User defined textureΒΆ

Learning targets

  • Construct a textured interface between adjacent layers by specifying a triangulated height map
_images/ex3d_user_surface.png

This example uses a user defined texture on a cartesian grid to define the interface between two homogeneous layers. The layout template contains a Triangulation section which allows to enter a triangulation of a user specified surface. A triangulation consists of a list of Points in 3D together with a list of triangles as indices into the list of points

          Triangulation { 
            Points = %(points)e
            Triangles = %(triangles)e
          }

The script run.m creates a height map over a cartesian grid (as given by the builtin functions sombrero or peaks), creates a triangulation of the xy coordinates and finally generates and displays the generated grid. The periodic boundary conditions of the texture are enforced by averaging of the first and last entries in the height map.

The script is easily adapted, e.g in order to load height maps on a cartesian grid from a file, by substituting the values for X, Y, Z.

.jcmt Input file and run script

  • run.m [ASCII]

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    clear variables;
jcm_root = getenv('JCMROOT'); % change this to match your
                              % installation or set environment variable
addpath(fullfile(jcm_root, 'ThirdPartySupport', 'Matlab'));
jcmwave_startup();


% create test surface to discretize, here: builtin function sombrero
N=20;
N = N+mod(N+1,2); % make N odd

% [X,Y,Z] = peaks(N);  
[X,Y,Z] = sombrero(N); 
surf(X,Y,Z)

% make surface periodic by averaging the values 
temp = Z(end,:)+Z(1,:);
Z(1,:)=temp/2.0;
Z(end,:)=temp/2.0;
temp = Z(:,end)+Z(:,1);
Z(:,1)=temp/2.0;
Z(:,end)=temp/2.0;

% create mesh of xy coordinates
tri = delaunay(X(:),Y(:));
trisurf(tri,X(:),Y(:),Z(:))

% rescale mesh to fit into the layout
x = X(:)/(max(X(:)) - min(X(:)))*10;
y = Y(:)/(max(Y(:)) - min(Y(:)))*10;
z = Z(:)/(max(Z(:)) - min(Z(:)))*2;;

keys.points = [x y z];
keys.triangles = tri;

% execute pattern substitution, generate and view grid
jcmwave_geo('.',keys,'jcmt_pattern','triangulation')
jcmwave_view('grid.jcm')

  • layout.jcmt [ASCII]

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    Layout3D {
  UnitOfLength = 1
  MeshOptions {
    MaximumSideLength = 1
  }
  BoundaryConditions {
    Boundary {
      Direction = Horizontal 
      Class = Periodic 
    }
    Boundary {
      Direction = Vertical 
      Class = Transparent 
    }
  }
  Extrusion {
    Objects {
      Parallelogram {
        DomainId = 101
        Priority = ComputationalDomain
        Name = "Base"
        Width = 10
        Height = 10
      }
    }
    MultiLayer {
      Layer {
        DomainId = 2
        Thickness = 2
      }   
      LayerInterface {
        Texture {
          Triangulation { 
            Points = %(points)e
            Triangles = %(triangles)e
          }
          MeshOptions {
            MaximumSideLength = 1
          }
        }
      }
      Layer {
        DomainId =1
        Thickness = 2
      }
    }
  }
}

.jcm Input File

  • layout.jcm [ASCII]

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    Layout3D {
  UnitOfLength = 1
  MeshOptions {
    MaximumSideLength = 1
  }
  BoundaryConditions {
    Boundary {
      Direction = Horizontal 
      Class = Periodic 
    }
    Boundary {
      Direction = Vertical 
      Class = Transparent 
    }
  }
  Extrusion {
    Objects {
      Parallelogram {
        DomainId = 101
        Priority = ComputationalDomain
        Name = "Base"
        Width = 10
        Height = 10
      }
    }
    MultiLayer {
      Layer {
        DomainId = 2
        Thickness = 2
      }
      LayerInterface {
        Texture {
          Triangulation {
            Points = [-5 -5 -0.137953386760748 ;-5 -4.5 -0.148560372342248 ;-5 -4 -0.117294403319964 ;-5 -3.5 -0.0561906415001772 ;-5 -3 0.0167520047098715 ;-5 -2.5 0.084919410156999 ;-5 -2 0.137934332251078 ;-5 -1.5 0.172819047798771 ;-5 -1 0.192151134873395 ;-5 -0.5 0.200860962548187 ;-5 0 0.203216665860533 ;-5 0.5 0.200860962548187 ;-5 1 0.192151134873395 ;-5 1.5 0.172819047798771 ;-5 2 0.137934332251078 ;-5 2.5 0.084919410156999 ;-5 3 0.0167520047098712 ;-5 3.5 -0.0561906415001772 ;-5 4 -0.117294403319964 ;-5 4.5 -0.148560372342248 ;-5 5 -0.137953386760748 ;-4.5 -5 -0.148560372342248 ;-4.5 -4.5 -0.110891982373126 ;-4.5 -4 -0.0353078998896986 ;-4.5 -3.5 0.0538184111631606 ;-4.5 -3 0.132390585620145 ;-4.5 -2.5 0.185085569332959 ;-4.5 -2 0.208488933091628 ;-4.5 -1.5 0.208982782723529 ;-4.5 -1 0.197783752068713 ;-4.5 -0.5 0.1859624560981 ;-4.5 0 0.181134855900037 ;-4.5 0.5 0.1859624560981 ;-4.5 1 0.197783752068713 ;-4.5 1.5 0.208982782723529 ;-4.5 2 0.208488933091628 ;-4.5 2.5 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