# ----------------------------------------------------------------------------- # # Gmsh Python extended tutorial 3 # # Post-processing data import: list-based # # ----------------------------------------------------------------------------- import gmsh import sys gmsh.initialize(sys.argv) # Gmsh supports two types of post-processing data: "list-based" and # "model-based". Both types of data are handled through the `view' interface. # List-based views are completely independent from any model and any mesh: they # are self-contained and simply contain lists of coordinates and values, element # by element, for 3 types of fields (scalar "S", vector "V" and tensor "T") and # several types of element shapes (point "P", line "L", triangle "T", quadrangle # "Q", tetrahedron "S", hexahedron "H", prism "I" and pyramid "Y"). (See `x4.py' # for a tutorial on model-based views.) # To create a list-based view one should first create a view: t1 = gmsh.view.add("A list-based view") # List-based data is then added by specifying the type as a 2 character string # that combines a field type and an element shape (e.g. "ST" for a scalar field # on triangles), the number of elements to be added, and the concatenated list # of coordinates (e.g. 3 "x" coordinates, 3 "y" coordinates, 3 "z" coordinates # for first order triangles) and values for each element (e.g. 3 values for # first order scalar triangles, repeated for each step if there are several time # steps). # Let's create two triangles... triangle1 = [0., 1., 1., # x coordinates of the 3 triangle nodes 0., 0., 1., # y coordinates of the 3 triangle nodes 0., 0., 0.] # z coordinates of the 3 triangle nodes triangle2 = [0., 1., 0., 0., 1., 1., 0., 0., 0.] # ... and append values for 10 time steps for step in range(0, 10): triangle1.extend([10., 11. - step, 12.]) # 3 node values for each step triangle2.extend([11., 12., 13. + step]) # List-based data is just added by concatenating the data for all the triangles: gmsh.view.addListData(t1, "ST", 2, triangle1 + triangle2) # Internally, post-processing views parsed by the .geo file parser create such # list-based data (see e.g. `t7.py', `t8.py' and `t9.py'), independently of any # mesh. # Vector or tensor fields can be imported in the same way, the only difference # beeing the type (starting with "V" for vector fields and "T" for tensor # fields) and the number of components. For example a vector field on a line # element can be added as follows: line = [ 0., 1., # x coordinate of the 2 line nodes 1.2, 1.2, # y coordinate of the 2 line nodes 0., 0. # z coordinate of the 2 line nodes ] for step in range(0, 10): # 3 vector components for each node (2 nodes here), for each step line.extend([10. + step, 0., 0., 10. + step, 0., 0.]) gmsh.view.addListData(t1, "VL", 1, line) # List-based data can also hold 2D (in window coordinates) and 3D (in model # coordinates) strings (see `t4.py'). Here we add a 2D string located on the # bottom-left of the window (with a 20 pixels offset), as well as a 3D string # located at model coordinates (0.5, 0.5. 0): gmsh.view.addListDataString(t1, [20., -20.], ["Created with Gmsh"]) gmsh.view.addListDataString(t1, [0.5, 1.5, 0.], ["A multi-step list-based view"], ["Align", "Center", "Font", "Helvetica"]) # The various attributes of the view can be queried and changed using the option # interface: gmsh.view.option.setNumber(t1, "TimeStep", 5) gmsh.view.option.setNumber(t1, "IntervalsType", 3) ns = gmsh.view.option.getNumber(t1, "NbTimeStep") print("View " + str(t1) + " has " + str(ns) + " time steps") # Views can be queried and modified in various ways using plugins (see `t9.py'), # or probed directly using `gmsh.view.probe()' - here at point (0.9, 0.1, 0): print("Value at (0.9, 0.1, 0)", gmsh.view.probe(t1, 0.9, 0.1, 0)) # Views can be saved to disk using `gmsh.view.write()': gmsh.view.write(t1, "x3.pos") # High-order datasets can be provided by setting the interpolation matrices # explicitly. Let's create a second view with second order interpolation on # a 4-node quadrangle. # Add a new view: t2 = gmsh.view.add("Second order quad") # Set the node coordinates: quad = [0., 1., 1., 0., # x coordinates of the 4 quadrangle nodes -1.2, -1.2, -0.2, -0.2, # y coordinates of the 4 quadrangle nodes 0., 0., 0., 0.] # z coordinates of the 4 quadrangle nodes # Add nine values that will be interpolated by second order basis functions quad.extend([1., 1., 1., 1., 3., 3., 3., 3., -3.]) # Set the two interpolation matrices c[i][j] and e[i][j] defining the d = 9 # basis functions: f[i](u, v, w) = sum_(j = 0, ..., d - 1) c[i][j] u^e[j][0] # v^e[j][1] w^e[j][2], i = 0, ..., d-1, with u, v, w the coordinates in the # reference element: gmsh.view.setInterpolationMatrices(t2, "Quadrangle", 9, [0, 0, 0.25, 0, 0, -0.25, -0.25, 0, 0.25, 0, 0, 0.25, 0, 0, -0.25, 0.25, 0, -0.25, 0, 0, 0.25, 0, 0, 0.25, 0.25, 0, 0.25, 0, 0, 0.25, 0, 0, 0.25, -0.25, 0, -0.25, 0, 0, -0.5, 0.5, 0, 0.5, 0, -0.5, 0, 0, 0.5, -0.5, 0, 0.5, 0, -0.5, 0, 0, 0, 0, -0.5, 0.5, 0, -0.5, 0, 0.5, 0, 0, 0.5, -0.5, 0, -0.5, 0, 0.5, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0]) # Note that two additional interpolation matrices could also be provided to # interpolate the geometry, i.e. to interpolate curved elements. # Add the data to the view: gmsh.view.addListData(t2, "SQ", 1, quad) # In order to visualize the high-order field, one must activate adaptive # visualization, set a visualization error threshold and a maximum subdivision # level (Gmsh does automatic mesh refinement to visualize the high-order field # with the requested accuracy): gmsh.view.option.setNumber(t2, "AdaptVisualizationGrid", 1) gmsh.view.option.setNumber(t2, "TargetError", 1e-2) gmsh.view.option.setNumber(t2, "MaxRecursionLevel", 5) # Launch the GUI to see the results: if '-nopopup' not in sys.argv: gmsh.fltk.run() gmsh.finalize()