octave-msh 1.0.10-5 / usr / share / octave / packages / msh-1.0.10 / doc-cache

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msh2m_displacement_smoothing


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 -- Function File: [AX,AY] = msh2m_displacement_smoothing(MSH,K)

     Displace the boundary of a 2D mesh setting a spring with
     force/length constant K along each edge and enforcing equilibrium.

     This function builds matrices containing the resulting (linearized)
     equation for x and y coordinates of each mesh node.  Boundary
     conditions enforcing the displacement (Dirichlet type problem) or
     the force (Neumann type) at the boundary must be added to make the
     system solvable, e.g.:

          msh = msh2m_structured_mesh(linspace(0,1,10), linspace(0,1,10), 1,1:4,"left");

          dnodes   = msh2m_nodes_on_sides(msh,1:4);
          varnodes = setdiff([1:columns(msh.p)],dnodes);
          xd     = msh.p(1,dnodes)';
          yd     = msh.p(2,dnodes)';
          dx     = dy    = zeros(columns(msh.p),1);
          dxtot  = dytot = -.5*sin(xd.*yd*pi/2);
          Nsteps = 10;

          for ii = 1:Nsteps
           dx(dnodes) = dxtot;
           dy(dnodes) = dytot;
           [Ax,Ay] = msh2m_displacement_smoothing(msh,1);
           dx(varnodes) = Ax(varnodes,varnodes) \ ...
               (-Ax(varnodes,dnodes)*dx(dnodes));
           dy(varnodes) = Ay(varnodes,varnodes) \ ...
               (-Ay(varnodes,dnodes)*dy(dnodes));
           msh.p += [ dx'/Nsteps; dy'/Nsteps ] ;
           triplot(msh.t(1:3,:)',msh.p(1,:)',msh.p(2,:)');
           pause(.01)
          endfor

     See also: msh2m_jiggle_mesh.


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Displace the boundary of a 2D mesh setting a spring with force/length
constant K



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msh2m_equalize_mesh


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 -- Function File: [MESH] = msh2m_equalize_mesh(MESH)

     Apply a baricentric regularization to equalize the size of triangle
     edges, i.e.  move each node to the center of mass of the patch of
     triangles to which it belongs.

     May be useful when distorting a mesh.  Type 'demo
     msh2m_equalize_mesh' to see some examples.

     See also: msh2m_displacement_smoothing.


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Apply a baricentric regularization to equalize the size of triangle
edges, i.e.



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msh2m_geometrical_properties


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 -- Function File: [VARARGOUT] =
          msh2m_geometrical_properties(MESH,[STRING1,STRING2,...])

     Compute MESH geometrical properties identified by input strings.

     Valid properties are:
        * '"bar"': return a matrix with size 2 times the number of mesh
          elements containing the center of mass coordinates.
        * '"cir"': return a matrix with size 2 times the number of mesh
          elements containing the circumcenter coordinates.
        * '"emidp"': return a matrix with size 2 times the number of
          side edges containing their midpoint coordinates.
        * '"slength"': return a matrix with size 3 times the number of
          mesh elements containing the length of each element side.
        * '"cdist"': return a matrix of size 3 times the number of mesh
          elements containing the distance among circumcenters of
          neighbouring elements.  If the corresponding side lies on the
          edge, the distance between circumcenter and border edge is
          returned in the matrix.
        * '"wjacdet"': return the weigthed Jacobian determinant used for
          the numerical integration with trapezoidal rule over an
          element.
        * '"shg"': return a matrix of size 3 times the number of
          elements matrix containing the gradient of P1 shape functions.
        * '"area"': return a row vector containing the area of every
          element.
        * '"midedge"': return a multi-dimensional array with size 2
          times 3 times the number of elements containing the
          coordinates of the midpoint of every edge.

     The output will contain the geometrical properties requested in the
     input in the same order specified in the function call.

     If an unexpected string is given as input, an empty vector is
     returned in output.

     See also: msh2m_topological_properties,
     msh3m_geometrical_properties.


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Compute MESH geometrical properties identified by input strings.



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msh2m_gmsh


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 -- Function File: [MESH] = msh2m_gmsh(GEOMETRY,OPTION,VALUE,...)
 -- Function File: [MESH, GMSH_OUT] = msh2m_gmsh(...)

     Construct an unstructured triangular 2D mesh making use of the free
     software gmsh.

     The compulsory argument GEOMETRY is the basename of the '*.geo'
     file to be meshed.

     The optional arguments OPTION and VALUE identify respectively a
     gmsh option and its value.  For more information regarding the
     possible option to pass, refer to gmsh manual or gmsh site
     <http://www.geuz.org/gmsh/>.

