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

[KAE]

You could use inpolyhedron from the FEX, discussed here.