Shape Computation Lab

Find Indefinite Polylines in a 5-star Polygon

Tzu-Chieh Kurt Hong

02/10/2019

This video showcases how an initial model of a regular 5-star polygon can be queried and restructured in a series of different polylines and arrangements of three lines under similarity transformations. The video starts with the queries of three-line shapes whose boundaries and intersections can also be found in the underlying structure of the 5-star polygon. The first shape consists of a single three-line polyline; the second consists of an arrangement of two polylines, a two-line polyline and a single one; and the third consists of three floating lines. All queries yield ten results to match the intuition of finding ten asymmetric shapes within the structure of the five-fold dihedral symmetry of the 5-star polygon of order 10. The next series of queries repeat the types of shapes discussed above with the extra provision that one or more of their boundaries are not registered in the database of the CAD system. The final example shows the search of a shape consisting of three lines of various lengths irrelevant to the lengths of the edges of the underlying star-polygon in such a spatial arrangement that no line touches one another. This search identifies ten similar copies in the model under similarity transformations specified by the user.

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