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Julian

"Approximating the Length of a Spline by its Control Polygon"

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In response to the "Math algorithm for distance between 2 CP ?" thread in the SDK forum, here is a PDF file of this 1995 paper printable on one landscape letter-size page.

ApproximatingSplineLength.pdf

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Thanks Julian. The paper is actually proving what we already know. That is to get the arc length, one need to increase the order of the spline and as the order approaches infinity, the resulting control polygons length approach the arc length. So basically, we're back at square one. That is the only way to get a spline (or arc) length is through integration or subdivision.

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