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

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

away from the beginning of the path.

If negative `length`

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

is higher than path length, a line tangent to the closest valid path endpoint is returned instead. If point at `length`

is a point of discontinuity (e.g. it is a point shared by two Lineto segments with different slopes), the tangent line is constructed for the earlier segment (i.e. the segment closer to the beginning of the path).

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

to `end`

is the same as the direction of the path segment at the specified point.

The algorithm skips over segments that are not differentiable. This includes all invisible segments (e.g. Moveto segments) and visible segments with zero length. If the path contains no valid segments, `null`

is returned. If the path has no segments at all, `null`

is returned, as well. The `segment.isDifferentiable()`

functions may be used to determine whether a given segment is valid; the `path.isDifferentiable()`

function may be used to determine whether the path contains at least one valid segment.

One valid segment is identified which contains the point at `length`

. Finding the desired point is straightforward for linear segments (see `line.pointAtLength()`

for reference). Finding the desired point in curved segments is more complex, as illustrated by the `curve.pointAtLength()`

function. A tangent line is then obtained that touches the path at the identified point (see `curve.tangentAtLength()`

for reference).

The `opt`

argument is optional. Two properties may be specified, `opt.precision`

and `opt.segmentSubdivisions`

, which determine maximum error allowed in `pointAtLength`

calculations for curved segments (default precision is 3; this corresponds to maximum observed error of 0.1%). The `opt.segmentSubdivisions`

property is an array of individual segments' subdivision arrays. The `path.getSegmentSubdivisions()`

function may be used to obtain the `segmentSubdivisions`

array. The `opt.precision`

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