Shape Computation Lab

Find Arcs in a Trefoil

Tzu-Chieh Kurt Hong


This video showcases how an initial model of a regular trefoil-like shape can be queried in terms of arcs and arrangements of arcs under similarity transformations. The video starts with the query of a lens or vesica piscis shape, a classic figure in Euclid - and Carlo Scarpa's work for that matter- and continues with a query for concatenated pairs of lens shapes, producing in both occasions three matches under similarity transformations. Different queries for open non symmetric polyarcs and arrangements of polyarcs whose endpoints are found in the database of the six points of the original CAD model produce six instances for each query respectively because of the dihedral symmetry of order six of the underlying trefoil.