Shape Computation Lab

Find Arrangements of Polygons in Squares

Tzu-Chieh Kurt Hong


This example shows how Shape Machine is able to access arrangements of subshapes within a shape even though these parts are not registered in the database of a CAD system (in this example: Rhinoceros 5.0). This video showcases how an initial model consisting of two squares drawn in two alternative ways can be queried and restructured in a number of different arrangements of closed polygons under isometric transformations. The first example shows how a pictorial query of a spatial relation between two root2 triangles sharing a vertex and have their respective hypotenuses embedded in a single line yields four distinct instances in the initial shape. The second example how a pictorial query of two root2 triangles having their hypotenuses parallel to each other and reflected along the leading diagonal of the underlying square yields two instances in the shape. Note that the shape machine can calculate the symmetries of the matches and give the correct number of non-equivalent instances. The video ends up with a query of spatial relation of three root2 triangles.