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Extract the pure world-space position/tangent math from the WinForms cut-direction arrow renderer into Core (ContourSampler), keeping screen conversion, arrowheads, and the per-move display policy in the view. Add a contour-wide arclength scheduler (RingMoves) for measurement use: distance carries across segment boundaries, short segments are never omitted, and the closing vertex is not duplicated. Characterization tests pin the arrow policy (counts, short-move skipping, CW/CCW and full-circle sweeps, subprogram offsets, suppressed/rapid moves, incremental mode) and the scheduler's start-vertex invariance.