{Translation}{\optional{b=[0,0,0]}}
542 defines a translation $x \to x+b$. \var{b} can be any object that can be converted
543 into a \numpy object of shape $(3,)$.
544 \end{classdesc}
545
546 \begin{classdesc}{Rotation}{\optional{axis=[1,1,1], \optional{ point = [0,0,0], \optional{angle=0*RAD} } } }
547 defines a rotation by \var{angle} around axis through point \var{point} and direction \var{axis}.
548 \var{axis} and \var{point} can be any object that can be converted
549 into a \numpy object of shape $(3,)$.
550 \var{axis} does not have to be normalised but must have positive length. The right hand rule~\cite{RIGHTHANDRULE}
551 applies.
552 \end{classdesc}
553
554
555 \begin{classdesc}{Dilation}{\optional{factor=1., \optional{centre=[0,0,0]}}}
556 defines a dilation by the expansion/contraction \var{factor} with
557 \var{centre} as the dilation centre.
558 \var{centre} can be any object that can be converted
559 into a \numpy object of shape $(3,)$.
560 \end{classdesc}
561
562 \begin{classdesc}{Reflection}{\optional{normal=[1,1,1], \optional{offset=0}}}
563 defines a reflection on a plane defined in normal form $n^t x = d$
564 where $n$ is the surface normal \var{normal} and $d$ is the plane \var{offset}.
565 \var{normal} can be any object that can be converted
566 into a \numpy object of shape $(3,)$.
567 \var{normal} does not have to be normalised but must have positive length.
568 \end{classdesc}
569
570 \begin{datadesc}{DEG}
571 A constant to convert from degrees to an internal angle representation in radians. For instance use \code{90*DEG} for $90$ degrees.
572 \end{datadesc}
573
574 \subsection{Properties}
575
576 If you are building a larger geometry you may find it convenient to
577 create it in smaller pieces and then assemble them into the whole.
578 Property sets make this easy, and they allow you to name the smaller
579 pieces for convenience.
580
581 Property sets are used to bundle a set of geometrical objects in a
582 group. The group is identified by a name. Typically a property set
583 is used to mark subregions with share the same material properties or
584 to mark portions of the boundary. For efficiency, the \Design class
585 object assigns a integer to each of its property sets, a so-called tag
586 \index{tag}. The appropriate tag is attached to the elements at
587 generation time.
588
589 See the file \code{pycad/examples/quad.py} for an example using a {\it PropertySet}.
590
591
592 \begin{classdesc}{PropertySet}{name,*items}
593 defines a group geometrical objects which can be accessed through a \var{name}
594 The objects in the tuple \var{items} mast all be \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD objects.
595 \end{classdesc}
596
597
598 \begin{methoddesc}[PropertySet]{getManifoldClass}{}
599 returns the manifold class \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD expected from the items
600 in the property set.
601 \end{methoddesc}
602
603 \begin{methoddesc}[PropertySet]{getDim}{}
604 returns the spatial dimension of the items
605 in the property set.
606 \end{methoddesc}
607
608 \begin{methoddesc}[PropertySet]{getName}{}
609 returns the name of the set
610 \end{methoddesc}
611
612 \begin{methoddesc}[PropertySet]{setName}{name}
613 sets the name. This name should be unique within a \Design.
614 \end{methoddesc}
615
616 \begin{methoddesc}[PropertySet]{addItem}{*items}
617 adds a tuple of items. They need to be objects of class \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD.
618 \end{methoddesc}
619
620 \begin{methoddesc}[PropertySet]{getItems}{}
621 returns the list of items
622 \end{methoddesc}
623
624 \begin{methoddesc}[PropertySet]{clearItems}{}
625 clears the list of items
626 \end{methoddesc}
627
628 \begin{methoddesc}[PropertySet]{getTag}{}
629 returns the tag used for this property set
630 \end{methoddesc}
631
632 \section{Interface to the mesh generation software}
633 \declaremodule{extension}{esys.pycad.gmsh}
634 \modulesynopsis{Python geometry description and meshing interface}
635
636 The class and methods described here provide an interface to the mesh
637 generation software, which is currently \gmshextern. This interface could be
638 adopted to triangle or another mesh generation package if this is
639 deemed to be desirable in the future.
