I'm always reading about this property of curves (e.g. Bézier or B-spline) but is there any curve, especially from those used in CAD or Computer graphics that does not have this property? If not, can we just generalize that and say that any curve used in computer graphics area has this property of being contained into convex hull of its own control points?
2026-03-27 16:27:45.1774628865
Is there any type of curve that is not contained in convex hull of its own control points polygon?
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The convex hull property for Bézier curves and B-spline curves is one of the reasons that they are widely used as the "standard" representation for freeform curves in CAD industry. However, there are other types of curves that are used internally (i.e., not as an entity visible to users) and these curves might not even have the control point polygon at all, e.g.: Catmull-Rom spline. So, to say "any curve used in CAD area has the convex hull property" is a bit over-stretched.