[OctDev] Changes for the geometry package

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

Hi,

I've been working lately on the geometry package. I have written a DLD
function named qhull that is working properly and that can be used as the
engine for delaunay(n), voronoi(n) and convhull(n) functions. I have also
written delaunayn.m voronoin.m and convhulln.m so that they use this new
qhull function.

This new functions are supposed to work like their Matlab counterparts. Now:
- [ch, v] convhulln(x), returns ch triangulated (thru Q0 option, not Qt) and
returns the hulls volume on v, just like Matlab.
- [V, C] voronoin(x) returns the Voronoi vertices including a first vertex at
infinity, and the vector array C in the same manner as Matlab (if a reference
to point 1 is found this means the voronoi cell is unbounded).

qhull function returns:

[H, a, vol, N, O, R, V, C, inf] = qhull (p [,opt])

H : an index vector to the points of the enclosing convex hull.
a : total area of hull
vol: total volume of hull
N : normal vector for each facet
O : offsets of the hyperplanes
R : a list with the neighbors to each facet.
V : voronoi vertex. Only usefull if 'd' or 'v' option specifiedj. Otherwise
 it should return the baricentrum of each facet...
C : voronoi cells. List related to V
inf: Vector with ones if corresponding voronoi cell is unbounded, 0 otherwise

I think this gives a better control over the geometry package than what we
have right now. Also it is more Matlab compatible.

I attach the corresponding files.

Regards,
Pedro