How do I export a plot comprising of multiple functions to .stl?

I have a plot created using multiple parametric functions that define an archimedean spiral. I want to export the plotted figure to stl or convert it into a mesh that resembles the plotted shape, however, am unable to do so. I have tried using triangulation and mesh grid but to no avail. The plot I want to export is shown above.

This plot was generated using:

% Spiral edges
x = (inner_radius + spiral_growth_rate.*angles).*cos(angles);
y = (inner_radius + spiral_growth_rate.*angles).*sin(angles);

syms theta

diff_x = diff((inner_radius +spiral_growth_rate*theta)*cos(theta));
diff_y = diff((inner_radius +spiral_growth_rate*theta)*sin(theta));

N_x = (-diff_y)/sqrt(diff_x^2 + diff_y^2);
N_y = (diff_x)/sqrt(diff_x^2 + diff_y^2);

shift_x = vpa(subs(N_x, theta, angles));
shift_y = vpa(subs(N_y, theta, angles));

outer_x_coords = x+shift_x.*thickness/2;
outer_y_coords = y+shift_y.*thickness/2;

inner_x_coords = x-shift_x.*thickness/2;
inner_y_coords = y-shift_y.*thickness/2;

% Joining curves
s = linspace(-1, 1);
inner_j_x = x(1) + s .* shift_x(1)*thickness/2;
inner_j_y = y(1) + s .* shift_y(1)*thickness/2;

outer_j_x = x(end) + s .* shift_x(end).*thickness/2;
outer_j_y = y(end) + s .* shift_y(end).*thickness/2;

x_coords = double([inner_x_coords, outer_x_coords, inner_j_x, outer_j_x]);

y_coords = double([inner_y_coords, outer_y_coords, inner_j_y, outer_j_y]);

% [X,Y] = meshgrid(x_coords, y_coords);
% 
% T = delaunay(X,Y);
% trimesh(T,x,y);

figure
hold on
plot(outer_x_coords, outer_y_coords);
plot(inner_x_coords, inner_y_coords);
plot(inner_j_x, inner_j_y);
plot(outer_j_x, outer_j_y);
hold off

Answer 1

[Aayush Chadha]

In case someone ever encounters a similar problem. I ended up doing this by generating the points in Python and then using pygmsh to generate the mesh. I wrote this mesh to STL, opened and saved it using Meshlab (I do not know why the mesh couldn't be read otherwise by customAntennaStl) before I was able to finally use it.

Answer 2

[DGM]

An example.

% some parameters
npointsperturn = 100;
nturns = 5;
trackwidth = 1;
trackthick = 0.5;
inner_radius = 10;
growth_rate = 0.3;

% just do the symbolic math once to get the required expression
% this is literally 1000 times faster, and can probably still be simplified.
angles = linspace(0,2*pi*nturns,npointsperturn*nturns);
costheta = cos(angles); % heavily reused terms
sintheta = sin(angles);
x = (inner_radius + growth_rate.*angles).*costheta;
y = (inner_radius + growth_rate.*angles).*sintheta;
denom = sqrt(angles.^2*growth_rate^2 + 2*angles*growth_rate*inner_radius + growth_rate^2 + inner_radius^2);
shift_x = -(inner_radius*costheta + growth_rate*(sintheta + angles.*costheta))./denom;
shift_y = -(inner_radius*sintheta - growth_rate*(costheta - angles.*sintheta))./denom;

% these were named backwards
xinner = x + shift_x.*trackwidth/2;
yinner = y + shift_y.*trackwidth/2;
xouter = x - shift_x.*trackwidth/2;
youter = y - shift_y.*trackwidth/2;

% just assemble an ordered vertex list
V = [flipud([xinner(:) yinner(:)]);
    xouter(:) youter(:)];

% construct the edge lists in the same direction
v = 1:size(V,1);
E = [v; circshift(v,-1)].';

% TRIANGULATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% do a constrained triangulation using delaunayTriangulation
T = delaunayTriangulation(V,E);
F = T.ConnectivityList(isInterior(T),:);
V = T.Points;

% display it using patch()
patch('faces',F,'vertices',V,'facecolor','w','edgecolor','k');
axis equal; grid on
xlabel('X'); ylabel('Y')

I'm assuming the result is supposed to be a 3D solid, so that's only part of the problem

% EXTRUSION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% extrude the part into 3D
[F V] = extrude(F,V,trackthick);

% write to file
stlwrite(triangulation(F,V),'testfile.stl')

% display it using patch()
figure
patch('faces',F,'vertices',V,'facecolor','w','edgecolor','none');
view(3); camlight; view(10,33)
axis equal; grid on
xlabel('X'); ylabel('Y'); zlabel('Z')

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There are other ways to do the triangulation, but this is a way.