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 1 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 % 4 % Copyright (c) 2003-2008 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 15 \chapter{The Module \pycad} \label{PYCAD CHAP} 16 17 18 \section{Introduction} 19 20 \pycad provides a simple way to build a mesh for your finite element 21 simulation. You begin by building what we call a {\it Design} using 22 primitive geometric objects, and then to go on to build a mesh from 23 the {\it Design}. The final step of generating the mesh from a {\it 24 Design} uses freely available mesh generation software, such as \gmshextern. 25 26 A {\it Design} is built by defining points, which are used to specify 27 the corners of geometric objects and the vertices of curves. Using 28 points you construct more interesting objects such as lines, 29 rectangles, and arcs. By adding many of these objects into what we 30 call a {\it Design}, you can build meshes for arbitrarily complex 2-D 31 and 3-D structures. 32 33 The example included below shows how to use {\it pycad} to create a 2-D mesh 34 in the shape of a trapezoid with a cutout area. 35 36 \begin{python} 37 from esys.pycad import * 38 from esys.pycad.gmsh import Design 39 from esys.finley import MakeDomain 40 41 # A trapezoid 42 p0=Point(0.0, 0.0, 0.0) 43 p1=Point(1.0, 0.0, 0.0) 44 p2=Point(1.0, 0.5, 0.0) 45 p3=Point(0.0, 1.0, 0.0) 46 l01=Line(p0, p1) 47 l12=Line(p1, p2) 48 l23=Line(p2, p3) 49 l30=Line(p3, p0) 50 c=CurveLoop(l01, l12, l23, l30) 51 52 # A small triangular cutout 53 x0=Point(0.1, 0.1, 0.0) 54 x1=Point(0.5, 0.1, 0.0) 55 x2=Point(0.5, 0.2, 0.0) 56 x01=Line(x0, x1) 57 x12=Line(x1, x2) 58 x20=Line(x2, x0) 59 cutout=CurveLoop(x01, x12, x20) 60 61 # Create the surface with cutout 62 s=PlaneSurface(c, holes=[cutout]) 63 64 # Create a Design which can make the mesh 65 d=Design(dim=2, element_size=0.05) 66 67 # Add the trapezoid with cutout 68 d.addItems(s) 69 70 # Create the geometry, mesh and Escript domain 71 d.setScriptFileName("trapezoid.geo") 72 d.setMeshFileName("trapezoid.msh") 73 domain=MakeDomain(d, integrationOrder=-1, reducedIntegrationOrder=-1, optimizeLabeling=True) 74 75 # Create a file that can be read back in to python with mesh=ReadMesh(fileName) 76 domain.write("trapezoid.fly") 77 \end{python} 78 79 This example is included with the software in 80 \code{pycad/examples/trapezoid.py}. If you have gmsh installed you can 81 run the example and view the geometry and mesh with: 82 83 \begin{python} 84 python trapezoid.py 85 gmsh trapezoid.geo 86 gmsh trapezoid.msh 87 \end{python} 88 89 A \code{CurveLoop} is used to connect several lines into a single curve. 90 It is used in the example above to create the trapezoidal outline for the grid 91 and also for the triangular cutout area. 92 You can use any number of lines when creating a \code{CurveLoop}, but 93 the end of one line must be identical to the start of the next. 94 95 Sometimes you might see us write \code{-c} where \code{c} is a 96 \code{CurveLoop}. This is the reverse curve of the curve \code{c}. 97 It is identical to the original except that its points are traversed 98 in the opposite order. This may make it easier to connect two curves 99 in a \code{CurveLoop}. 100 101 The example python script above calls both 102 \code{d.setScriptFileName()} and \code{d.setMeshFileName()}. You need 103 only call these if you wish to save the gmsh geometry and mesh files. 104 105 Note that the underlying mesh generation software will not accept all 106 the geometries you can create with {\it pycad}. For example, {\it 107 pycad} will happily allow you to create a 2-D {\it Design} that is a 108 closed loop with some additional points or lines lying outside of the 109 enclosed area, but gmsh will fail to create a mesh for it. 110 111 112 113 114 115 116 \section{\pycad Classes} 117 \declaremodule{extension}{esys.pycad} 118 \modulesynopsis{Python geometry description and meshing interface} 119 120 \subsection{Primitives} 121 122 Some of the most commonly-used objects in {\it pycad} are listed here. For a more complete 123 list see the full API documentation. 