     The returned value MESH is a PDE-tool like mesh structure.  If the
     function is called with two outputs GMSH_OUT is the verbose output
     of the gmsh subprocess.

     See also: msh2m_structured_mesh, msh3m_gmsh,
     msh2m_mesh_along_spline.


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Construct an unstructured triangular 2D mesh making use of the free
software gms



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msh2m_gmsh_write


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 -- Function File: = msh2m_gmsh_write (FILENAME, MSH)

     See also: msh3m_gmsh_write.


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See also: msh3m_gmsh_write.



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msh2m_jiggle_mesh


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 -- Function File: [NEWMSH] = msh2m_jiggle_mesh(MSH,STEPS)

     Equalize the size of triangle edges setting a spring of rest length
     FACTOR*AREA along each edge of the mesh and solving for static
     equilibrium.

     The non-linear eqautions of the system obtained are solved via a
     non-linear Gauss-Seidel method.  STEP is the number of steps of the
     method to be applied.

     May be useful when distorting a mesh, type 'demo msh2m_jiggle_mesh'
     to see some examples.

     See also: msh2m_displacement_smoothing, msh2m_equalize_mesh.


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Equalize the size of triangle edges setting a spring of rest length
FACTOR*AREA 



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msh2m_join_structured_mesh


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 -- Function File: [MESH] =
          msh2m_join_structured_mesh(MESH1,MESH2,S1,S2)

     Join the two structured meshes MESH1 and MESH2 into one single
     mesh.

     The two meshes must share a common edge identified by S1 and S2.

     *WARNING*: the two meshes must share the same vertexes on the
     common edge.

     See also: msh2m_structured_mesh, msh2m_gmsh, msh2m_submesh,
     msh3m_join_structured_mesh.


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Join the two structured meshes MESH1 and MESH2 into one single mesh.



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msh2m_mesh_along_spline


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 -- Function File: [MESH] = msh2m_mesh_along_spline(XC,YC,NNX,NNY,SIGMA)

     Generate a structured mesh in a thin layer of size SIGMA sitting on
     a natural Catmull-Rom type cubic spline with control points XC, YC.

     If NNX and NNY are scalars, the mesh has NNX nodes in the direction
     along the spline and NNY in the normal direction.

     If NNX and NNY are vectors they indicate the curvilinear
     coordinates of the mesh nodes.

     The returned value MESH is a PDE-tool like mesh structure.

     Be aware that if SIGMA is not much smaller than the curvature of
     the line the resulting mesh may be invalid.

     See also: msh2m_structured_mesh, msh2m_gmsh, msh3m_structured_mesh.


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Generate a structured mesh in a thin layer of size SIGMA sitting on a
natural Ca



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msh2m_nodes_on_sides


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 -- Function File: [NODELIST] = msh2m_nodes_on_sides(MESH,SIDELIST)

     Return a list of MESH nodes lying on the sides specified in
     SIDELIST.

     See also: msh2m_geometrical_properties,
     msh2m_topological_properties, msh3m_nodes_on_faces.


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Return a list of MESH nodes lying on the sides specified in SIDELIST.



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msh2m_structured_mesh


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 -- Function File: [MESH] =
          msh2m_structured_mesh(X,Y,REGION,SIDES,STRING)

     Construct a structured triangular 2D mesh on a rectangular domain.

        * X and Y are the one dimensional mesh vector of the
          corresponding Cartesian axis.
        * REGION is a number identifying the geometrical surface region,
          while SIDES is a 4 components vector containing the numbers
          used to identify the geometrical side edges.
        * STRING is an optional value specifying the orientation of the
          diagonal edge of the structured mesh.  It may take the value
          '"right"' (default), '"left"', '"random"'.

     The returned value MESH is a PDE-tool like mesh structure composed
     of the following fields:
        - P: matrix with size 2 times number of mesh points.
             * 1st row: x-coordinates of the points.
             * 2nd row: y-coordinates of the points.
        - E: matrix with size 7 times number of mesh side edges.
             * 1st row: number of the first vertex of the side edge.
             * 2nd row: number of the second vertex of the side edge.
             * 3rd row: set to 0, present for compatibility with MatLab
               PDE-tool.
             * 4th row: set to 0, present for compatibility with MatLab
               PDE-tool.
             * 5th row: number of the geometrical border containing the
               side edge.
             * 6th row: number of the geometrical surface to the right
               of side edge.
             * 7th row: number of the geometrical surface to the left of
               the side edge.
        - T: matrix with size 4 times number of mesh elements.
             * 1st row: number of the first vertex of the element.
             * 2nd row: number of the second vertex of the element.
             * 3rd row: number of the third vertex of the element.
             * 4th row: number of the geometrical surface containing the
               element.

