Object3D Arc Quad

Generates a curved-edge quadrilateral mesh from four corner vertices, bending two opposite edges (v0→v1 and v2→v3) into arcs of adjustable radius, dihedral angle, and triangle count. Produces the triangulated mesh, the index list, and a wireframe of its silhouette edges.

The module takes a flat quad (four 3D vertices) and replaces its two opposite edges by circular arcs, then re-triangulates the resulting shape into a clean mesh. Each arc is independently:

• convex when its radius factor is positive (arc bulges out, away from the quad centre),
• concave when the radius factor is negative (arc bows in, inside the quad),

with an optional rotation around the chord (the dihedral angle) that lets the arc tilt out of the quad's plane — useful for line-array housings, curved cabinet faces, or any developable surface that needs to be visualised in 3D.

The module also produces a wireframe output that keeps only the silhouette edges (boundary edges + edges where adjacent faces are not coplanar), so the curved arcs can be drawn over the filled mesh without showing every internal triangulation line.

Note — vertex / radius arrays are read pair-wise (one value per arc). The first index drives the v0→v1 arc, the second the v2→v3 arc. Inputs shorter than 2 (for the per-arc arrays) or 12 (for vertices, i.e. 4 × XYZ) are silently ignored.

Settings

vertices

The four corners of the quad, flat-packed as X₀, Y₀, Z₀, X₁, Y₁, Z₁, X₂, Y₂, Z₂, X₃, Y₃, Z₃. The two arcs are built on edges v0→v1 and v2→v3. Range -1…+1. The array must be at least 12 long.

factor

Two-value array. Per-arc radius factor (related to the arc's sagitta vs. chord length):

• > 0 — convex arc bulging outwards.
• < 0 — concave arc bowing inwards. The sign is read, then the absolute value is used as the radius factor.
• = 0 — the corresponding arc is disabled and the edge stays straight.

Range 0 – 2. A value of 1 gives a half-circle on the chord; values between 0 and 1 give shallow arcs; values above 1 push the arc closer to a deep bow.

dihedral angle

Two-value array, in degrees, range −360 – +360. Per-arc rotation of the arc plane around the chord. 0 keeps the arc in the plane of the quad; non-zero values tilt the arc out of the quad's plane, useful for curved enclosures where the arc isn't coplanar with the base quad.

When the matching factor is negative (concave arc), the dihedral angle is forced to 0 — concave arcs always stay in-plane.

num of triangles

Two-value integer array, range 1 – 1000 (no hard limit). Per-arc number of triangle segments used to discretise the arc. Higher values give smoother arcs at the cost of more triangles. The convex arc fan around the chord midpoint contains num of triangles triangles; the concave triangulation adds num of triangles − 1 extra vertices along the arc.

invert

When ON, all faces are inverted (winding reversed). The module already auto-detects when the generated faces are oriented against the source quad and re-inverts them — use this switch to flip the final orientation on top of that.

vertices

Flat array of mesh vertices, X, Y, Z, X, Y, Z, …. To be wired into object3d-primitive-triangles with indices.

indices

Flat triangle index list (0-based, three indices per triangle, no separator). Quads in the internal mesh are fan-triangulated; n-gons (≥ 5 vertices) are fan-triangulated from the first vertex.

lines

Flat array of point pairs X₀, Y₀, Z₀, X₁, Y₁, Z₁, … describing the silhouette wireframe: every boundary edge (edges adjacent to a single face) plus every edge where the two adjacent faces are not coplanar (normal · normal < 0.999). Edges sitting inside flat regions of the mesh are dropped. Wire into object3d-primitive-lines for diagnostic display.

See also

• Adamson
• Panel Patching Matrix
• Distance Attenuation
• Device ASIO Driver
• Object3D Arc Quad
• Object3D Ray Tracing And Directivity
• Math Delay Amplitude Calculation