Topology finding tackles topological exploration of shapes and patterns of shell-like structures, by analogy and in complement to form finding, thanks to a specific data structure decoupling topological and geometrical design.

This research focuses on the singularities in force patterns, like thrust networks and load paths, and materialized patterns like voussoir tessellation for masonry vaults, beam grids for elastic gridshells, corrugation reinforcements for shells or strips for membranes.

A feature-based approach provides an intuitive manner for designers to generate patterns with singularities allowing them to respect features like a surface boundaries, based on a topological skeleton, as well as point and curve features, which can heuristically stem from statics considerations.

A rule-based approach provides a strip grammar for comprehensive exploration of the design space, providing structuredness to this topological space using a rule-based distance, allowing adjacent designs to be generated, evaluated and combined.

Specific topological properties, like vertex-, face- or strip-two-colorability can be enforced through projection to two-colorable sub-spaces using the grammar rules.

Topology finding empowers the designer by enriching workflows including downstream geometrical exploration, various analyses and performance assessment.