SPIRA — Deformation Geometry Explorer

α(z) = (z / h) · α_max

α_max0°

α at h/20°

height (h)–

base area–

deformed volume–

prism volume–

volumes match — Cavalieri holds

max panel warp–

panel warp (off-planar)

0 25mm 50mm+

View

Exercises

Operation

Cross-section (profile in plane B)

width (x)2.0 m

depth (z)2.0 m

Units

Projection

Deformation parameters

α_max (twist of top plane T)120°

Case studies (real 90°-twist buildings)

Height, floor count, and total twist are sourced figures; footprint size is an illustrative estimate.

Compound — apply a second operation after this one

floors8

floor-to-floor height3.5 m

resolution (slices)48

Overlays

Axis A

Base plane B

Ruling lines (edge curves)

Slice rings (resolution)

Floor lines (per floor)

Wireframe

Point labels (a, b, c → a₁, b₁, c₁)

Surface normals (debug)

Panel flatness (warp)

Colorblind-safe palette

Compare

What does this do?

Captures the current shape as a translucent reference ghost, so you can change any parameter — even switch Operation entirely — and see exactly how the new shape differs, overlaid in the same view rather than side by side. The snapshot lives only in this session; it isn't saved, shared, or affected by Reset Values.

Show comparison

Export

What does this do?

Captures the 3D view exactly as shown — current camera angle, Perspective/Orthographic projection, the solid, and every 3D overlay (axis, rulings, point labels, panel colors). The sidebar HUD numbers and the panel-warp legend are separate page elements, not part of the 3D view, so they aren't included.

What does this do?

Copies a URL that reproduces this exact configuration — mode, preset, every deformation parameter, footprint, floors, units, projection, and overlay settings — for anyone who opens it. Everything lives in the link itself (nothing sent to a server), so it works from any copy of this page.

loft profiles (for JSON export)20

What does this do?

For rebuilding the current form natively in Revit (via the Dynamo script below). Exports evenly-spaced cross-section profiles up the height — more profiles track a curved operation (Twist/Taper/Bend) more closely, since Revit's own loft fits a true curved surface through them rather than approximating with flat facets. Deliberately a separate count from "resolution (slices)" above: a loft only needs enough profiles for Revit's own curve fit to converge, not enough triangles to look smooth on screen — usually far fewer.

What does this do?

Paste into a Python Script node (File Path node → its IN[0]) in a blank Dynamo graph — Dynamo ships with Revit, nothing extra to install. Run it with a Conceptual Mass family document active to build a real, loadable Mass Form; run it with a project active for a one-off Mass-category DirectShape instead. Same script either way.

Reference

Twist keeps a base plane B and a vertical axis A fixed, and rotates every horizontal slice at height z by α(z) = (z/h)·α_max. Straight vertical edges become helices; a flat wall through the axis becomes a helicoid. Try α_max = 90° or 180° to see a quarter or half turn, or push past 360° for multiple full turns.