From Euclidean to Topological: Visual Exploration of Transformations Types in Shape-Changing Interfaces

This pictorial explores the challenge of distinguishing between shape-changing and actuated interfaces by applying a foundational geometry framework from mathematics to categorise different types of transformations. The framework introduces six geometric transformation types: Euclidean transformations, similarity transformations, affine transformations, projective transformations, topological transformations, and non-topological transformations. Through visual analysis, the pictorial contributes a new vocabulary for de-scribing the transformations of shape-changing interfaces. It offers reflections on which transformations can be considered shape changing, as well as how features of the physical design might impact the perceived shape change.