InPolyedron is a handy Matlab addon that detects points inside a manifold closed surface (even non convex ones). The normal orientation is assumed to be outwards. Warning there is no check for closed surface or normal orientation, open surfaces will give nonsense results.
In the limit of numerical accuracy, points lying on the surface will be considered in.
p: points of the surface npx3 array
t: triangles indexes, first points flagged as one, ntx3 array
tnorm: outward normals of traingles, ntx3 array
qp: points to be queried, nqx3 array
in: nqx1 logical vector, true for in, false for out
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p, q, t and tnorm are vectors of size npx3, nqx3, ntx3, and ntx3 respectively. These vectors are filled with respective n-coordinates in the polyhedron.
To save some memory, the dimension is reduced to dimension 3.
Matlab script is available at
The main drawback to this approach is that it will give a positive result if the point is in the outside of the polyhedron, as well as if it is inside it.
This is because the result comes directly from the distance of the point from the surface.
There is another method to test whether a point is inside a surface, but it’s not trivial to get the vector from the point to the surface. This other method does not give the same results.
If you do not care about the exact value, you could also use the dot product. If the dot product is smaller than some small number, then the point is inside. This method gives the same results as the method above, only a more efficient.
The dot product is defined as follows:
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Computing normal on non-flat manifold
In Polyedron test, the point cloud is triangulated as:
Using Othogonal projections:
Using PLT with normal direction reversed:
Running points in the triangulated surface:
Running points in the triangulated surface with normals outwards:
I was expecting it to show me outwards.
Thanks in advance
If you really want to check that it works, you can check the distance between each point and the normal.
points(:,1) – nnormal(points(:,1))
That will give you a vector of all the points compared to the normal of that point. Each negative number means the point lies outside the manifold, each positive number means the point lies inside.
If you are working with a small enough dataset it shouldn’t be too bad to do this in your own code, but there are faster ways. If you have a library like Omero, the functions can do this for you.
Omero has a cpos() function that finds the closest point to a point, and a cluster_calc() function that uses a closed region model and calculates the closest point to any point. So if you have some points in your dataset you can try a cpos() call on each point and see if any of them are in. If you do, you have a point inside the region, if you don’t, you have a point outside. If you can find enough points inside, then you know the cluster is good and you can use cluster_calc() to calculate the center of the cluster.
The cpos() function returns an oct2, which you can then cast to a poly2. The poly2 has a tpoint() function, which returns a point in the triangulated mesh. Then you just need to find the normal of the point, and see if it’s the same as the normal of the point you found with cpos().
A simple Omero script to do this is given in this answer, or you could look at the source of the cpos() function in the Omero demos.
Here’s how you can check for in and out for a simple mesh:
N = 50; %# number of points
p = rand(N,3); %# points
What’s New In In-Polyhedron Test?
This Matlab addon is a handy way to detect points
inside a manifold closed surface, e.g. a closed
surface in a 3D mesh. The tool will return true
for points inside the surface and false for points
outside. The surface is not necessarily convex.
The tool will return true for points on the
surface, even on non convex parts. The calculation
of points outside is well documented in the next
sub section. The calculation of points inside
the surface is explained in the next section.
Here is a short manual for the user:
The tool compute the sign of the 2nd
order derivatives of the manifold (i.e.
the normal field for the surface). For
this it does not return the normal
orientation, only the sign of the
tangential derivative. There are two
1. The normals are assumed to be
outward. If the normals are not
outward, an error will be returned.
2. The tool
System Requirements For In-Polyhedron Test:
Requires Windows XP or higher.
Requires Windows 7 or higher.
Requires Windows 8 or higher.
Requires Windows 8.1 or higher.
Requires Windows 10 or higher.
Requires Windows 10 RS2 or higher.
Requires Windows 10 RS3 or