Purnendu, ATLAS Institute, University of Colorado Boulder The mathematical secrets of Computational Origami Origami is the Japanese name for the centuries-old art of folding paper into representations of birds, insects, animals, plants, human figures, inanimate objects, and abstract shapes. In the purest form of origami, the figure is folded from a single uncut square of paper. Throughout the history of origami, most origami design has been carried out by a combination of trial and error and/or heuristic techniques based on the folder’s intuition. However, in the past 20-25 years, things have changed dramatically and the field of origami design has become more and more algorithmic based on mathematical ideas from geometry. The principles of geometry were first applied to origami around the mid-twentieth century when Japanese physicists and mathematicians began to formulate axioms that explain how folding creates three-dimensional objects from flat material. In this work, we will go through the mathematical principles which underlie the art of paper folding and present a complete algorithm for the design of an arbitrary origami figure. The algorithm is based on a set of mathematical conditions on the crease pattern which can be mapped to a tree graph. In this fashion, the... https://calendar.colorado.edu/event/stats_optimization_and_machine_learn...