640
641 \begin{classdesc}{Design}{
642 \optional{dim=3, \optional{element_size=1., \optional{order=1, \optional{keep_files=False}}}}}
643 The \class{Design} describes the geometry defined by primitives to be meshed.
644 The \var{dim} specifies the spatial dimension. The argument \var{element_size} defines the global
645 element size which is multiplied by the local scale to set the element size at each \Point.
646 The argument \var{order} defines the element order to be used. If \var{keep_files} is set to
647 \True temporary files a kept otherwise they are removed when the instance of the class is deleted.
648 \end{classdesc}
649
650
651 \begin{memberdesc}[Design]{GMSH}
652 gmsh file format~\cite{GMSH}.
653 \end{memberdesc}
654
655 \begin{memberdesc}[Design]{IDEAS}
656 I-DEAS universal file format~\cite{IDEAS}.
657 \end{memberdesc}
658
659 \begin{memberdesc}[Design]{VRML}
660 VRML file format, \cite{VRML}.
661 \end{memberdesc}
662
663 \begin{memberdesc}[Design]{STL}
664 STL file format~\cite{STL}.
665 \end{memberdesc}
666 \begin{memberdesc}[Design]{NASTRAN}
667 NASTRAN bulk data format~\cite{NASTRAN}.
668 \end{memberdesc}
669
670 \begin{memberdesc}[Design]{MEDIT}
671 Medit file format~\cite{MEDIT}.
672 \end{memberdesc}
673
674 \begin{memberdesc}[Design]{CGNS}
675 CGNS file format~\cite{CGNS}.
676 \end{memberdesc}
677
678 \begin{memberdesc}[Design]{PLOT3D}
679 Plot3D file format~\cite{PLOT3D}.
680 \end{memberdesc}
681
682
683 \begin{memberdesc}[Design]{DIFFPACK}
684 Diffpack 3D file format~\cite{DIFFPACK}.
685 \end{memberdesc}
686
687 \begin{memberdesc}[Design]{DELAUNAY}
688 the Delauny triangulator, see \gmshextern,~\cite{TETGEN}.
689 \end{memberdesc}
690
691 \begin{memberdesc}[Design]{MESHADAPT}
692 the gmsh triangulator, see \gmshextern.
693 \end{memberdesc}
694
695 \begin{memberdesc}[Design]{FRONTAL}
696 the NETGEN~\cite{NETGEN} triangulator.
697 \end{memberdesc}
698
699 \begin{methoddesc}[Design]{generate}{}
700 generates the mesh file. The data are are written to the file \var{Design.getMeshFileName}.
701 \end{methoddesc}
702
703
704 \begin{methoddesc}[Design]{setDim}{\optional{dim=3}}
705 sets the spatial dimension which needs to be $1$, $2$ or $3$.
706 \end{methoddesc}
707
708 \begin{methoddesc}[Design]{getDim}{}
709 returns the spatial dimension.
710 \end{methoddesc}
711
712 \begin{methoddesc}[Design]{setElementOrder}{\optional{order=1}}
713 sets the element order which needs to be $1$ or $2$.
714 \end{methoddesc}
715
716 \begin{methoddesc}[Design]{getElementOrder}{}
717 returns the element order.
718 \end{methoddesc}
719
720 \begin{methoddesc}[Design]{setElementSize}{\optional{element_size=1}}
721 set the global element size. The local element size at a point is defined as
722 the global element size multiplied by the local scale. The element size must be positive.
723 \end{methoddesc}
724
725
726 \begin{methoddesc}[Design]{getElementSize}{}
727 returns the global element size.
728 \end{methoddesc}
729
730
731
732 \begin{methoddesc}[Design]{setKeepFilesOn}{}
733 work files are kept at the end of the generation.
734 \end{methoddesc}
735
736 \begin{methoddesc}[Design]{setKeepFilesOff}{}
737 work files are deleted at the end of the generation.
738 \end{methoddesc}
739
740 \begin{methoddesc}[Design]{keepFiles}{}
741 returns \True if work files are kept. Otherwise \False is returned.
