Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data
Fig 18
Transformation of coordinates.
This diagram schematically represents the transformation given to the experimentally obtained data such that the transformed x-axis, i.e., x′ is along the bisector of the two group direction vectors. The arrows in blue and red indicate the two group direction vectors and the dotted green arrow indicates the bisector. θB is the angle between the bisector and the original x-axis. A clockwise rotation by an angle θB in this case makes the bisector as the new x-axis. The transformed axes x′ and y′ are shown by green arrows. The bold line in purple represents a stripe, which makes an angle γ (measured anti-clockwise) with the bisector of group direction or the x′-axis. The purpose of the pattern matching technique is to find out the orientation of stripes γ.