Question: How Do I Fill a Concave 3d Parametric Plane Curve?

Hi MaplePrimes team,

Is there a generalized way to fill an extremely CONCAVE closed 3d parametric plane curve in Maple with spacecurve command (NO implicitplot3d), preferably without doing any multi-decomposition or creating a particular skeleton, or algorithm/programming?

Here my example:


#Circle of reference
R0 := 1:
C0 := t-> < cos(t), sin(t), 0 >:

#Variable radius
R := t-> R0*(1 + 1/2*sin(t)):

#Variable phase
Dt := t-> Pi/2*sin(2*t):

C := t-> R(t)*C0(t - Dt(t)):
'C(t)' = C(t);

t1, t2 := 0, 2*Pi:

GC := spacecurve(C(t), t = t1..t2, color = "Red", thickness = 3
, linestyle = solid
, scaling = constrained, axes = frame, orientation = [50,40,0]):

We know how to do it easily for any convex 3d plane curve (circle, ellipse, regular polygon, etc ...).

We also know how to do it for 2d curve with the Maple’s plot option filled = true but obviously not in 3d.

Thank you for your time.



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