742 \end{methoddesc}
743
744 \begin{methoddesc}[Design]{setScriptFileName}{\optional{name=None}}
745 set the file name for the gmsh input script. if no name is given a name with extension "geo" is generated.
746 \end{methoddesc}
747
748 \begin{methoddesc}[Design]{getScriptFileName}{}
749 returns the name of the file for the gmsh script.
750 \end{methoddesc}
751
752
753 \begin{methoddesc}[Design]{setMeshFileName}{\optional{name=None}}
754 sets the name for the mesh file. if no name is given a name is generated.
755 The format is set by \\ \var{Design.setFileFormat}.
756 \end{methoddesc}
757
758 \begin{methoddesc}[Design]{getMeshFileName}{}
759 returns the name of the mesh file
760 \end{methoddesc}
761
762
763 \begin{methoddesc}[Design]{addItems}{*items}
764 adds the tuple of var{items}. An item can be any primitive or a \class{PropertySet}.
765 \warning{If a \PropertySet is added as an item added object that are not
766 part of a \PropertySet are not considered in the messing.
767 }
768 \end{methoddesc}
769
770 \begin{methoddesc}[Design]{getItems}{}
771 returns a list of the items
772 \end{methoddesc}
773
774 \begin{methoddesc}[Design]{clearItems}{}
775 resets the items in design
776 \end{methoddesc}
777
778 \begin{methoddesc}[Design]{getMeshHandler}{}
779 returns a handle to the mesh. The call of this method generates the mesh from the geometry and
780 returns a mechanism to access the mesh data. In the current implementation this
781 method returns a file name for a file containing the mesh data.
782 \end{methoddesc}
783
784 \begin{methoddesc}[Design]{getScriptString}{}
785 returns the gmsh script to generate the mesh as a string.
786 \end{methoddesc}
787
788 \begin{methoddesc}[Design]{getCommandString}{}
789 returns the gmsh command used to generate the mesh as string.
790 \end{methoddesc}
791
792 \begin{methoddesc}[Design]{setOptions}{
793 \optional{optimize_quality=\True
794 \optional{, smoothing=1
795 \optional{, curvature_based_element_size=\False\\
796 \optional{, algorithm2D=\var{Design.MESHADAPT}
797 \optional{, algorithm3D=\var{Design.FRONTAL}\\
798 \optional{, generate_hexahedra=False}}}}}}}
799 sets options for the mesh generator. \var{algorithm2D} sets the 2D meshing algorithm to be used.
800 The algorithm needs to be \var{Design.DELAUNAY}
801 \var{Design.FRONTAL}
802 or \var{Design.MESHADAPT}. By default \var{Design.MESHADAPT} is used.
803 \var{algorithm3D} sets the 3D meshing algorithm to be used.
804 The algorithm needs to be \var{Design.DELAUNAY}
805 or \var{Design.FRONTAL}
806 . By default \var{Design.FRONTAL} is used.
807 \var{optimize_quality}=\True invokes an optimization of the mesh quality.
808 \var{smoothing} sets the number of smoothing steps to be applied to the mesh.
809 \var{curvature_based_element_size}=\True switches on curvature based definition of element size.
810 \var{generate_hexahedra}=\True switches on the usage of quadrilateral/hexahedra elements.
811 \end{methoddesc}
812
813 \begin{methoddesc}[Design]{getTagMap}{}
814 returns a \class{TagMap} to map the name \class{PropertySet} in the class to tag numbers generated by gmsh.
815 \end{methoddesc}
816
817 \begin{methoddesc}[Design]{setFileFormat}{\optional{format=\var{Design.GMSH}}}
818 set the file format. \var{format} must be one of the values:\\
819 \var{Design.GMSH} \\
820 \var{Design.IDEAS}\\
821 \var{Design.VRML}\\
822 \var{Design.STL}\\
823 \var{Design.NASTRAN}\\
824 \var{Design.MEDIT}\\
825 \var{Design.CGNS}\\
826 \var{Design.PLOT3D}\\
827 \var{Design.DIFFPACK}.
828 \end{methoddesc}
829
830 \begin{methoddesc}[Design]{getFileFormat}{}
831 returns the file format.
832 \end{methoddesc}

  ViewVC Help
Powered by ViewVC 1.1.26