pub fn true_point_fractions(i: usize, intervals: usize) -> &'static [(i64, i64)]Expand description
Where, within interval i of intervals between consecutive samples, a
caller of interpolate_enclosing should locate its true points: these
fractions of the way from one sample to the next.
One point, in the middle, for an interior interval — that is where a
cubic interpolant’s drift peaks, and it keeps the extra work at one
projection per interval. The two end intervals get seven, at eighths:
next to a clamped end the drift is lopsided and several times larger than
inside, so it sets the width of the whole enclosure, and its peak lies
wherever the end conditions put it. Measured at quarters, a smooth hump
can peak between the points by ~10% of its height: on a traced
plane × cylinder branch that left the branch 1.36e-8 from its curve,
widened to 1.25e-8 (see
cylinder_joined_over_a_hole in geop-cad-base). At eighths the
shortfall is ~2%, and on a circle sampled in 8 intervals a single midpoint
there left a true point unenclosed.