Re: Object separation under perspective projection
- From: "Dave Eberly" <dNOSPAMeberly@xxxxxxxxxxxxxxx>
- Date: Fri, 18 Aug 2006 19:26:20 GMT
"News Reader" <sorry@xxxxxxxxx> wrote in message
news:ec4emv$9qn$1@xxxxxxxxxxxxxxxxx
Here it goes:
Given a set of non-intersecting, convex 3D-objects O.
Sought is a decomposition of O into a minimal number of disjoint sets D_i
such that the union of D_i is O and for the elements of each subset D_i it
holds that their footprints under perspective projection do not overlap.
Btw. it is garanteed that no subset of O forms a Z-loop.
Of course the calculation should be "cheap" in terms of computational
complexity.
- The constraint "minimal" can be substituded by "sigificantly smaller
than the number of elements of O"
- It is neither necessary to calculate a unique solution nor all
solutions.
After the projection, you could compute axis-aligned bounding
rectangles for the convex (2D) objects. Use a sort-and-sweep
algorithm for determining which of the bounding rectangles intersect.
This process will also let you know separations between rectangles,
so you can probably postprocess the pairs of intersecting rectangles
into some type of hierarchical structure (similar to a quadtree). If
you have the pathological problem of rectangles A, B, C, D, ...
for which (A and B intersect but A does not intersect others),
(B and C intersect but B does not intersect others),..., then you
have to come up with some way to decompose this chain.
--
Dave Eberly
http://www.geometrictools.com
.
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