124 125 \begin{classdesc}{Point}{x1, x2, x3} 126 Create a point with from coordinates. 127 \end{classdesc} 128 129 \begin{classdesc}{Line}{point1, point2} 130 Create a line with between starting and ending points. 131 \end{classdesc} 132 133 \begin{classdesc}{Curve}{point1, point2, ...} 134 Create a \code{Curve}, which is simply a list of points. 135 \end{classdesc} 136 137 \begin{classdesc}{Spline}{curve} 138 Interpret a \code{Curve} using a spline. 139 \end{classdesc} 140 141 \begin{classdesc}{BSpline}{curve} 142 Interpret a \code{Curve} using a b-spline. 143 \end{classdesc} 144 145 \begin{classdesc}{BezierCurve}{curve} 146 Interpret a \code{Curve} using a Bezier curve. 147 \end{classdesc} 148 149 \begin{classdesc}{CurveLoop}{list} 150 Create a closed \code{Curve} connecting the lines and/or points given in the \code{list}. 151 \end{classdesc} 152 153 \begin{classdesc}{Arc}{center_point, start_point, end_point} 154 Create an arc by specifying a center for a circle and start and end points. An arc may subtend an angle of at most $\pi$ radians. 155 \end{classdesc} 156 157 \begin{classdesc}{PlaneSurface}{loop, \optional{holes=[list]}} 158 Create a surface for a 2-D mesh, which may have one or more holes. 159 \end{classdesc} 160 161 \begin{classdesc}{RuledSurface}{list} 162 Create a surface that can be interpolated using transfinite interpolation. 163 \end{classdesc} 164 165 \begin{classdesc}{SurfaceLoop}{list} 166 Create a loop of 2D primitives, which defines the shell of a volume. 167 \end{classdesc} 168 169 \begin{classdesc}{Volume}{loop, \optional{holes=[list]}} 170 Create a volume for a 3-D mesh given a SurfaceLoop, which may have one or more holes. 171 \end{classdesc} 172 173 \begin{classdesc}{PropertySet}{list} 174 Create a PropertySet given a list of 1-D, 2-D or 3-D items. See the section on Properties below for more information. 175 \end{classdesc} 176 177 %============================================================================================================ 178 \subsection{Transformations} 179 180 Sometimes it's convenient to create an object and then make copies at 181 different orientations and in different sizes. Transformations are 182 used to move geometrical objects in the 3-dimensional space and to 183 resize them. 184 185 \begin{classdesc}{Translation}{\optional{b=[0,0,0]}} 186 defines a translation $x \to x+b$. \var{b} can be any object that can be converted 187 into a \numarray object of shape $(3,)$. 188 \end{classdesc} 189 190 \begin{classdesc}{Rotatation}{\optional{axis=[1,1,1], \optional{ point = [0,0,0], \optional{angle=0*RAD} } } } 191 defines a rotation by \var{angle} around axis through point \var{point} and direction \var{axis}. 192 \var{axis} and \var{point} can be any object that can be converted 193 into a \numarray object of shape $(3,)$. 194 \var{axis} does not have to be normalized but must have positive length. The right hand rule~\cite{RIGHTHANDRULE} 195 applies. 196 \end{classdesc} 197 198 199 \begin{classdesc}{Dilation}{\optional{factor=1., \optional{center=[0,0,0]}}} 200 defines a dilation by the expansion/contraction \var{factor} with 201 \var{center} as the dilation center. 202 \var{center} can be any object that can be converted 203 into a \numarray object of shape $(3,)$. 204 \end{classdesc} 205 206 \begin{classdesc}{Reflection}{\optional{normal=[1,1,1], \optional{offset=0}}} 207 defines a reflection on a plane defined in normal form $n^t x = d$ 208 where $n$ is the surface normal \var{normal} and $d$ is the plane \var{offset}. 