_{1}, 0 , C

_{1}) and B = R(C

_{ø}S

_{2}, S

_{ø}S

_{2}, C

_{2}).

ie we imagine the right handed coordinate system placed at the center of the sphere so that point A is on the zero longitude line and B is on the ø longitude line (with ø increasing in an easterly direction). The polar angle between OA and the z axis (north) is θ

_{A}, and the angle between OB and z axis is θ

_{B}. The following short hand notation is employed;

C

_{1}= Cos θ

_{A}

S

_{1}= Sin θ

_{A}

C

_{2}= Cos θ

_{B}

S

_{2}= Sin θ

_{B}

C

_{ø}= Cos ø

S

_{ø}= Sin ø

then:-

x/R = [Cosψ].S

_{1}+ [Sin ψ].{C

_{ø}.C

_{1}

^{2}.S

_{2}- S

_{1}C

_{1}C

_{2}}/Sinδ

y/R = [Sinψ].{S

_{ø}.S

_{2}}/Sinδ

z/R = [Cosψ].C

_{1}+ [Sinψ].{S

_{1}

^{2}.C

_{2}- C

_{ø}.C

_{1}.S

_{1}.S

_{2}}/Sinδ

δ is the angle between OA and OB and is given by

Cosδ = C

_{ø}.S

_{1}.S

_{2}+ C

_{1}.C

_{2}

ψ is the only free parameter, as it increases from 0 to δ we sweep around the great circle from A

to B. as it continues to increase to 2π we go right around the great circle.