Re: [OctDev] convhulln options.

[Pedro T. <pt...@te...>]

El Jueves, 18 de Diciembre de 2003 02:07, a Paul Kienzle  se le ocurri=F3 d=
ecir=20
lo siguiente:
> > Instead of doing that, we might return a cell array instead of a
> > matrix when
> > non simplicial facets are found.  For instance, the following result:
> >. . . . . . . . . . . .
> > would be represented in Octave like this:
> >
> >     A =3D {[3 4 2 1],
> >          [7 4 3],
> >          [5 7 3 1],
> >          [4 6 2],
> >          [6 7 5],
> >          [7 6 4],
> >          [6 5 1 2]}
> >
> >
> > (Notice that vertex indices in Octave start at 1 instead of zero.)
> >
> > I do not know how backward incompatible would be such a change.
>
> I think the most convenient would be to return a cell-array of
> matrices, one
> for each dimension of returned facet.

I don't understand this. Each of these matrices would contain an unique num=
ber=20
referecing a vertex?.

>
> I think it would also be convenient if the default were to arbitrarily
> split
> those facets that are non-simplicial so that those who just want
> triangles
> don't have to deal with the occasional square.  I'm guessing that this
> is
>
> what matlab does --- convhulln returns this for the cube:
>  >> convhulln(cube)
>
> ans =3D
>
>       3     4     1
>       4     2     1
>       2     4     6
>       2     5     1
>       5     2     6
>       7     5     6
>       4     7     6
>       7     4     3
>       7     3     1
>       5     7     1
>

This is what Qt is supposed to do. QJ also does it although using some othe=
r=20
method (joggling vertices until only simplicial facets are found). Anyway Q=
t=20
option is not working under octave. Is it just my case?

>
> So long as the default  all-simplicial case is returned as a matrix,
> backward
> compatibility doesn't matter.  The user will need special code to
> handle the
> non-simplicial facets anyway.

Ok on that.

> Are these two cases different enough that we need different functions?
>
> I think you are going to need an interface layer above the QHull options
> so that users can ask for them nicely:
>
> [X,Y,Z] =3D convhulln(cube,'output',{'simplicial','ideal','geomview'})
>
> This says that X will contain the simplicial output (as a full matrix),
> Y will contain a cell array of facet sizes, and Z will contain a string
> used to control geomview.  The default for output must be 'simplicial'
> for compatibility.
>
> That means you will need other options for controlling the QHull
> algorithm,
> such as 'qhull','QJ' to feed a raw option string, or if you are feeling
> creative, meaningful names for all the options.

I think so.=20
In fact. Maybe we should use convhulln for matlab compatibility if this is =
an=20
issue. Some of the important info that I think should be accesible from=20
octave is stored in qh struct in qhull. What I mean is:
	- A polyhedron is just an ordered list of facets.
	- A facet should contain:
		- id number
		- normals and offset (hyperplane supporting the facet)
		- area
		- set of vertices (n if simplicial, >n if non-simplicial)
		- set of neighbours (again n  if simplicial...). Here's the need for the =
id.
		- set of ridges. (?)

I don't know how difficult this is but it looks like in the same=20
=46ORALLfacets{} loop  the above can be retrieved and written to octave.

Regards,
Pedro