polyTEM.spatial.stats.vector_curvature

polyTEM.spatial.stats.vector_curvature(v1, v2, r1, r2)

Calculates the numerical components of curvature of v1(r1) using finite, single-sided (forward) difference between two unit vectors v1 and v2, whose origins are projected into the xy plane onto r1 and r2

splay: s1 = dvx/dx, s2 = dvy/dy twist: t1 = -dvy/dx, t2 = dvx/dy bend: b1 = dvx/dz, b2 = dvy/dz

These equations assume that the nematic vector is parallel to the z direction Assumed that r1!=r2

Parameters:

  • v1 – unit tangent vectors

  • v2 – unit tangent vectors

  • r1 – location of origin of v1 and v2

  • r2 – location of origin of v1 and v2

Returns:

s1,s2,b1,b2