Given a camera at C and
n correspondences
between 3D reference points 
and their images 
,
each pair of correspondences 
and 
gives a constraint on the unknown
camera-point distances 
and 
:
where 
is the known distance between
the i-th and j-th reference
points and
is the 3D viewing angle
subtended at
the perspective center by the i-th and j-th points,
which can be measured from the calibrated images using (1).
This quadratic constraint can be rewritten as follows:
For n=3, the following polynomial system is obtained
for the three unknown distances 
.
Using classical Sylvester resultants to eliminate 
between
and 
to get a polynomial 
,
then further eliminating
between 
and 
gives an 8th degree polynomial in 
with only even terms,
i.e. a 4th degree polynomial in 
:
This has at most four solutions for x and can be solved in closed form.
As 
is positive,
.
Then 
and 
are uniquely determined from 
.
The coefficients of the 4th degree polynomial is provided in the appendix.