209 \var{normal} can be any object that can be converted 210 into a \numarray object of shape $(3,)$. 211 \var{normal} does not have to be normalized but must have positive length. 212 \end{classdesc} 213 214 \begin{datadesc}{DEG} 215 A constant to convert from degrees to an internal angle representation in radians. For instance use \code{90*DEG} for $90$ degrees. 216 \end{datadesc} 217 218 \subsection{Properties} 219 220 If you are building a larger geometry you may find it convenient to 221 create it in smaller pieces and then assemble them into the whole. 222 Property sets make this easy, and they allow you to name the smaller 223 pieces for convenience. 224 225 Property sets are used to bundle a set of geometrical objects in a 226 group. The group is identified by a name. Typically a property set 227 is used to mark subregions with share the same material properties or 228 to mark portions of the boundary. For efficiency, the \Design class 229 object assigns a integer to each of its property sets, a so-called tag 230 \index{tag}. The appropriate tag is attached to the elements at 231 generation time. 232 233 See the file \code{pycad/examples/quad.py} for an example using a {\it PropertySet}. 234 235 236 \begin{classdesc}{PropertySet}{name,*items} 237 defines a group geometrical objects which can be accessed through a \var{name} 238 The objects in the tuple \var{items} mast all be \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD objects. 239 \end{classdesc} 240 241 242 \begin{methoddesc}[PropertySet]{getManifoldClass}{} 243 returns the manifold class \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD expected from the items 244 in the property set. 245 \end{methoddesc} 246 247 \begin{methoddesc}[PropertySet]{getDim}{} 248 returns the spatial dimension of the items 249 in the property set. 250 \end{methoddesc} 251 252 \begin{methoddesc}[PropertySet]{getName}{} 253 returns the name of the set 254 \end{methoddesc} 255 256 \begin{methoddesc}[PropertySet]{setName}{name} 257 sets the name. This name should be unique within a \Design. 258 \end{methoddesc} 259 260 \begin{methoddesc}[PropertySet]{addItem}{*items} 261 adds a tuple of items. They need to be objects of class \ManifoldOneD, \ManifoldTwoD or \ManifoldThreeD. 262 \end{methoddesc} 263 264 \begin{methoddesc}[PropertySet]{getItems}{} 265 returns the list of items 266 \end{methoddesc} 267 268 \begin{methoddesc}[PropertySet]{clearItems}{} 269 clears the list of items 270 \end{methoddesc} 271 272 \begin{methoddesc}[PropertySet]{getTag}{} 273 returns the tag used for this property set 274 \end{methoddesc} 275 276 \section{Interface to the mesh generation software} 277 \declaremodule{extension}{esys.pycad.gmsh} 278 \modulesynopsis{Python geometry description and meshing interface} 279 280 The class and methods described here provide an interface to the mesh 281 generation software, which is currently gmsh. This interface could be 282 adopted to triangle or another mesh generation package if this is 283 deemed to be desirable in the future. 284 285 \begin{classdesc}{Design}{ 286 \optional{dim=3, \optional{element_size=1., \optional{order=1, \optional{keep_files=False}}}}} 287 The \class{Design} describes the geometry defined by primitives to be meshed. 288 The \var{dim} specifies the spatial dimension. The argument \var{element_size} defines the global 289 element size which is multiplied by the local scale to set the element size at each \Point. 290 The argument \var{order} defines the element order to be used. If \var{keep_files} is set to 291 \True temporary files a kept otherwise they are removed when the instance of the class is deleted. 292 \end{classdesc} 293 294 295 \begin{methoddesc}[Design]{setDim}{\optional{dim=3}} 296 sets the spatial dimension which needs to be $1$, $2$ or $3$. 