Special case of SFL with reference on the Equator

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Special case of SFL with reference on the Equator

The case where the reference point is chosen on the Equator ( ) is interesting because of the conversion from GLS to SFL suggested by CG02 and described in section 1. Injected in the previous formulas and rules, this gives:

|  |  | (27)
|  |  | (28)
|  |  | (29)

The longitude simplifies as:

| (30)

because atan2 atan2 (opposite quadrant). Similarly the latitude is in this case:

| (31)

Finally:

|  |  | (32)
|  |  | (33)

In this case have almost the same definition as the GLS definition provided in Eqs. 1 and 2. If we write a y-shifted version of the GLS equations as:

GLS |  | GLS | (34)
GLS |  | GLS | (35)

i.e. GLSGLS. This shows we can write the GLS projection at any declination as a SFL projection at zero declination with the relationship GLS and GLS.