On 2026-05-09 09:36, ingo wrote:
> The CatmullRom is a case of Cardinal spline

Added Cardinal and played with tension.

---%<------cardinal for curve.inc---%<------%<---
#macro CIcardinal(CIarr, Tension)
   //:Quadratic Cardinal curve
   #local DimSeg = 4;
   #local Step = 1;
   #local Div = 1;
   #local T = (1 - Tension) / 2;
   #local Matrix = array[4]{
       array[4]{     -T, 2.0 - T,         T - 2.0,   T},
       array[4]{2.0 * T, T - 3.0, 3.0 - (2.0 * T),  -T},
       array[4]{     -T,     0.0,               T, 0.0,},
       array[2]{    0.0,     1.0}
   }
   _CIinit(CIarr, DimSeg, Step, Matrix)
#end
---%<------%<------%<------%<---


---%<------cardinal for scene file---%<------%<---
#declare Test = CIcardinal(vC, 0.65);
#for(T, 0, 1, 0.0015)
   sphere{CIget(Test, T), 0.05 pigment{rgb <1,0,0>} translate <0.1,0,0>}
#end
---%<------%<------%<------%<---

neither of both curves give the C2 continuity that a natural cubic 
spline gives. The slight curvature in the glass and the stem. My guess 
would be SOR is a natural cubic spline. I.i.r.c. ABX had the SOR spline 
implemented as a spline in one of patched versions. SuperPov, UeberPov?

ingo

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