Abstract
Checkerboard quadrilateral mosaics were introduced by Robert Bosch. They are formed from a black and white
checkerboard. A quadrilateral is positioned in each square; white quadrilaterals in black squares, and black quadrilaterals
in white squares. Each quadrilateral has a vertex on each of the edges of the square. Quadrilaterals in
neighboring squares share vertices. In this highly constrained environment, it is possible to create figurative mosaics
that resemble user supplied images. Designing these mosaics requires sophisticated algorithmic design because the
objective function for the tiling system is non-convex, non-linear, and contains a large number of variables. Downsampling
is used to resize a target picture to a desired mosaic size. The downsampled image is split into 5 5
grids. To calculate the coordinates of each of the vertices in the 55 grids, sequential least squares programming is
implemented with the appropriate constraints. Finally, each of the 55 grids are stitched together to create the final
mosaic.
