Thread Subject:

Insdie or outside of a volume?

Hi,

I have an STL file which I can read in so that I get face number, co-ords of each face (triangle) and the normal vector for each face. The faces form a closed volume.

I would like to create a 3D matrix representation of this volume, with matrix elements representing either inside the volume or outside the volume.

So my question is how do determine if a given coordinate is inside the volume or not?

"Nic Roberts" wrote in message <jgdtsa$cnt$1@newscl01ah.mathworks.com>...
> Hi,
>
> I have an STL file which I can read in so that I get face number, co-ords of each face (triangle) and the normal vector for each face. The faces form a closed volume.
>
> I would like to create a 3D matrix representation of this volume, with matrix elements representing either inside the volume or outside the volume.
>
> So my question is how do determine if a given coordinate is inside the volume or not?

For a point P: (x,y,z) count the number n of triangle face {Ti} such that

1. (x,y) inside the projection of {Ti} on xy plane (use Tseach function for that)
2. zi > z, where zi is coordinate that Ti meat the line { (x,y,t) t in R } (simple linear algebra).

P is inside the volume if the number n is odd, P is outside otherwise.

Bruno

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <jge159$mbo$1@newscl01ah.mathworks.com>...
> "Nic Roberts" wrote in message <jgdtsa$cnt$1@newscl01ah.mathworks.com>...
> > Hi,
> >
> > I have an STL file which I can read in so that I get face number, co-ords of each face (triangle) and the normal vector for each face. The faces form a closed volume.
> >
> > I would like to create a 3D matrix representation of this volume, with matrix elements representing either inside the volume or outside the volume.
> >
> > So my question is how do determine if a given coordinate is inside the volume or not?
>
> For a point P: (x,y,z) count the number n of triangle face {Ti} such that
>
> 1. (x,y) inside the projection of {Ti} on xy plane (use Tseach function for that)
> 2. zi > z, where zi is coordinate that Ti meat the line { (x,y,t) t in R } (simple linear algebra).
>
> P is inside the volume if the number n is odd, P is outside otherwise.
>
> Bruno
- - - - - - - -
  Another method might be to use outward pointing normals to calculate the signed solid angle projected by each triangle onto a given point (x,y,z). The algebraic sum of these should be 4*pi if (x,y,z) is interior and 0 otherwise.

Roger Stafford

> I would like to create a 3D matrix representation of this volume, with matrix elements representing either inside the volume or outside the volume.

That sounds like you're trying to voxelize the mesh. If so, this function might be useful to you:

http://www.mathworks.co.uk/matlabcentral/fileexchange/27390-mesh-voxelisation

"Adam A" wrote in message <jgte3o$mib$1@newscl01ah.mathworks.com>...
> > I would like to create a 3D matrix representation of this volume, with matrix elements representing either inside the volume or outside the volume.
>
> That sounds like you're trying to voxelize the mesh. If so, this function might be useful to you:
>
> http://www.mathworks.co.uk/matlabcentral/fileexchange/27390-mesh-voxelisation

Thanks for the replies. Y'all have made me do quite a bit of reading to understand what you posted but it was worth it.

And big thanks for the link to the voxeliing code.

Nic