     See also: msh3m_structured_mesh, msh2m_gmsh,
     msh2m_mesh_along_spline, msh2m_join_structured_mesh, msh2m_submesh.


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Construct a structured triangular 2D mesh on a rectangular domain.



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msh2m_submesh


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 -- Function File: [OMESH,NODELIST,ELEMENTLIST] =
          msh2m_submesh(IMESH,INTRFC,SDL)

     Extract the subdomain(s) in SDL from IMESH.

     The row vector INTRFC contains the internal interface sides to be
     maintained (field 'mesh.e(5,:)').  It can be empty.

     Return the vectors NODELIST and ELEMENTLIST containing respectively
     the list of nodes and elements of the original mesh that are part
     of the selected subdomain(s).

     See also: msh2m_join_structured_mesh, msh3m_submesh,
     msh3e_surface_mesh.


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Extract the subdomain(s) in SDL from IMESH.



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msh2m_topological_properties


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 -- Function File: [VARARGOUT] =
          msh2m_topological_properties(MESH,[STRING1,STRING2,...])

     Compute MESH topological properties identified by input strings.

     Valid properties are:
        * '"n"': return a matrix with size 3 times the number of mesh
          elements containing the list of its neighbours.  The entry
          'M(i,j)' in this matrix is the mesh element sharing the side
          'i' of triangle 'j'.  If no such element exists (i.e.  for
          boundary edges) a value of 'NaN' is set.
        * '"sides"': return a matrix with size 2 times number of
          sides.The entry 'M(i,j)' is the index of the i-th vertex of
          j-th side.
        * '"ts"': return a matrix with size 3 times the number of mesh
          elements containing the sides associated with each element.
        * '"tws"':return a matrix with size 2 times the number of mesh
          sides containing the elements associated with each side.  For
          a side belonging to one triangle only a value of 'NaN' is set.
        * '"coinc"': return a matrix with 2 rows.  Each column contains
          the indices of two triangles sharing the same circumcenter.
        * '"boundary"': return a matrix with size 2 times the number of
          side edges.  The first row contains the mesh element to which
          the side belongs, the second row is the local index of this
          edge.

     The output will contain the geometrical properties requested in the
     input in the same order specified in the function call.

     If an unexpected string is given as input, an empty vector is
     returned in output.

     See also: mshm2m_geometrical_properties,
     msh3m_geometrical_properties.


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Compute MESH topological properties identified by input strings.



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msh2p_mesh


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 -- Function File: msh2p_mesh(MESH, LINESPEC)

     Plot MESH with the line specification in LINESPEC using 'triplot'.

     See also: triplot.


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Plot MESH with the line specification in LINESPEC using 'triplot'.



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msh3e_surface_mesh


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 -- Function File: [EMESH,SNODES,SSIDES,STRIANGLES] =
          msh3e_surface_mesh(MESH,NSRF,NSIDES)

     Extract the plane surface NSRF delimited by NSIDES from MESH.

     Return the vector SNODES containing the references to input mesh
     nodes (field 'mesh.p'), the vector SSIDES containing the references
     to input mesh side (field 'mesh.s') and the vector STRIANGLES
     containing the references to input mesh side edges (field
     'mesh.e').

     *WARNING*: the suface MUST be ortogonal to either X, Y or Z axis.
     This should be changed to account for generic 2D surface.


# name: <cell-element>
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Extract the plane surface NSRF delimited by NSIDES from MESH.



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msh3m_geometrical_properties


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 -- Function File: [VARARGOUT] =
          msh3m_geometrical_properties(MESH,[STRING1,STRING2,...])

     Compute MESH geometrical properties identified by input strings.

     Valid properties are:
        * '"bar"': return a matrix with size 3 times the number of mesh
          elements containing the center of mass coordinates.
        * '"wjacdet"': return the weigthed Jacobian determinant used for
          the numerical integration with trapezoidal rule over an
          element.
        * '"shg"': return a matrix of size 3 times the number of
          elements matrix containing the gradient of P1 shape functions.
        * '"shp"': return a matrix containing the the value of P1 shape
          functions.
        * '"area"': return a row vector containing the volume of each
          element.

     The output will contain the geometrical properties requested in the
     input in the same order specified in the function call.

     If an unexpected string is given as input, an empty vector is
     returned in output.

     See also: msh2m_topological_properties,
     msh2m_geometrical_properties.


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Compute MESH geometrical properties identified by input strings.



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msh3m_gmsh


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 -- Function File: [MESH] = msh3m_gmsh(GEOMETRY,OPTION,VALUE,...)
 -- Function File: [MESH, GMSH_OUT] = msh3m_gmsh(...)

