Figure 6
From: Structural footprinting in protein structure comparison: the impact of structural fragments
Computing the average crossing number. (a) Projection directions that result in one overcrossing are parallel to vectors of the form t v - t u , where t u is on u and t v on v. (b) Those directions trace a parallelogram P = P1P2P3P4, where P1 = vsp- usp, P2 = vep- usp, P3 = vsp- uepand P4 = vep- uep. The average crossing number equals the signed area of P projected on S2 and normalized by half of the area of S2, which can be computed using tools of Spherical Geometry [28].