Create laplacian smoothing matlab

Question

damin 2017-10-20

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https://ww2.mathworks.cn/matlabcentral/answers/362345-create-laplacian-smoothing-matlab

编辑： damin 2017-10-26

Hi! I would like to create a laplacian smoothing like on the image i attach below. The necessary files I need to make this quadmesh (the mesh generator) and the nodeconnect.m file is also attached here. I managed to create a regular mesh using the quadmesh generator, but I dont know how to increase the boundaries to create a laplician smoothing mesh like on the picture.

The attached nodeconnect.m -> nodeconnect computes all nodes connected to a given node. Called as nnods = nodeconnect(nodes,inod); here nnods i a list of connected nodes to the node and nodes=p.Connectivity is the connectivity matrix. Thank you so much for your help! :)

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Answer 1

Precise Simulation 2017-10-24

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https://ww2.mathworks.cn/matlabcentral/answers/362345-create-laplacian-smoothing-matlab#answer_287440

编辑：Precise Simulation 2017-10-26

在 MATLAB Online 中打开

You can get something quite similar with the following code, and tune it by playing around with the gridsmooth function, number of smoothing steps, and relaxation parameter.

    nx   = 24;
    ny   = 8;
    xmin = 0;
    xmax = 3;
    ymin = -0.5;
    ymax = 1.5;
    grid = rectgrid( nx, ny, [xmin,ymin,xmax,ymax] );
    subplot(2,2,1)
    plotgrid(grid)
    if( 1 )   % Squeeze only right side y-coordinates.
      grid.p(2,grid.p(1,:)==3) = linspace(0,1,ny+1);
    else   % Squeeze y-coordinates.
      yl = linspace(-0.5,1.5,ny+1);
      yr = linspace(0,1,ny+1);
      y  = [];
      for i=1:ny+1
  y = [ y linspace(yl(i),yr(i),nx+1) ];
      end
      grid.p(2,:) = y;
    end
    subplot(2,2,2)
    plotgrid(grid)
    % Remove boundary indicators from upper/lower 
    % boundaries to allow smoothing.
    b_orig = grid.b;
    grid.b(:,grid.b(3,:)==1) = [];   % Remove lower boundary indices.
    grid.b(:,grid.b(3,:)==3) = [];   % Remove upper boundary indices.
    grid = gridsmooth( grid, 60, 0.1, 2 );
    grid.b = b_orig;
    subplot(2,2,3)
    plotgrid( grid )

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somesh bharadwaj 2017-10-25

for this was getting error in smooth grid so how can i overcome that

Precise Simulation 2017-10-25

编辑：Precise Simulation 2017-10-26

在 MATLAB Online 中打开

What did the error message say?

If you just want something that looks like the image you neither need QuadMesh nor Laplacian smoothing:

    nx = 24; ny = 8; xmin = 0; xmax = 3; ymin = -0.5; ymax = 1.5;
    [x,y] = meshgrid( linspace(xmin,xmax,nx+1), ...
                      linspace(ymin,ymax,ny+1));
    % Shape/distribution 't' of y-points.
    t = linspace(0,1,nx+1).^(1./(2+[1:nx+1]));
    yl = linspace(-0.5,1.5,ny+1);
    yr = linspace(0,1,ny+1);
    y2 = [];
    for i=1:ny+1
      y_i = yl(i) - t*(yl(i)-yr(i));
      y2 = [ y2; y_i ];
    end
    surf(x,y2,ones(size(x))); view(2), axis equal