Illustration of parallel transport. Vector v₁ corresponding to a position angle θ_p1 and vector v₂ corresponding to position angle θ_p2 are shown. In order to compare v₁ to v₂, v₁ must be parallel-transported along the great circle indicated by the curve from location P₁ to location P₂. The transported vector is indicated by and the local basis vectors are denoted by (u_δ, u_α). In parallel transport, the angle α between the vector tangent to the sphere u_t and the vector v remains fixed. Figure adapted from Jain et al. (2004).