This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-4258U CPU at 2.40GHz.
There were 20 solutions found in 0.2575 seconds (with a Bezout bound of 64).
Reference:
Ioannis Z. Emiris. "Sparse Elimination and Application in Kinematics". PhD Thesis, Computer Science, University of California at Berkeley, 1994.
Ioannis Z. Emiris. "A general Solver Based on Sparse Resultants: Numerical Issues and Kinematic Applications", INRIA Rapport de Recherche no 3110, January 1997, 29 pages. Available via anonymous ftp to ftp.inria.fr
See also: http://homepages.math.uic.edu/~jan/Demo/camera1s.html
i1 : camera1s(RR_101)
o1 = {- d q - d q - d q + 1, - 3.6d q + 4.1d q + 2d q + 4.1d q +
1 1 2 2 3 3 1 1 2 1 3 1 1 2
------------------------------------------------------------------------
1.8d q + 3.7d q + 2d q + 3.7d q - 4d q + .1d - .2d + .3d + .1q
2 2 3 2 1 3 2 3 3 3 1 2 3 1
------------------------------------------------------------------------
- .2q + .3q + 5.8, - 2.1408d q - 3.99879d q + 3.71599d q -
2 3 1 1 2 1 3 1
------------------------------------------------------------------------
3.99879d q - 1.5752d q - 3.99879d q + 3.71599d q - 3.99879d q -
1 2 2 2 3 2 1 3 2 3
------------------------------------------------------------------------
2.1408d q - .2828d + .2828d - .2828q + .2828q + 5.85679, .3464d q
3 3 1 3 1 3 1 1
------------------------------------------------------------------------
+ .1732d q - 5.99965d q + .1732d q - 5.99965d q - .1732d q -
2 1 3 1 1 2 2 2 3 2
------------------------------------------------------------------------
5.99965d q - .1732d q - .3464d q - .1732d + .3464d - .1732d -
1 3 2 3 3 3 1 2 3
------------------------------------------------------------------------
.1732q + .3464q - .1732q + 5.99965, - 5701.3d q - 2.9d q +
1 2 3 1 1 2 1
------------------------------------------------------------------------
3796.7d q - 2.9d q - 5698.7d q + 1897.3d q + 3796.7d q + 1897.3d q
3 1 1 2 2 2 3 2 1 3 2 3
------------------------------------------------------------------------
+ 5703.1d q - 1902.7d + 3803.3d + .7d - 1902.7q + 3803.3q + .7q +
3 3 1 2 3 1 2 3
------------------------------------------------------------------------
5696.9, - 6.8d q - 3.2d q + 1.3d q - 3.2d q - 4.8d q - .7d q +
1 1 2 1 3 1 1 2 2 2 3 2
------------------------------------------------------------------------
1.3d q - .7d q + 9d q + 5.1d - 7.1d - d + 5.1q - 7.1q - q +
1 3 2 3 3 3 1 2 3 1 2 3
------------------------------------------------------------------------
2.6}
o1 : List
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The object camera1s is a method function.