Shape Computation Lab

Find Polylines Under Affinities

Tzu-Chieh Kurt Hong


This series of vignettes showcases the expressive power of Shape Machine to find arrangements of polygons, polylines and their combinations under affine transformations. The first vignette shows how a search for a spatial relation between two root-2 isosceles triangles in two squares yields two spatial relations between two affine triangles in two parallelograms. The second vignette shows how a second spatial relation between two instances of two collinear root-2 triangles with one coincident vertex can produce four matchings split in two families of two. The next four vignettes showcase searches for open polylines resembling letters of the alphabet like "R", "M", "A" and a deformed "U", including polylines whose endpoints are not registered in the database of the CAD system. The penultimate two vignettes are poignant because they showcase how expressive Shape Machine can be and how it can help designers find parts that otherwise might be left unnoticed: these two vignettes take on the spatial relations between two open L-shape polylines one against the other. The resulting eight matches are hard to spot even for an experienced designer! The last vignette showcases the power of Shape Machine in bookkeeping giving only the unique number of matches counting symmetry.