3867

Aaron Kreiner

Bridges

2020

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.