camera1s -- a system for camera displacement between two positions, with scaled first frame.

Synopsis

Usage:

camera1s(kk)
Inputs:
- kk, a ring, the coefficient ring
Outputs:
- a list, of the polynomials in the system

Description

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

Ways to use camera1s :

camera1s(Ring)

For the programmer

The object camera1s is a method function.