Is the sum of cubic Bezier curve segment arc lengths the arc length of the whole spline?

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I have created a spline made of several cubic Bezier curve segments. I have been able to calculate the arc length of each of these cubic segments. I would like to know in the sum of all the individual arc lengths would give the arc of the whole spline. If not, how can I calculate the arc length of the spline?

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A spline is simply the concatenation of its constituent segments, so its total length is naturally the sum of the lengths of its segments. Your intuition is correct.