Self-stress dimension in the Desargues configuration

Determine whether making the line of perspective incident with the point of perspective in the Desargues configuration changes the dimension of its self-stress space.

Background

The Desargues configuration is used in the paper as an example of a dependent incidence structure with a projective self-stress. The authors propose modifying the incidence relation by adding incidence between the perspectivity line and perspectivity point and ask whether this changes the space of equilibrium stresses.

References

For example, if in the Desargues Configuration, the line of perspective is incident with the point of perspective, does the dimension of the self-stress space change?

— Counting for rigidity under projective transformations in the plane  (2503.07228 - Berman et al., 10 Mar 2025) in Section "Open problems and future work," subsection "Self-stresses"