Minimal 2D Grid generation based on Transfinite Interpolation

mole_MATLAB/gridGen.m

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+% https://en.wikipedia.org/wiki/Transfinite_interpolation
+function [X, Y] = gridGen(grid_name, m, n, plot_grid)
+% Returns X and Y which are both m by n matrices that contains the physical
+% coordinates
+%
+% Parameters:
+%        grid_name : String with the name of the grid folder
+%                m : Number of nodes along the horizontal axis
+%                n : Number of nodes along the vertical axis
+%        plot_grid : If defined -> grid will be plotted
+
+    assert(nargin == 4, 'Must specify all input arguments')
+    assert(m > 4 && n > 4, 'm and n must be greater than 4')
+
+    addpath(['grids/' grid_name])
+
+    % Logical grid
+    Xl = linspace(0, 1, m);
+    Yl = linspace(0, 1, n);
+
+    % Allocate space for physical grid
+    X = zeros(m, n);
+    Y = zeros(m, n);
+
+    for i = 1 : m
+        u = Xl(i);
+        for j = 1 : n
+            v = Yl(j);
+            % Transfinite interpolation
+            XY = (1-v)*bottom(u)+v*top(u)+(1-u)*left(v)+u*right(v)-...
+                (u*v*top(1)+u*(1-v)*bottom(1)+v*(1-u)*top(0)+(1-u)*(1-v)*bottom(0));
+            X(i, j) = XY(1);
+            Y(i, j) = XY(2);
+        end
+    end
+
+    if plot_grid
+        figure
+        mesh(X, Y, zeros(m, n), 'Marker', '.', 'MarkerSize', 10, 'EdgeColor', 'b')
+        title(['Physical grid. m = ' num2str(m) ', n = ' num2str(n)])
+        set(gcf, 'color', 'w')
+        axis equal
+        axis off
+        view([0 90])
+    end
+end

mole_MATLAB/grids/chevron/bottom.m

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+function XY = bottom(s)
+    X = s;
+    if s <= 0.5
+        Y = -s;
+    elseif s > 0.5
+        Y = s-1;
+    end
+    XY = [X Y];
+end

mole_MATLAB/grids/chevron/left.m

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+function XY = left(s)
+    X = 0;
+    Y = s;
+    XY = [X Y];
+end

mole_MATLAB/grids/chevron/right.m

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+function XY = right(s)
+    X = 1;
+    Y = s;
+    XY = [X Y];
+end

mole_MATLAB/grids/chevron/top.m

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+function XY = top(s)
+    X = s;
+    if s <= 0.5
+        Y = 1-s;
+    elseif s > 0.5
+        Y = s;
+    end
+    XY = [X Y];
+end

mole_MATLAB/grids/horseshoe/bottom.m

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+function XY = bottom(s)
+    X = 2*cos(pi/2*(1-2*s));
+    Y = sin(pi/2*(1-2*s));
+    XY = [X Y];
+end

mole_MATLAB/grids/horseshoe/left.m

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+function XY = left(s)
+    X = 0;
+    Y = 1+s;
+    XY = [X Y];
+end

mole_MATLAB/grids/horseshoe/right.m

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+function XY = right(s)
+    X = 0;
+    Y = -1-s;
+    XY = [X Y];
+end

mole_MATLAB/grids/horseshoe/top.m

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+function XY = top(s)
+    X = 4*cos(pi/2*(1-2*s));
+    Y = 2*sin(pi/2*(1-2*s));
+    XY = [X Y];
+end

mole_MATLAB/grids/swan/bottom.m

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+function XY = bottom(s)
+    X = s;
+    Y = 0;
+    XY = [X Y];
+end

mole_MATLAB/grids/swan/left.m

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+function XY = left(s)
+    X = 0;
+    Y = s;
+    XY = [X Y];
+end

mole_MATLAB/grids/swan/right.m

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+function XY = right(s)
+    X = 1+2*s-2*s^2;
+    Y = s;
+    XY = [X Y];
+end

mole_MATLAB/grids/swan/top.m

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+function XY = top(s)
+    X = s;
+    Y = 1-3*s+3*s^2;
+    XY = [X Y];
+end