pub fn chain_chord_bound(chain: &Chain2, a: f64, b: f64) -> Option<f64>Expand description
Certified bound on the distance from a chain over arc lengths [a, b]
inside one piece to the chord joining its evaluated ends (#232, #438);
None across a join, for a span outside the chain, a piece whose curve
has no certified bound, a chain no ChainPositionTable covers, or a
chain that does not evaluate.
The exact arc lies within the curvature bound of the chord of its
exact ends. The evaluated ends are off the exact ones (a quadrature on an
intrinsic piece, an arc-length inverse on a parametric one, carried
through every placement before them), and a chord whose ends move by at
most g moves by at most g everywhere, so the bound adds the larger of
the two ends’ distances from a certified table’s points, each with that
point’s own error (#414’s rule for intrinsic curves). The lower end is
read as the piece that starts there, the upper end as the piece that
ends there, so a parametric piece that starts off the end of the one
before it charges its jump.