Some basic geometric test conditions in terms of Plücker coordinates and Plücker coefficients

We propose some basic geometric tests that are unified, projectively invariant, and do not require any auxiliary points. We include (1) linearly independent conditions of homogeneous flats and simplices; (2) coincidence, coplanarity, concurrency, and collinearity conditions of homogeneous flats; and (3) interference conditions between homogeneous simplices, defined both in projective space and in two-sided space. All the conditions are represented in terms of Plücker coordinates and Plücker coefficients.