     Construct an unstructured tetrahedral 3D mesh making use of the
     free software gmsh.

     The required argument GEOMETRY is the basename of the '*.geo' file
     to be meshed.

     The optional arguments OPTION and VALUE identify respectively a
     gmsh option and its value.  For more information regarding the
     possible option to pass, refer to gmsh manual or gmsh site
     <http://www.geuz.org/gmsh/>.

     The returned value MESH is a PDE-tool like mesh structure.  If the
     function is called with two outputs GMSH_OUT is the verbose output
     of the gmsh subprocess.

     See also: msh3m_structured_mesh, msh2m_gmsh,
     msh2m_mesh_along_spline.


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Construct an unstructured tetrahedral 3D mesh making use of the free
software gm



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msh3m_gmsh_write


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 -- Function File: = msh3m_gmsh_write (FILENAME, MSH)

     See also: msh2m_gmsh_write.


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See also: msh2m_gmsh_write.



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msh3m_join_structured_mesh


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 -- Function File: [MESH] =
          msh3m_join_structured_mesh(MESH1,MESH2,S1,S2)

     Join the two structured meshes MESH1 and MESH2 into one single
     mesh.

     The two meshes must share a common face identified by S1 and S2.

     *WARNING*: the two meshes must share the same vertexes on the
     common face.

     See also: msh3m_structured_mesh, msh3m_gmsh, msh3m_submesh,
     msh2m_join_structured_mesh.


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Join the two structured meshes MESH1 and MESH2 into one single mesh.



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msh3m_nodes_on_faces


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 -- Function File: [NODELIST] = msh3m_nodes_on_faces(MESH,FACELIST)

     Return a list of MESH nodes lying on the faces specified in
     FACELIST.

     See also: msh3m_geometrical_properties, msh2m_nodes_on_faces.


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Return a list of MESH nodes lying on the faces specified in FACELIST.



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msh3m_structured_mesh


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 -- Function File: [MESH] = msh3m_structured_mesh(X,Y,Z,REGION,SIDES)

     Construct a structured tetrahedral 3D mesh on a parallelepipedal
     domain.

        * X, Y and Z are the one dimensional mesh vector of the
          corresponding Cartesian axis.
        * REGION is a number identifying the geometrical volume, while
          SIDES is a 6 components vector containing the numbers used to
          identify the geometrical face edges.

     The returned value MESH is a PDE-tool like mesh structure composed
     of the following fields:
        - P: matrix with size 3 times number of mesh points.
             * 1st row: x-coordinates of the points.
             * 2nd row: y-coordinates of the points.
             * 3rd row: z-coordinates of the points.
        - E: matrix with size 10 times number of mesh face edges.
             * 1st row: number of the first vertex of the face edge.
             * 2nd row: number of the second vertex of the face edge.
             * 3rd row: number of the third vertex of the face edge.
             * 4th row: set to 0, present for compatibility with MatLab
               PDE-tool.
             * 5th row: set to 0, present for compatibility with MatLab
               PDE-tool.
             * 6th row: set to 0, present for compatibility with MatLab
               PDE-tool.
             * 7th row: set to 0, present for compatibility with MatLab
               PDE-tool.
             * 8th row: number of the geometrical volume to the right of
               the face edge.
             * 9th row: number of the geometrical volume to the left of
               the face edge.
             * 10th row: number of the geometrical border containing the
               face edge.
        - T: matrix with size 5 times number of mesh elements.
             * 1st row: number of the first vertex of the element.
             * 2nd row: number of the second vertex of the element.
             * 3rd row: number of the third vertex of the element.
             * 4th row: number of the fourth vertex of the element.
             * 5th row: number of the geometrical volume containing the
               element.

     See also: msh2m_structured_mesh, msh3m_gmsh,
     msh2m_mesh_along_spline, msh3m_join_structured_mesh, msh3m_submesh.


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Construct a structured tetrahedral 3D mesh on a parallelepipedal domain.



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msh3m_submesh


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 -- Function File: [OMESH,NODELIST,ELEMENTLIST] =
          msh3m_submesh(IMESH,INTRFC,SDL)

     Extract the subdomain(s) in SDL from IMESH.

     The row vector INTRFC contains the internal interface sides to be
     maintained (field 'mesh.e(5,:)').  It can be empty.

     Return the vectors NODELIST and ELEMENTLIST containing respectively
     the list of nodes and elements of the original mesh that are part
     of the selected subdomain(s).

     See also: msh3m_join_structured_mesh, msh2m_join_structured_mesh,
     msh3m_submesh.


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Extract the subdomain(s) in SDL from IMESH.