Shape Computation Lab

Find Indefinite Polylines Under Affinities

Tzu-Chieh Kurt Hong

02/10/2019

This series of vignettes showcases the expressive power of Shape Machine to find matches of arrangements of indefinite polylines and their combinations under affine transformations. The first vignette shows that the search of an equilateral triangle under affine transformations produces four matches characterized by triangles with diverse proportions. The second vignette shows that the search of an open three-line polyline - or a triangle that has one edge incomplete - produces twenty-four matches because of the symmetry of the polyline of order 1 vs. the symmetry of the four underlying triangles each of order 6. The third vignette shows that the search of a shape consisting of an open two-line polyline or an L-shape and a floating line produces again 24 matches because of the symmetry of the arrangement of order 1 vs. the symmetry of order 6 of each the four underlying triangles. The fourth vignette shows that the search of a shape consisting of three lines exhibiting rotational symmetry of order 3 produces 8 matches because of the symmetry of the arrangement of order 3 vs. the symmetry of order 6 of each the four underlying triangles. Finally, the fifth vignette shows that the search of a shape consisting of three lines exhibiting three-fold dihedral symmetry produces 4 matches because of the symmetry of the arrangement of order 6 vs. the symmetry of order 6 of each the four underlying triangles.

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