gaal@cernvax.cern.ch (tamas gaal) (02/15/91)
Miklos Kanyo asked me to forward a problem of his to the net:
Please e-mail him direct:
kurz@ZEL780.dnet.zam049.zam.kfa-juelich.de (Miklos Kanyo)
(in emergency I shall forward answers on his behalf, too).
If there is enough interest I volunteer to summarize and post answers.
The problem:
An unknown 3D shape is placed between two parallel 2D sensors (planes).
Individual inner points of the 3D shape emit radiation that is being
perceived on the sensor planes. One radiation event can be separated
from another one: the perception is quasi-simultaneous. A "hit event"
is a coordinate point on the respective plane, that is, a radiation event
creates two simultaneous hit events.
In a given time interval a data set of connected pairs (one point from
the "left" plane with the corresponding "right" counterpart) is being
collected. The pairs constitute a set of lines between the respective
points on the planes. The number of the pairs/lines (ie. the time
interval) can be increased at will. The surface of the planes can be
increased, too. The probabilistic distribution of the radiation
is known.
Is there any method to reproduce (or approximate) the original 3D
shape from the collection of lines? Reference? Program?
Shall the 3D shape be convex? Please forget the actual physical setup:
it is the reproduction of the original 3D shape from the mapping
lines that is of interest.
Tamas Gaal (zdv052@djukfa11.bitnet) (but again, please try and mail
Miklos Kanyo first.)