And he built a crooked camera: a mobile visualization tool to view four-dimensional geometric objects

Abstract

The limitations of human perception make it impossible to grasp four spatial dimensions simultaneously. Visualization techniques of four-dimensional (4D) geometrical shapes rely on visualizing limited projections of the true shape into lower dimensions, often hindering the viewer's ability to grasp the complete structure, or to access its spatial structure with a natural 3D perspective. We propose a mobile visualization technique that enables viewers to better understand the geometry of 4D shapes, providing spatial freedom and leveraging the viewer's natural knowledge and experience of exploring 3D geometric shapes. Our prototype renders 3D intersections of the 4D object, while allowing the user continuous control of varying values of the fourth dimension, enabling the user to interactively browse and explore a 4D shape using a simple camera-lens-style physical zoom metaphor.