MATLAB: How to generate an .stl file from a symbolically generated 3D surface

3d plotsexportstlsymbolic

I used ezsurf() to generate a 3D surface of 3 parameterized equations. I'd like to export the data as an stl file, but surf2stl() does not seem to working, any suggestions?

For reference, here is the code used to generate the 3D surface.

syms u v
x = (-2/15)*cos(u)* (3*cos(v) - 30*sin(u) + 90*(cos(u))^4*sin(u) - 60*(cos(u))^6*sin(u) + 5*cos(u)*cos(v)*sin(u))
y = (-1/15)*sin(u)* (3*cos(v) - 3*(cos(u))^2*cos(v) + 48*(cos(u))^4*cos(v) - 48*(cos(u))^6*cos(v) - 60*sin(u) + 5*cos(u)*cos(v)*sin(u) - 5*(cos(u))^3*cos(v)*sin(u) - 80*(cos(u))^5*cos(v)*sin(u) + 80*(cos(u))^7*cos(v)*sin(u))
z = (2/15)*(3+5*cos(u)*sin(u))*sin(v)
figure(2)
ezsurf(x,y,z,[0, pi, 0, 2*pi])

Best Answer

syms u v
x = (-2/15)*cos(u)* (3*cos(v) - 30*sin(u) + 90*(cos(u))^4*sin(u) - 60*(cos(u))^6*sin(u) + 5*cos(u)*cos(v)*sin(u))
y = (-1/15)*sin(u)* (3*cos(v) - 3*(cos(u))^2*cos(v) + 48*(cos(u))^4*cos(v) - 48*(cos(u))^6*cos(v) - 60*sin(u) + 5*cos(u)*cos(v)*sin(u) - 5*(cos(u))^3*cos(v)*sin(u) - 80*(cos(u))^5*cos(v)*sin(u) + 80*(cos(u))^7*cos(v)*sin(u))
z = (2/15)*(3+5*cos(u)*sin(u))*sin(v)
figure(2)
h = ezsurf(x,y,z,[0, pi, 0, 2*pi]) ;
X = h.XData ; 
Y = h.YData ; 
Z = h.ZData ;

Now use surf2stl: https://in.mathworks.com/matlabcentral/fileexchange/4512-surf2stl X,Y,Z.

Related Solutions

MATLAB: Can someone help me with these 3D plots

you can plot these shapes in the following two ways(you can choose better way you like):

%%Seashell

[u, v] = meshgrid(linspace(0, 6 * pi, 100), linspace(0, 2 * pi, 100));
x = 2 * (1 - exp(u / (6 * pi))) .* cos(u) .* (cos(0.5 * v))^2;
y = 2 * (-1 + exp(u / (6 * pi))) .* sin(u) .* (cos(0.5 * v))^2;
z = 1 - exp(u / (3 * pi)) - sin(v) + exp(u / (6 * pi)) .* sin(v);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Seashell')
%%Eight torus

c = 1;
[u, v] = meshgrid(linspace(-pi, pi, 100));
x = cos(u) .* (c + sin(v) .* cos(u) - sin(2 * v) .* (sin(u) / 2));
y = sin(u) .* (c + sin(v) .* cos(u) - sin(2 * v) .* (sin(u) / 2));
z = sin(u) .* sin(v) + cos(u) .* (sin(2 * v) / 2);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Eight torus')
%%Helical spring

r1 = 0.25;
r2 = 0.25;
T = 2;
n = 6;
[u, v] = meshgrid(linspace(0, 2 * n * pi, 100), linspace(0, 2 * pi, 100));
x = (1 - r1 * cos(v)) .* cos(u);
y = (1 - r1 * cos(v)) .* sin(u);
z = r2 * (sin(v) + T * u / pi);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Helical spring')
%%Cornucopia

a = 0.3;
b = 0.5;
[u, v] = meshgrid(linspace(0, 2 * pi, 100), linspace(-3, 3, 100));
x = exp(b * v) .* cos(v) + exp(a * v) .* cos(u) .* cos(v);
y = exp(b * v) .* sin(v) + exp(a * v) .* cos(u) .* sin(v);
z = exp(a * v) .* sin(u);
figure, surf(x, y, z), xlabel('x'), ylabel('y'), zlabel('z'), title('Cornucopia')

