A cut-out made in the flat pattern could cross a bend only with edges
running along the bend or square to it: a round hole or a slanted slot
over a bend line failed to fold ("not supported yet: curved cut-outs
across a bend", "... cut-out edges running across a bend at an angle").
Sheet: a flat edge in a bend zone now folds whichever way it runs: along
the bend to a line, across it to an arc, and any other way to a curve on
the bend's cylinder (a slanted line to a helix). The curve is carried as
a chain of cubic Hermite pieces fitted within 1e-7 mm on both faces of
the sheet, with breaks that depend on the flat edge only, so the top
face, the bottom face and the wall share them. The wall between the two
chains is a ruled surface with radial rulings: the cut-out's wall stays
square to the sheet. The bend's own faces stay exact cylinders, now sized
to the whole boundary of their cell (a curved edge may bulge past its
corners).
Kernel: such an edge has no line, arc or conic form, so the sewing
interface gets EdgeSpec::Chain (a chain of cubic Bézier pieces: a cubic
B-spline with triple inner knots, its ends on the shared vertices) and
SurfSpec::Ruled (two chains joined by straight lines, so a wall built
from the chains holds them exactly). The sheet module's rev_edge becomes
EdgeSpec::reversed, so the new variant is handled where edges are
reversed.
The test for "along" and "across" is in millimetres (1e-6 mm at the
edge's ends) instead of relative 1e-9, so coordinates rounded by a script
fold as drawn.
Tests. Kernel: a box with one wall bulging as a cubic (chains of two
pieces at the bottom and the top, the wall ruled between them) sews to a
valid solid of the analytic volume, 27.6 (measured 27.59965); chains with
the wrong number of control points, a NaN or too many pieces, and a ruled
wall between chains of different piece counts, are refused. Sheet: a slot
turned 30° and a round hole across 72°, 90° and 108° bends fold to valid
solids that lose the cut-out's flat area times the thickness (K = 0.5:
400 and 100.53 mm³, measured within 0.02); a slanted flat edge folds to
its exact helix within 1e-7 mm (measured 1.9e-8) on both faces; lines
along and across the bend keep their line and arc. Engine:
fold_through_cut_outs now expects a round hole across a fold to fold, and
to unfold to the same round hole; the per-bend machining guard (#296)
sews a bend that carries a round cut-out, so a hole beside it cuts and a
hole in the bend is still refused.
Co-authored-by: Claude Opus 5.5 <[email protected]>
Co-authored-by: bherbruck <[email protected]>
