length

function length(interval: number[], ps: number[][], tolerance?: number): number

Returns the curve length (for a linear, quadratic or cubic bezier curve) in the specified interval.

lines and quadratic bezier curves are calculated using (numerically stable) closed form expressions
cubic bezier curves are calculated using adaptive Gauss-Kronrod quadrature (with tanh-sinh quadrature as a fallback near cusps) after first splitting the interval at the points where the speed is stationary (so that (near) cusps always lie at sub-interval endpoints where the quadrature can handle them)
accuracy: typically within a few ulps (relative) of the true length; one exception is a tiny interval straddling a (near) cusp of a cubic in which case the relative error is limited by the cancellation in evaluating the derivative in double precision near the cusp (the absolute error is still tiny relative to the total curve length though)

Note!

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Name	Type	Default value	Description
`interval`	number[]	-	the paramter interval over which the length is to be calculated (typically `[0,1]`)
`ps`	number[][]	-	an order 0,1,2 or 3 bezier curve given as an array of its control points, e.g. `[[1,2],[3,4],[5,6],[7,8]]`
`tolerance`	number	defaultLengthTolerance	optional; defaults to `2-44`; the (approximate) relative error tolerance (only relevant for cubic bezier curves); note that the error estimate used internally is conservative so that the actual error is typically much smaller; values below `2-45` are clamped to `2**-45`