`curve.tangentAtLength(length [, opt])`

Return a line that is tangent to the curve at a point that lies `length`

away from the beginning of the curve.

If negative `length`

is provided, the algorithm starts looking from the end of the curve. If `length`

is higher than curve length, a line tangent to the closest curve endpoint is returned instead.

The tangent line starts at the specified point. The direction from `start`

to `end`

is the same as the direction of the curve at the specified point.

If the control points of the curve all lie at the same coordinates, `null`

is returned (it is impossible to determine the slope of a point). The `curve.isDifferentiable()`

function may be used in advance to determine whether tangents can exist for a given curve.

The curve is first subdivided, according to `opt.precision`

(refer to `curve.length()`

documentation for more information about precision and curve flattening). Then, one subdivision is identified which contains the point at `length`

. A binary search is then performed on that subdivision, until a curve is found whose endpoint lies within `opt.precision`

away from `length`

. That endpoint is used as the start of the tangent line.

The default value for `opt.precision`

is 3; this corresponds to maximum observed error of 0.1%.

The `opt.subdivisions`

property may be specified, directly providing an array of pre-computed curve subdivisions from which to calculate curve length. Use the `curve.getSubdivisions()`

function to obtain an array of curve subdivisions. The `opt.precision`

property is still necessary, however; it determines the precision of the point search algorithm.