I now understand, why G15/G16 doesn't fit at all to my situation. I tried out the proposal of BR549 to use "formula axis correction" instead. It would be perfect if

a) I could distinct between cases (if ... then .. else) that appear in the trigonometric math and

b) if Mach3 would not only apply the formula to the endpoints of G1-lines, but also to all intermediate points. Without this, all lines appear to be arc. Why? Consider the example of moving from cartesian points (1,0) to (0,1). The polar coordinates are (1,0°) and (1,90°). So, Mach3 thinks: "twice the same x-values - so I don't have to move the x-axis" - yielding an arc from 0° to 90°, which is not what I expected. I expected a COORDINATED move from point to point, whereby the formula is applied to each intermediate point. That would give a real straight line.

I read about the cylindrical coordinates in the XZC-coordinate system: X and Z linear axis, C the rotational axis parallel to the Z-axis. Would that solve the problem maybe?