Two of the GEN's generators — Wall panel and Hypar — make architectural shapes that look impossibly curved but are ruled surfaces: every point on them lies on a straight line. That is exactly what a straight hot wire sweeps, so a 4-wire cutter reproduces them perfectly in one clean pass.
What is a ruled surface?
Take two edge curves and connect every point on one to the matching point on the other with a straight line. The family of lines sweeps a ruled surface. Because the connecting elements are straight, a taut hot wire — which is always straight between its two ends — can lie along each line in turn and cut the whole surface. A wing is the simplest example (root section → tip section); these two generators push the same idea into architecture.
Wall panels
The Wall panel generator gives the panel a wavy front face that morphs from one sine wave on the left edge to a different one on the right. Because the surface between them is ruled, it cuts in a single pass; because the waves are periodic, the panels tile seamlessly side by side and (with whole-number wave counts) stack cleanly too.
- Left / right amplitude — how deep the ripple is at each edge.
- Left / right waves — how many full waves over the height. Different counts make the surface flow and braid across the panel; equal counts give a steady corrugation.
- Phase — slides the right wave up/down so crests meet troughs for woven effects.
Make: feature walls and reception backdrops, acoustic/ceiling baffles, headboards, retail and exhibition stands, signage backers, light diffusers. Cut in foam to use directly (paint/skin it) or as a mould to cast plaster, GRG, GRP or concrete tiles.
Hyperbolic paraboloids (hypars)
A hypar is the classic architectural saddle — up at two opposite corners, down at the other two. Its surface follows z = x²/a² − y²/b², equivalently the bilinear blend of its four corner heights. Astonishingly, although it curves in two directions, it is doubly ruled — you can lay straight lines across it two different ways — so a hot wire cuts it flawlessly. Spanish-Mexican engineer Félix Candela built dozens of breathtaking thin-shell concrete roofs from hypars in the 1950s precisely because the curved formwork could be built from straight timber.
- Width / length — the footprint of the saddle.
- Rise — how far the high corners lift above the low ones (the saddle depth).
- Base thickness — solid foam left under the surface so the part stays rigid.
Make: positive moulds for thin-shell concrete roofs and canopies, plaster or GRG shells, composite (GRP/carbon) lay-up tools, architectural models, fountains and sculpture. Foam takes a release agent and a few coats of filler/epoxy to become a reusable casting tool.
Tips
- Cut big, then cast. These shine as moulds. Seal the foam (filler primer or epoxy), wax/PVA release, then lay up your shell on top.
- Mind the kerf + foam. Denser XPS holds a crisp ruled surface; EPS is cheaper for big one-off moulds.
- Tiling: for panels, keep wave counts whole and reuse the same width so copies line up. Share the design and re-cut it any size from the OBJECT bar.
- Scale freely — a ruled surface stays ruled at any size, so rescale in the OBJECT bar without losing cuttability.
Related
See Morphing two profiles for the 4-wire mechanism behind both, and the wing generator for the other ruled-surface tool.