Plotting the map projection graticule involving discontinuities based on combined sampling

on the interval Ω = Ωϕ × Ωλ based on the combined sampling technique. The proposed
method synthesizes the uniform and adaptive sampling approaches and treats the discontinuities
of the coordinate functions F, G. A full set of the projection constant values represented
by the projection pole K = [ϕk, λk], two standard parallels ϕ
0
1
, ϕ0
2
and the central meridian
shift λ
0
0
are supported. In accordance with the discontinuity direction it utilizes a subdivision
of the given latitude/longitude intervals Ωϕ = [ϕ, ϕ], Ωλ = [λ, λ] to the set of disjoint
subintervals Ω
g
k,ϕ,Ωg
k,λ forming tiles without the internal singularities, containing only “good”
data; their parameters can be easily adjusted. Each graticule tile borders generated over
Ω
g
k = Ω
g
k,ϕ × Ω
g
k,λ run along the singularities. For combined sampling with the given threshold
α between the adjacent segments of the polygonal approximation, the recursive approach
has been used; meridian/parallel offsets are ∆ϕ, ∆λ. Finally, several tests of the proposed
algorithms are involved.