Meshing with Kagome Singularities: Topology adjustment for representing weaves with double curvature

In this paper, we present a planar mesh topology adjustment scheme for the automated production of principled Kagome weave patterns.Kagome is a triaxial weave system based on a hexagonal lattice. Double curvature is induced by replacing hexagonal cells with alternative polygons. These singularities are digitally represented by constructing a tri-mesh with appropriate valence.
However, the automated adjustment of meshes remains an open challenge. The topology adjustment scheme presented here employs edge flipping to modify a regular valence 6 mesh. A key insight is that embedding a local valence modification necessitates a cascade of edge flips that extend out to the mesh boundary.
We demonstrate the application of this principle to represent a range of singularity valences and verify these individually with simulation. A series of case studies demonstrate how: 1) the scheme can accommodate multiple singularities within a mesh; 2) the scheme can be integrated into a digital design pipeline that includes fabrication documentation production for producing physically woven Kagome approximations using only straight strips of material.
Within the paper, we contextualise this work with reference to the state-of-the-art, articulate its contribution, discuss the limits of the scheme and reflect upon its broader relevance to architectural design and construction.