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Automatically select composite Bezier curve degrees

Example 1 step, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1
pts1 = Tuples[{Range[4], Range[4]}];
pts2 = Tuples[{Range[3], Range[3], Range[3]}];
Grid[{
{Graphics[{Green, Line[pts1], Red, Point[pts1], Blue, BezierCurve[pts1, SplineDegree -> 5]}], Graphics3D[{BezierCurve[pts2, SplineDegree -> 4], Green, Opacity[.5], Line[pts2], Red, Point[pts2]}]}, {Graphics[BezierCurve[Table[{Cos[2k Pi / 13], Sin[2 k Pi / 13]}, {k, 0, 156, 4}]]],
	Graphics3D[BezierCurve[Table[{Cos[2k Pi / 13], Sin[2 k Pi / 13], k  / 156}, {k, 0, 156, 4}]]]}}]
Output
Grid[{{-Graphics-, -Graphics3D-}, {-Graphics-, -Graphics3D-}}]
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Functions used

BezierCurveCosGraphicsGraphics3DGridLineOpacityPointRangeSinTableTuples

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