Is there a function in MATLAB for detecting points inside a polyhedron?

The INPOLYGON function in MATLAB detects points inside a polygonal region. I would like to determine whether a given three-dimensional point is inside a polyhedron.

Answer 1

[MathWorks Support Team]

The TSEARCHN and DELAUNAY functions in MATLAB can be used to detect whether a given three-dimensional point is inside a convex polyhedron for a small datasets. For example, consider the polyhedron defined by the vertices generated by the following commands:

n = 12; % Number of vertices

theta = 2*pi*rand(n,1)-pi; % Random theta

phi = pi*rand(n,1) - pi/2; % Random phi

x = cos(phi).*cos(theta); % Create x values

y = cos(phi).*sin(theta); % Create y values

z = sin(phi); % Create z values

The following commands determine if 20 randomly generated points within the unit square are also within the given polyhedron.

xyz = rand(3, n); % Generate random points

tri = delaunayn([x y z]); % Generate delaunay triangulization

tn = tsearchn([x y z], tri, xyz'); % Determine which triangle point is within

IsInside = ~isnan(tn) % Convert to logical vector

Answer 2

[Thorey]

Hello,

We have the same kind of problem, but our polyhedron is defined by the isosurface function. That is why we have a list of vertices and faces. We would like to either calculate the volume of the polyhedron defined by faces and vertices or detect which points are inside the polyhedron.

Unfortunately, the polyhedron is not necessarily convex.

Thanks

[John Magradey]

Hello,

Did you ever find a resolution to this problem? I am in the exact same predicament as you are.

Thanks

Answer 3

[KAE]

You could use inpolyhedron from the FEX, discussed here.