297 \end{methoddesc} 298 299 \begin{methoddesc}[Design]{getDim}{} 300 returns the spatial dimension. 301 \end{methoddesc} 302 303 \begin{methoddesc}[Design]{setElementOrder}{\optional{order=1}} 304 sets the element order which needs to be $1$ or $2$. 305 \end{methoddesc} 306 307 \begin{methoddesc}[Design]{getElementOrder}{} 308 returns the element order. 309 \end{methoddesc} 310 311 312 \begin{methoddesc}[Design]{setElementSize}{\optional{element_size=1}} 313 set the global element size. The local element size at a point is defined as 314 the global element size multiplied by the local scale. The element size must be positive. 315 \end{methoddesc} 316 317 318 \begin{methoddesc}[Design]{getElementSize}{} 319 returns the global element size. 320 \end{methoddesc} 321 322 \begin{memberdesc}[Design]{DELAUNAY} 323 the gmsh Delauny triangulator. 324 \end{memberdesc} 325 326 \begin{memberdesc}[Design]{TETGEN} 327 the TetGen~\cite{TETGEN} triangulator. 328 \end{memberdesc} 329 330 \begin{memberdesc}[Design]{NETGEN} 331 the NETGEN~\cite{NETGEN} triangulator. 332 \end{memberdesc} 333 334 \begin{methoddesc}[Design]{setKeepFilesOn}{} 335 work files are kept at the end of the generation. 336 \end{methoddesc} 337 338 \begin{methoddesc}[Design]{setKeepFilesOff}{} 339 work files are deleted at the end of the generation. 340 \end{methoddesc} 341 342 \begin{methoddesc}[Design]{keepFiles}{} 343 returns \True if work files are kept. Otherwise \False is returned. 344 \end{methoddesc} 345 346 \begin{methoddesc}[Design]{setScriptFileName}{\optional{name=None}} 347 set the filename for the gmsh input script. if no name is given a name with extension "geo" is generated. 348 \end{methoddesc} 349 350 \begin{methoddesc}[Design]{getScriptFileName}{} 351 returns the name of the file for the gmsh script. 352 \end{methoddesc} 353 354 355 \begin{methoddesc}[Design]{setMeshFileName}{\optional{name=None}} 356 sets the name for the gmsh mesh file. if no name is given a name with extension "msh" is generated. 357 \end{methoddesc} 358 359 \begin{methoddesc}[Design]{getMeshFileName}{} 360 returns the name of the file for the gmsh msh 361 \end{methoddesc} 362 363 364 \begin{methoddesc}[Design]{addItems}{*items} 365 adds the tuple of var{items}. An item can be any primitive or a \class{PropertySet}. 366 \warning{If a \PropertySet is added as an item added object that are not 367 part of a \PropertySet are not considered in the messing. 368 } 369 370 \end{methoddesc} 371 372 \begin{methoddesc}[Design]{getItems}{} 373 returns a list of the items 374 \end{methoddesc} 375 376 \begin{methoddesc}[Design]{clearItems}{} 377 resets the items in design 378 \end{methoddesc} 379 380 \begin{methoddesc}[Design]{getMeshHandler}{} 381 returns a handle to the mesh. The call of this method generates the mesh from the geometry and 382 returns a mechanism to access the mesh data. In the current implementation this 383 method returns a file name for a gmsh file containing the mesh data. 384 \end{methoddesc} 385 386 \begin{methoddesc}[Design]{getScriptString}{} 387 returns the gmsh script to generate the mesh as a string. 388 \end{methoddesc} 389 390 \begin{methoddesc}[Design]{getCommandString}{} 391 returns the gmsh command used to generate the mesh as string. 392 \end{methoddesc} 393 394 \begin{methoddesc}[Design]{setOptions}{\optional{algorithm=None, \optional{ optimize_quality=True,\optional{ smoothing=1}}}} 395 sets options for the mesh generator. \var{algorithm} sets the algorithm to be used. 396 The algorithm needs to be \var{Design.DELAUNAY} 397 \var{Design.TETGEN} 398 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. 399 \end{methoddesc} 400 401 \begin{methoddesc}[Design]{getTagMap}{} 402 returns a \class{TagMap} to map the name \class{PropertySet} in the class to tag numbers generated by gmsh. 403 \end{methoddesc}