Given a curve $C$, I need to construct another curve $C'$ approximating $C$ under the following constraints: (1) $C'$ needs to be smooth, (2) $C'$ is composed of only line sections and arcs, (3) $C'$ is sufficiently close to $C$. How to design such approximation algorithm to construct $C'$? Is there any existing literature that I can look into?
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$\begingroup$ (i) What is a "line section"? (ii) What exactly do you mean by "smooth"? How can a curve be smooth and composed of only "line sections" and arcs (so as to contain at least one "line section" and at least one arc? $\endgroup$– Iosif PinelisCommented Sep 13 at 14:06
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$\begingroup$ We can speak about an algorithm only if the given data is of combinatorial nature. However we can always approximate the curve by a piecewise linear curve (by choosing the set of breaking points to be a sufficiently dense subset of the given curve) and then smooth out the corners by sufficiently small arcs. $\endgroup$– Maxim PrasolovCommented Sep 13 at 16:45
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