Or alternatively you can also plot them using ezsurf as follows:

syms u v
%%Seashell
x = 2 * (1 - exp(u / (6 * pi))) * cos(u) * (cos(0.5 * v))^2;
y = 2 * (-1 + exp(u / (6 * pi))) * sin(u) * (cos(0.5 * v))^2;
z = 1 - exp(u / (3 * pi)) - sin(v) + exp(u / (6 * pi)) * sin(v);
figure, ezsurf(x, y, z)
%%Eight torus
c = 1;
x = cos(u) * (c + sin(v) * cos(u) - sin(2 * v) * (sin(u) / 2));
y = sin(u) * (c + sin(v) * cos(u) - sin(2 * v) * (sin(u) / 2));
z = sin(u) * sin(v) + cos(u) * (sin(2 * v) / 2);
figure, ezsurf(x, y, z)
%%Helical spring
r1 = 0.25;
r2 = 0.25;
T = 2;
n = 6;
x = (1 - r1 * cos(v)) .* cos(u);
y = (1 - r1 * cos(v)) .* sin(u);
z = r2 * (sin(v) + T * u / pi);
figure, ezsurf(x, y, z)
%%Cornucopia
a = 0.3;
b =0.5;
x = exp(b * v) .* cos(v) + exp(a * v) .* cos(u) .* cos(v);
y = exp(b * v) .* sin(v) + exp(a * v) .* cos(u) .* sin(v);
z = exp(a * v) .* sin(u);
figure, ezsurf(x, y, z)

I hope it helps. Good luck!

MATLAB: Solve overspecified equation system

If you have symbolic toolbox, use:

% This part builds a system to solve with fsolve
syms u1 u2 up2 l1 l2 xa ya xpa ypa ap0
x = sym('x', [1 3]);
eqns(1) = cos(u1)*l1 + cos(u2)*l2 - xa;
eqns(2) = sin(u1)*l1 + sin(u2)*l2 - ya;
eqns(3) = ap0 -(xpa*cos(u2))/(4*(cos(u1)*sin(u2) - cos(u2)*sin(u1))) +...
    (ypa*sin(u2))/(4*(cos(u1)*sin(u2) - cos(u2)*sin(u1)));
eqns(4) = up2 + (xpa*cos(u1))/(4*(cos(u1)*sin(u2) - cos(u2)*sin(u1))) -...
    (ypa*sin(u1))/(4*(cos(u1)*sin(u2) - cos(u2)*sin(u1)));
eqns = subs(eqns,[u1, u2, up2],[x(1), x(2), x(3)]);
fun = matlabFunction(eqns,'vars',{x,'l1','l2','xa','ya','xpa','ypa'...
    'ap0'});
fun = str2func(replace(func2str(fun),"in1","x"));

Then fun is a function handle that you can work with:

% solve the system with fantasy values - use your values
l1 = 3;
l2 = 2;
xa = 3;
ya = 6;
xpa = 0.5;
ypa = -1;
ap0 = 5.7;
% solve the system using fsolve
opts = optimoptions('fsolve','Algorithm','Levenberg-Marquardt');
sol = fsolve(@(x)fun(x,l1,l2,xa,ya,xpa,ypa,ap0),rand(1,3),opts)
% look at the results using the solution fsolve calculated
% ideally there should be 4 zeros, if it worked good - ohterwise
% your system may have a problem
test_results = fun(sol,l1,l2,xa,ya,xpa,ypa,ap0)

For my fantasy values there was not a good result - you have to check using your values and also have a look at the correct implementation of the equations in the first part. They should all be formulated as F = 0, to work with them using fsolve.

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Related Solutions

MATLAB: Can someone help me with these 3D plots

MATLAB: Solve overspecified equation system

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