1. As AI Cash asked, can each design have two or more points with the same location? 2. "the pre-jury wants to find the designs which only differ in rearrangement of points and their affine transformation that doesn't change the orientation" does it mean that two designs (P1, P2, P3, ..., Pm) and (Q1, Q2, Q3, ..., Qm) will be considered same if there is an affine transformation Qi=A*Pi+b for all i such that A is matrix 2x2 that detA>0 ?
Not "positively defined" but "with positive determinant" as it is said in russian text, and which is used in correct definition of affine transformation. For example matrix -1 3 -2 1 is not positively defined, but has positive determinant.