Panelizer — the curve has a price

Pick a surface and set the tolerances.

solving…

Developable strips — unrolled flat

Each strip of quads is unrolled by successive rigid unfolding of the quads' best-fit planes (a stated teaching approximation: a warped quad contributes its own warp). Two separated numbers per strip: closing error — how far the far edge lands from where the geometry says it should — and the per-quad warp total. On a genuinely developable surface (the cone) both are zero.

Surface

Import OBJ / .3dm (quad mesh)

Tolerances — visible and arguable

Planarity ratio

Cold-bend limit (warp, mm)

A teaching knob, never a warranty — seeded from published cold-bent-glass ranges (Datsiou & Overend; Eversmann et al. IASS 2016), deliberately widened and UNVERIFIED: glass and metal makers set their own limits by product, thickness and warranty.

Mould tolerance (mm)

Mirrored panel = same mould

Off by default (conservative): a directional coating, a drainage slope or an asymmetric edge detail makes the mirrored twin a different part.

Rationalize as — two different buildings

Force it flat planarizes the quads and counts panel types by rigid congruence. It is the right question for a surface that wants to be flat — and the wrong one for a dome, which it prices at hundreds of unique panels because it refuses to let any of them curve.

The gate — predict, then reveal

How many genuinely different panels?

Locked until you commit a guess — that's the whole game. The surface has — panels; how many moulds would it really take?

View

Round history

No rounds yet. Guessing badly and remembering is the point.

Sources & method — what is exact, what is not

Exact: planarity is the distance between a quad's diagonals over the mean diagonal — the convention in Pottmann, Asperl, Hofer & Kilian, Architectural Geometry (2007) and Glymph et al., Automation in Construction 13:2 (2004). Curvature is the discrete angle defect (Meyer et al. 2003). Congruence is a closed-form rigid best fit (Kabsch 1976 / Umeyama 1991, computed as Horn 1987).

First-order: the planarize solve is Relax's weighted-projection kernel (Kangaroo2's move form) with a leash — not the second-order PQ/conical optimizers of Liu et al. 2006 or Zadravec et al. 2010. It converges where the panel net's alignment admits a nearby planar-quad mesh and stalls honestly where it doesn't (the ruling-aligned hypar and the twisted tower stall; the residual distribution is always reported). The conical condition — what makes a planar mesh offsetable into a buildable multi-layer structure (Pottmann et al. 2007) — is measured as a diagnostic, never solved.

Upper bound: the unique-part count is a greedy, order-fixed, fixed-surface clustering. The real problem moves the surface and the moulds together: Eigensatz, Kilian, Schiftner, Mitra, Pottmann & Pauly, "Paneling architectural freeform surfaces", ACM TOG 29:4 (2010). No cost model: a mould count is a proxy for money, not money.

Letting it curve: the second mode drops each panel onto the cheapest rung of the panel-type ladder that holds it — flat, one radius, two equal radii, two different radii, bespoke — which is the cost hierarchy Eigensatz et al. optimize over. What is exact here is the sharing rule: two moulds differ over a panel of half-diagonal a by |Δκ|·a²/2 (the sagitta identity), so one tolerance decides FLAT, SPHERICAL, SINGLE-CURVED and mould reuse alike, and none of it is hidden. What is estimated is the curvature: a locally-weighted quadric fit (Cazals & Pouget, CAGD 22:2, 2005) through each panel's vertex neighbourhood, accurate to the mesh you gave it and not to a design surface you did not. Panels the quadric cannot hold are reported FREEFORM rather than given an invented radius, and boundary panels are fitted one-sided — the ruled cone's top ring reads DOUBLE-CURVED for that reason while every interior ring reads SINGLE-CURVED. Hard edges are respected: a neighbour past a 40° crease is dropped from the fit, so a twisted tower's plan corners do not poison the panels beside them.

Still not done here: we read the surface as drawn and count what it already needs. We do not move the surface and choose the panel set jointly, which is the actual contribution of Eigensatz et al.; both counts on this page are upper bounds for that reason. A mould schedule is not a shop drawing — no thickness, no springback, no trim allowance, no tolerance stack-up.

The pro tools: EvoluteTools (production paneling, the commercial descendant of this research), Kangaroo in Grasshopper (the real projection solvers), RhinoVAULT (funicular shells). Panel warranties, mould costs and node geometry come from the fabricator, not from software.