How to compute inside points in n dim convex hull?

I'm working on convex hull and facing problem in computation of inside points. In 2D convex hull we can use inpolygon function for calculating inside points. But inpolygon function didn't work in n dim convexhull (convhulln function). Please help me out.

Answer 1

[John D'Errico]

I wrote inhull for this purpose. Find it here on the file exchange.

https://www.mathworks.com/matlabcentral/fileexchange/10226-inhull

You can use it on a set of points directly, where it computes the convex hull for you.

xyz = rand(1000,5);

inhull([.5 .5 .5 .5 .5; 2 .5 .5 .5 .5],xyz)
ans =
  2×1 logical array
   1
   0

Or you can precompute the convex hull.

tess = convhulln(xyz);

inhull([.5 .5 .5 .5 .5; 2 .5 .5 .5 .5],xyz,tess)
ans =
  2×1 logical array
   1
   0

It even allows you to provide a tolerance.

[stuti chug]

Thankyou sir.

I also have one more query.

Actulally in inpolygon function it consider border point as inside points. so i want know that inhull function only compute inside points or it consider border points as inside points.

[John D'Errico]

inhull does not distinguish between a point that lies exactly on the boundary or inside. It works in floating point arithmetic as it must. As such, it tests for an inequality of the general form <=0. But you should never worry about a floating point value being exacly zero, and that is what would need to happen for a point to be seen as exactly on a boundary. There will alsys be some floating point trash in the result, so values that are within +/- delta, for some small value of delta would arguably be viewed as being on the boundary itself.