Shape Computation Lab

Find Indefinite Arcs in a Trefoil

Tzu-Chieh Kurt Hong


This example shows how Shape Machine is able to access any part of a arc of a shape even though the queried parts of the arc are not registered in the database of the CAD system (in this example: Rhinoceros 5.0) The video consists of a series of queries of three-arc shapes whose endpoints are progressively not registered in the underlying structure of the underlying 3-lens shape. The first shape consists of a single connected three-arc shape; the second consists of an arrangement of a joint two-arc and a floating one; and the third and fourth consist of three floating arcs. The first shape has one endpoint not registered in the database; the second has two endpoints not registered; the third has three endpoints and the fourth all six not registered. All queries yield six results to match the intuition of finding six asymmetric shapes within the structure of the three-fold dihedral symmetry of the 3-lens polygon of order 6.