Interactive 4 D Visualization of Stereographic Images From the Double Orthogonal Projection ICGG2020

My contribution at International Conference on Geometry and Graphics 2020 The double orthogonal projection of the 4space onto two mutually perpendicular 3spaces is a method of visualization of fourdimensional objects in a threedimensional space. We present an interactive animation of the stereographic projection of a hyperspherical hexahedron on a 3sphere embedded in the 4space. Described are synthetic constructions of stereographic images of a point, hyperspherical tetrahedron, and 2sphere on a 3sphere from their double orthogonal projections. Consequently, the doubleorthogonal projection of a freehand curve on a 3sphere is created inversely from its stereographic image. Furthermore, we show an application to a synthetic construction of a spherical inversion and visualizations of double orthogonal projections and stereographic images of Hopf tori on a 3sphere generated from Clelia curves on a 2sphere. paper ar