Curves: Improve accuracy and clarity of NURBS knots calculation

This commit improves NURBS knot generation by adding proper support
for the combination of the Bezier and cyclic options. In other cases
the resulting knot doesn't change. This cyclic Bezier knot is used to
create accurate accurate "Nurbs Circle", "Nurbs Cylinder" primitives.
"Nurbs Sphere" and "Nurbs Torus" primitives are also improved by
tweaking the spin operator.

The knot vector in 3rd order NURBS curve with Bezier option turned on
(without cyclic) is changed in comparison to previous calculations,
although it doesn't change the curve shape itself.

The accuracy of the of NURBS circle is fixed, which can be checked by
comparing with mesh circle. Tessellation spacing differences in
circular NURBS is also fixed, which is observable with the NURBS
cylinder and sphere primitives. These were causing seam-like effects.

This commit contains comments from Piotr Makal (@pmakal).

Differential Revision: https://developer.blender.org/D11664

1 files changed, 7 insertions, 4 deletions

diff --git a/source/blender/editors/curve/editcurve.c b/source/blender/editors/curve/editcurve.c
index a034e4bb10e..a70bc1c0350 100644
--- a/source/blender/editors/curve/editcurve.c
+++ b/source/blender/editors/curve/editcurve.c
@@ -4953,19 +4953,22 @@ bool ed_editnurb_spin(
 
     if ((a & 1) == 0) {
       rotateflagNurb(editnurb, SELECT, cent, scalemat1);
-      weightflagNurb(editnurb, SELECT, 0.25 * M_SQRT2);
+      weightflagNurb(editnurb, SELECT, 0.5 * M_SQRT2);
     }
     else {
       rotateflagNurb(editnurb, SELECT, cent, scalemat2);
-      weightflagNurb(editnurb, SELECT, 4.0 / M_SQRT2);
+      weightflagNurb(editnurb, SELECT, 2.0 / M_SQRT2);
     }
   }
 
   if (ok) {
     LISTBASE_FOREACH (Nurb *, nu, editnurb) {
       if (ED_curve_nurb_select_check(v3d, nu)) {
-        nu->orderv = 4;
-        nu->flagv |= CU_NURB_CYCLIC;
+        nu->orderv = 3;
+        /* It is challenging to create a good approximation of a circle with uniform knots vector
+         * (which is forced in Blender for cyclic NURBS curves). Here a NURBS circle is constructed
+         * by connecting four Bezier arcs. */
+        nu->flagv |= CU_NURB_CYCLIC | CU_NURB_BEZIER;
         BKE_nurb_knot_calc_v(nu);
       }
     }