The attitude for flying a LinePath: nose along the line, horizon leveled
against upHint.
It takes the path rather than a frame because the answer does not depend on the frame. A straight line has one flight direction, so the derived attitude is a constant and the nose cannot drift off the velocity — there is nothing for it to drift with respect to. Sliding is impossible by construction rather than within a tolerance, which is the whole argument for fitting lines. Authored facing beats carry no such guarantee: between two hand-written vectors the slerp passes through whatever it passes through, and the f1000→f1035 pair swings about 120° in 35 frames with no intermediate that is a flight attitude at all.
direction is the direction of flight, which is why an approach is
authored as a negative advance closing on the anchor rather than a positive
one shrinking toward it — written the other way the ship flies tail-first.
This deliberately does not read the advance to work the sense out: an
attitude that silently flips on the sign of a number elsewhere in the
literal is worse than one that is wrong in plain sight, and reversing a pass
is negating direction and every t, which describes the identical line.