Mishra, Pankaj K (2019). NodeLab: A MATLAB package for meshfree node-generation and adaptive refinement. Journal of Open Source Software, 4(40), 1173, https://doi.org/10.21105/joss.01173
NodeLab is a simple MATLAB-package for unstructured node-generation and refinement for meshfree modeling in 2D arbitrary domains. The final output can be seen in the 'workspace'. Following are the description of Input/Output variables of NodeLab:
- box - a vector defining the bounding box of the domain.
- hbdy - the density of the boundary poit-cloud
- ptol - minimum distance between two nodes
- ctps - control-points for density variation
- radius - distance function for node density metric
- xy — an array containing interior nodes.
- bdy— an array containing boundary nodes.
- Download the package on your PC.
- Open MATLAB
- Go to the directory 'NodeLab'
- run the script 'setup.m'. This will add different directories of the NodeLab on your MATLAB path — only for the current session. Now you are ready to run the demos and generate nodes for your own project. Note: make sure you have MATLAB's statistics toolbox.
Generate nodes inside a circle within a bounding box (-1,1)^2 with no control points.
clear varibale; close all; clc
box = [-1,-1; 1,1];
hbdy = 0.02;
ptol = 0.001;
[b] = draw_circ(0,0,1,2/hbdy);
ctps = [];
%ctps = [linspace(-0.5, 0.5,10); zeros(1,10)]';
radius = @(p,ctps) 0.05; % for fixed node-density
%radius = @(p,ctps) 0.005+0.08*(min(pdist2(ctps, p))); % for variable node-density
[xy] = NodeLab2D(b.sdf,box,ctps,ptol, radius);
[bdy] = b.xy;
clear box hbdy ptol ctps radius b
%-------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12)
hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize',12)
axis('square'); set(gca,'visible','off') 
Generate nodes inside a circle within a bounding box (-1,1)^2 but keep a varibale-density being highest at the single control point (0,0).
clear varibale; close all; clc
box = [-1,-1; 1,1];
hbdy = 0.02;
ptol = 0.001;
[b] = draw_circ(0,0,1,2/hbdy);
ctps = [0, 0];
radius = @(p,ctps) 0.005+0.08*(min(pdist2(ctps, p))); % for variable node-density
[xy] = NodeLab2D(b.sdf,box,ctps,ptol, radius);
[bdy] = b.xy;
clear box hbdy ptol ctps radius b
%-------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12)
hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize',12)
axis('square'); set(gca,'visible','off')
Generate nodes inside a circle within a bounding box (-1,1)^2 but keep a varibale-density being highest along a line between (-0.75,0) and (0.75,0).
%-----------------------------------
clear varibale; close all; clc
box = [-1,-1; 1,1];
hbdy = 0.02;
ptol = 0.001;
[b] = draw_circ(0,0,1,2/hbdy);
%ctps = [0, 0];
ctps = [linspace(-0.5, 0.5,10); zeros(1,10)]';
%radius = @(p,ctps) 0.05; % for fixed node-density
radius = @(p,ctps) 0.005+0.08*(min(pdist2(ctps, p))); % for variable node-density
[xy] = NodeLab2D(b.sdf,box,ctps,ptol, radius);
[bdy] = b.xy;
clear box hbdy ptol ctps radius b
%-------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12)
hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize',12)
axis('square'); set(gca,'visible','off')
Generate nodes inside a circle within a bounding box (-1,1)^2 but keep a varibale-density being highest along two seperate points: (-0.75,0), and (0.75,0).
%-----------------------------------
clear varibale; close all; clc
box = [-1,-1; 1,1];
hbdy = 0.02;
ptol = 0.001;
[b] = draw_circ(0,0,1,2/hbdy);
ctps = [-0.75,0; 0.75,0];
radius = @(p,ctps) 0.005+0.08*(min(pdist2(ctps, p)));
[xy] = NodeLab2D(b.sdf,box,ctps,ptol, radius);
[bdy] = b.xy;
clear box hbdy ptol ctps radius b
%-------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12)
hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize',12)
axis('square'); set(gca,'visible','off')
Generate nodes in a rectangle within a bounding box (-1,1)^2.
clear variables; close all; clc
%------------------------------------------------
box = [-1,-1; 1,1];
hbdy = 0.05;
ptol = 0.01;
ctps = [];
radius = @(p, ctps) 0.05;
[b] = draw_rect(-1,-1,1,1,2/hbdy);
[xy] = NodeLab2D(b.sdf,box,ctps,ptol,radius);
[bdy] = b.xy;
clear box hbdy ptol ctps radius b
%---------------------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12);hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize',12); axis('square')
set(gca,'visible','off')
Generate nodes in a rectangle within a bounding box (-1,1)^2. Make varibale density at two point-source.
