Shape Computation Lab

Find Polygons Under Affinities

Tzu-Chieh Kurt Hong


This example shows how Shape Machine is able to make queries of shapes under affine transformations. While this ability is a straightforward extension of the matching algorithms of the Shape Machine to include affinity transformations, the results are often less intuitive for the novice designer because under these transformations the shapes that are found often look and feel different from the ones used for the query. The first series of vignettes illustrate the point clearly: A search for a root 2 isosceles triangle yields four right angle triangles while a search of a square yields a rectangle and a rhombus. The third vignette shows how a search of a pentagonal envelope shape produces two sets of pentagonal shapes of different proportions. The fourth vignette shows how a search of hexagon produces two enantiomorphic versions of elongated hexagons. The last vignette shows the power of the Shape Machine to find affine copies that are harder to spot by the novice designer.