The geometry does change. The fool-proof way to figure it out is to actually lay it out in a drawing. It takes a little more time, but it also gives you the flexibility to make a fretboard that's exactly the way you want it to be. You're in control, not your plan. Had I drawn my latest fretboard rather than trusting FretFind2D, I woud've gotten it right much faster
1. Measure out your scale length from the saddle to nut, then mark the 12th or 14th fret location (whichever you prefer).
2. Draw your nut width at one end, and string spacing at the saddle end.
3. At the nut end, mark how far in from the edge of the fretboard you'd like your 1st and 6th strings. Draw a line connecting those marks to their location on the saddle. Now you have string paths for the 1st and 6th strings.
4. Determine how far in from the fretboard edge you'd like your strings to be at the 12th or 14th fret. Do you want it to be the same as at the nut? A little less? A little more? It's your choice. Make the mark at the 12th or 14th fret.
5. Draw a line from that mark to the edges of the nut. Now you have your taper.