 Commented declaremodule and modulesynopsis.

 1 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 % 4 % Copyright (c) 2003-2010 by University of Queensland 5 % Earth Systems Science Computational Center (ESSCC) 6 7 % 8 % Primary Business: Queensland, Australia 9 % Licensed under the Open Software License version 3.0 10 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}