How do you convert a surf object to an isosurface?

How to convert a regular surf surface (rectangular mesh) to a patch isosurface (triangular mesh)?

I have seen how to go the other direction, but this one eludes me. After creating the isosurface, I need to run inpolyhedron() to see if points are inside or outside the object.

theta = (pi:0.1:pi);
phi = 0:0.1:pi);
[THETA, PHI] = meshgrid(theta, phi);
x = cos(THETA).* sin(PHI);
y = sin(THETA).*sin(PHI);
z = cos(PHI;
ellipsoid = surf(x,y,z);

(Extract the isosurface from the ellipsoid...)

fv = isosurface(something something ...)
pts = rand(5,3);
in = inpolyhedron(fv,pts);  % check if points are inside or outside object

[John D'Errico]

It is an ellipsoid though! It is far simpler to test if a point lies inside an ellipsoid, if that is all you need.

[Kurt]

It's actually more complex than that. I bend and shape the ellipsoid to resemble a radar beam.

Answer 1

[Yatharth]

Hi Kurt,

You can use the "delaunayTriangulation" function, to convert the rectangular mesh to a triangular mesh.

for your given code, here is how you can use the function:

theta = (0:0.1:2*pi); % Corrected range for theta
phi = (0:0.1:pi);
[THETA, PHI] = meshgrid(theta, phi);
x = cos(THETA).* sin(PHI);
y = sin(THETA).*sin(PHI);
z = cos(PHI);
h = surf(x,y,z);

axis equal; % Equal aspect ratio for all axes

X = get(h, 'XData');
Y = get(h, 'YData');
Z = get(h, 'ZData');

% Flatten the matrices
x = X(:);
y = Y(:);
z = Z(:);

figure;
DT = delaunayTriangulation(x, y, z);

Warning: Duplicate data points have been detected and removed.
The Triangulation indices are defined with respect to the unique set of points in delaunayTriangulation.

tetramesh(DT, 'FaceAlpha', 0.3); % Adjust 'FaceAlpha' for transparency
axis equal;

You can refer to the "delaunaytriangulation" function documentation here https://www.mathworks.com/help/matlab/ref/delaunaytriangulation.html

[Kurt]

Thanks! This is a good start. Now, is there any way to convert this tetramesh to ECEF coordinates?

Normally, for a surf object I would call enu2ecef(XData,YData,ZData,lat,lon,alt,grs80) but that doesn't work here since the mesh data is ordered differently.

I would also like to make it invisible. Can I use alpha to do that?

[Yatharth]

Hello, have you tried using "pointLocation" function? https://www.mathworks.com/help/matlab/ref/delaunaytri.pointlocation.html

for making it invisible set the "FaceAlpha" to 0.

[Kurt]

I think if I do my ECEF coordinate conversion first and then extract the tetramesh, it just might work.