Close an open surface in matlab before writing it to an STL-file

The below code is generating a bezier surface of a turbine runner blade. The blade is open at the top and bottom an i would like to close it with an other surface before writing it to an STL-file. The reason i want it closed is so that it will be imported as a solid object in Comsol Multiphysics.

I have tried the patch function which fills in the open space but i am not able to get the coordinates for that surface which is needed for the surf2stl function. I have alos tried to do a 2D interpolation using griddata which is partially closing the open surface of the blade.

%function [surf] = surface_gen(x, y, z)

clc;clear all;close all
uCtrl = 3; % Control points in u
wCtrl = 9; % Control points in w

uCell = 50; % Number of cells in u
wCell = 50; % Number of cells in w

% Control points
x = [1.9700    5.3200    9.6400   15.6000   22.9900   16.3800   10.5300    5.9300    1.97;
    7.5500   10.4600   13.4600   17.7000   23.5600   18.3300   14.2000   10.9600    7.5500;
   19.3900   20.3100   20.7400   21.6200   24.3300   21.9600   21.1600   20.6000   19.3900];

y =    [-3.6300   -4.2700   -5.3100   -5.6300   -1.6100   -2.5500   -3.2100   -3.3800   -3.6300;
        -7.6800   -6.5300   -6.1900   -5.4800   -0.9800   -2.6700   -4.2400   -5.6600   -7.6800;
        -11.2800   -8.3100   -6.3900   -4.4300         0   -2.2700   -4.8400   -7.5700  -11.2800];

z = [-10.2600   -3.7300    1.9500    6.2600    9.0900    6.2600    1.9500   -3.7300  -10.2600;
    -20.5000  -14.5500   -8.9300   -4.0500   -0.6000   -4.0500   -8.9300  -14.5500  -20.5000;
    -24.9100  -20.7600  -16.5800  -12.4300   -9.0900  -12.4300  -16.5800  -20.7600  -24.9100];

n = uCtrl - 1;
m = wCtrl - 1;
u = linspace(0,1,uCell); % Parametric variable in u
w = linspace(0,1,wCell); % Parametric variable in w
i = 0:n;
j = 0:m;

% Binomial Coefficients
uCoeff = factorial(n)./(factorial(i).*factorial(n-i));
wCoeff = factorial(m)./(factorial(j).*factorial(m-j));

J = NaN(uCtrl,uCell);
K = NaN(wCtrl,wCell);
% Bernstein Basis Functions
for k = 1:uCtrl
    J(k,:) = uCoeff(k)*u.^i(k).*(1-u).^(n-i(k));
end

for k = 1:wCtrl
    K(k,:) = wCoeff(k)*w.^j(k).*(1-w).^(m-j(k));
end

xPoints = zeros(uCell,wCell);
yPoints = zeros(uCell,wCell);
zPoints = zeros(uCell,wCell);



for i = 1:n+1
    for j = 1:m+1
        xPoints = J(i,:)'*K(j,:)*x(i,j)+xPoints;
        yPoints = J(i,:)'*K(j,:)*y(i,j)+yPoints;
        zPoints = J(i,:)'*K(j,:)*z(i,j)+zPoints;
    end
end


figure(1)
surf(xPoints,yPoints,zPoints)
xlabel('xPoints')
ylabel('yPoints')
zlabel('zPoints')
% [x_hub,y_hub] = meshgrid(xPoints(1,:),yPoints(1,:));
% z_hub = griddata(xPoints(1,:),yPoints(1,:),zPoints(1,:),x_hub,y_hub);
% [y_shroud,z_shroud] = meshgrid(yPoints(end,:),zPoints(end,:));
% x_shroud = griddata(yPoints(end,:),zPoints(end,:),xPoints(end,:),y_shroud,z_shroud);
% xBlade = zeros(uCell,uCell*3);
% yBlade = zeros(uCell,uCell*3);
% zBlade = zeros(uCell,uCell*3);
% xBlade(:,1:uCell) = xPoints;
% xBlade(:,uCell+1:2*uCell) = x_hub;
% xBlade(:,2*uCell+1:end) = x_shroud;
% yBlade(:,1:uCell) = yPoints;
% yBlade(:,uCell+1:2*uCell) = y_hub;
% yBlade(:,2*uCell+1:end) = y_shroud;
% zBlade(:,1:uCell) = zPoints;
% zBlade(:,uCell+1:2*uCell) = z_hub;
% zBlade(:,2*uCell+1:end) = z_shroud;
% surf(xBlade,yBlade,zBlade)
hold on
plot3(x,y,z,'o','MarkerFaceColor','k')


%surf2stl('blade_closed.stl', xBlade, yBlade, zBlade, 'ascii')

Answer 1

[Maneet Kaur Bagga]

Hi,

As per my understanding you are generating a turbine blade and want to close the open surface of the top and bottom of the blade preparing it for export to an STL file. Following can be a possible workaround for the same:

Extract the coordinates of the blade surface from the "xPoints", "yPoints" and "zPoints" array, for closing the top and bottom of the surface generate planar caps based on the boundary of these surfaces.

% Top Cap
topCapX = [xPoints(1, :); xPoints(1, :)];
topCapY = [yPoints(1, :); yPoints(1, :)];
topCapZ = [zPoints(1, :); max(zPoints(:)) * ones(size(zPoints(1, :)))];

% Bottom Cap
bottomCapX = [xPoints(end, :); xPoints(end, :)];
bottomCapY = [yPoints(end, :); yPoints(end, :)];
bottomCapZ = [zPoints(end, :); min(zPoints(:)) * ones(size(zPoints(end, :)))];

Combine the original blade surface with the top and bottom caps. Since the aim is to export to an STL file, which is a mesh of triangles, we need to create a triangulated representation of our surfaces. The "surf2patch" function from MATLAB can be used to convert surfaces to patch data.

For using the surf2stl function you can refer to the File Exchange link, or alternatively you can define a custom function as below which performs a Delaunay triangulation, and then export the result to an STL File.

function exportBladeSTL(filename, xPoints, yPoints, zPoints, topCapX, topCapY, topCapZ, bottomCapX, bottomCapY, bottomCapZ)
    % Combine all points
    X = [xPoints(:); topCapX(:); bottomCapX(:)];
    Y = [yPoints(:); topCapY(:); bottomCapY(:)];
    Z = [zPoints(:); topCapZ(:); bottomCapZ(:)];
    
    % Create a delaunay triangulation
    DT = delaunayTriangulation(X, Y, Z);
    
    % Write to STL
    stlwrite(filename, DT.ConnectivityList, DT.Points);
end

Call the function with your data

exportBladeSTL('blade_closed.stl', xPoints, yPoints, zPoints, topCapX, topCapY, topCapZ, bottomCapX, bottomCapY, bottomCapZ);

Please refer to the File Exchange link below to use the "surf2stl" function in MATLAB:

www.mathworks.com/matlabcentral/fileexchange/4512-surf2stl

Hope this helps!