% unit circle
clear variables; close all; clc
%------------------------------------------------
box = [-1,-1; 1,1];
hbdy = 0.02;
ptol = 0.001;
ctps = [-0.5,1; 0.5, 1];
radius = @(p,ctps) 0.005+0.05*(min(pdist2(ctps, p)));
[b] = draw_rect(-1,-1,1,1,2/hbdy);
[xy] = NodeLab2D(b.sdf,box,ctps,ptol,radius);
[bdy] = b.xy;
clear box hbdy ptol ctps radius b
%---------------------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12);hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize',12); axis('square')
set(gca,'visible','off')
Generate nodes in a L-shape domain for point-singularity problems.
clear variables; close all; clc
%----------------------------------------------------
box = [-1, -1; 1, 1 ];
hbdy = 0.025;
ptol = 0.001;
[b] = make_domain('Lshape.txt');
ctps = [0, 0];
radius = @(p,ctps) 0.005+0.05*(min(pdist2(ctps, p)));
[xy] = NodeLab2D(b.sdf,box,ctps,ptol,radius);
bdy = bsmooth(b.xy, hbdy);
clear b box hbdy ctps radius ptol
%-----------------------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',12); hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize', 12); axis('square')
set(gca,'visible','off')
Generate nodes in a Island model.
clear variables; close all; clc
%--------------------------------------------
box = [100.0, 145.0; 634.0, 799.0 ];
hbdy = 5;
ptol = 1;
[b] = make_domain('lake.txt'); % process lake points as boundary
[bdy] = bsmooth(b.xy, hbdy);
ctps = bdy;
radius = @(p,ctps) 6 ;
[xy] = NodeLab2D(b.sdf,box,ctps,ptol,radius);
%--------------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',10); hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize', 10); axis('square')
set(gca,'visible','off')
Generate nodes in a Island model. Variable-density being maximum at the boundary.
clear variables; close all; clc
%--------------------------------------------
box = [100.0, 145.0; 634.0, 799.0 ];
hbdy = 5;
ptol = 1;
[b] = make_domain('lake.txt'); % process lake points as boundary
[bdy] = bsmooth(b.xy, hbdy);
ctps = bdy;
radius = @(p,ctps) 6 ;
[xy] = NodeLab2D(b.sdf,box,ctps,ptol,radius);
%--------------------------------------------
plot(xy(:,1), xy(:,2),'.k','MarkerSize',10); hold on
plot(bdy(:,1), bdy(:,2), '.k','MarkerSize', 10); axis('square')
set(gca,'visible','off')
Generate nodes in a Island model having a small lake inside it. Varibale-density being maximum at each boundaries.
% unit circle
clear variables; close all; clc
%-----------------------------------------
box = [100.0, 145.0; 634.0, 799.0 ];
hbdy = 3;
ptol = 1;
[b1] = make_domain('lake.txt'); % process lake points as boundary
[b2] = make_domain('island.txt');
b.sdf = @(p) max(b1.sdf(p), -b2.sdf(p)) ;
b1.xy = bsmooth(b1.xy, hbdy);
b2.xy = bsmooth(b2.xy, hbdy);
b.xy = [b1.xy; b2.xy];
ctps = b.xy;
radius = @(p,ctps) 2 + 0.2*(min(pdist2(ctps, p)));
[x] = NodeLab2D(b.sdf,box,ctps,ptol,radius);
%-----------------------------------------
plot(x(:,1), x(:,2),'.k','MarkerSize',8); hold on
plot(b.xy(:,1), b.xy(:,2), '.k','MarkerSize', 8); axis('square');
set(gca,'visible','off')