Long-span stadium roofs often weave two families of arches between a ground ring and a raised inner opening, the oculus. Each arch here runs from a point on the ground, over the rim and down to the oculus, a few places further round; the other family turns the other way. It is the guilloché rose lifted into three dimensions.

A white lattice bowl of interlacing arches around a central oculus

Reference: choose Examples  Woven-bowl stadium roof on the canvas toolbar to load the finished definition.

Build it

  1. Place nine sliders: Radius: 50 (25 – 90), Rim scale: 0.7 (0.4 – 0.95) and Oculus scale: 0.35 (0.1 – 0.6) with Decimals 2, Rim height: 18 (5 – 40), Oculus height: 14 (2 – 40); Arches: 36 (12 – 72), Rim turn: 4 (0 – 12) and Oculus turn: 8 (0 – 24) with Decimals 0; and Member radius: 0.5 (0.1 – 1.5) with Decimals 2.

  2. Place two Multiplication (Maths) components, Radius × Rim scale and Radius × Oculus scale. Place three Circle (Curve) components: Ground ring (Radius), Rim (rim radius, Rim height → Z) and Oculus (oculus radius, Oculus height → Z).

  3. Place three Divide Curve (Curve) components with Arches → N.

  4. Place two Multiplication components with B -1 after the two turn sliders, and four Shift List (Sets) components: the rim points shifted by ± Rim turn and the oculus points by ± Oculus turn.

  5. Place two Arc 3Pt (Curve) components: ground points → A, rim points shifted + → B, oculus points shifted + → C; and the same with the − lists.

  6. Place two Pipe (Surface) components for the arches with Member radius → R. Add a Multiplication (Member radius × 2) and three more Pipe components for the three rings.

  7. Place a Loft (Surface), Roof, and wire Rim and then Oculus into its C (hold Shift for the second): a translucent roof between them.

  8. Turn Preview off on the Circles, Divide Curves, Shift Lists and Arcs.

The stadium roof definition on the canvas
Figure 1. The finished definition
The red preview of the stadium roof
Figure 2. The preview in FreeCAD’s 3D view

What is happening

Each arch is the circle through three points: on the ground, on the rim Rim turn places round, and on the oculus Oculus turn places round. Because the turns are counted in places on rings divided equally, every arch of a family is the same arch rotated, and the two families cross symmetrically. The geometry tests check that every arch starts on the ground ring and ends on the oculus at its height.

The roof updates in under a second, most of it drawing 75 pipes.

Things to try

  • Set both turns to 0: the arches run straight up and over, like the ribs of an umbrella.

  • Raise Oculus height above Rim height (30) for a domed crown.

  • Set Arches to 72 for a fine weave, and lower Member radius.

  • Set Oculus turn to twice Rim turn and then to the same value, and compare the lattice.