Let cubic Bézier curve $C$ be based on points $p_0, p_1, p_2, p_3$. Suppose $L$ is the polyline through $p_0, p_1, p_2, p_3$. Is there some well known analytical relation between lengths of these two geometrical objects?
2026-03-26 11:18:08.1774523888
How did length of base polyline relate with length of Bézier curve?
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This paper has some material that might be relevant:
For example he shows that the length of the curve is less than the length of the polyline. The proof is fairly simple.