Visualization of 4D Hyperobjects by Hypersurface Pseudo Reflection

Abstract

An original method for visualizing 4D hyperobjects is presented. The color of a point on the 2D projection of a 4D hyperobject is determined by the geometry information integrated along the intersection between hypersurfaces of the hyperobject and a 'planar ray' from the observer's eye, a set of these planar rays covers the whole hypersurface area in 4D space. The geometry information reads out with light, which is pseudoreflected by not the hypersurface itself but the displacement of its normal to allow the observer to be aware of hypersurface boundaries and curving on the hyperobject. This method can visualize both hyperobjects made of flat hypersurfaces like 4D polytopes and ones made of curved hypersurface like 4D hypersphere.