With the #secondaryCurves derived from #primaryCurves in https://pixelfed.social/p/Splines/794105734853818690, we are almost ready to sweep the #scroll surface. I say "almost" because there is at least one more refinement needed before we can use any of these curves.

Look at the front view of three sections of the scroll surface labeled A, B, and C, and you will see a qualitative difference among them. Surface A appears crude and surface C appears refined, while surface B lies somewhere in between. While B and C are both acceptable, A is not.

The difference is due to two factors — the nature of the curves themselves and the degree of precision used.

Surface A is built using the circular arc sections for #volute #spiral (original and scaled) as #railCurves and the secondary curve sections as #sweepingCurves. The nature of the two sets of curves is different. Straight lines are 1st-degree curves, #circular or #conic sections (including ellipse) are 2nd-degree curves, but the projected sweeping curves (secondary curves) are 3rd-degree #NURBS curves.

Sweeping 3rd-degree NURBS curves along 2nd-degree arcs does not produce a salubrious effect. So we #rebuild the arcs into a 3rd-degree curve using the #CAD tool. When we do that, we are able to control how close the rebuilt curve should be to the original arcs in terms of precision.

I rebuilt each arc in the spirals using 16 subsections, and the effect is visible in surface C.

Look at surface A again. The cross-section arcs appear unevenly spaced compared to those of the other surface sections. To fix that, I also rebuilt the projected NURBS curves (secondary curves) to obtain what I call #tertiaryCurves.

For the frontmost sections, I rebuilt the sweeping curves using 64 subsections, and for the rear sections, I rebuilt them with 8 subsections.

Experiment with what produces pleasing results, but remember that higher precision curves require more processing time as well as more storage space.

Mensch und Berg - Man and mountain #Scotland #Balmaha #lochlomond #Conic

Walk: https://www.walkhighlands.co.uk/lochlomond/conic-hill.shtml