Zamboj, Michal Interactive 4-d visualization of stereographic images from the double orthogonal projection. (English) Zbl 1464.68422 Cheng, Liang-Yee (ed.), ICGG 2020 – Proceedings of the 19th international conference on geometry and graphics, São Paulo, Brazil, January 18–22, 2021. Cham: Springer. Adv. Intell. Syst. Comput. 1296, 115-126 (2021). Summary: The double orthogonal projection of the 4-space onto two mutually perpendicular 3-spaces is a method of visualization of four-dimensional objects in a three-dimensional space. We present an interactive animation of the stereographic projection of a hyperspherical hexahedron on a 3-sphere embedded in the 4-space. Described are synthetic constructions of stereographic images of a point, hyperspherical tetrahedron, and 2-sphere on a 3-sphere from their double orthogonal projections. Consequently, the double-orthogonal projection of a freehand curve on a 3-sphere 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 3-sphere generated from Clelia curves on a 2-sphere.For the entire collection see [Zbl 1458.00031]. MSC: 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 51N05 Descriptive geometry Keywords:four-dimensional visualization; orthogonal projection; stereographic projection; Hopf fibration; Clelia curve; spherical inversion; descriptive geometry PDFBibTeX XMLCite \textit{M. Zamboj}, Adv. Intell. Syst. Comput. 1296, 115--126 (2021; Zbl 1464.68422) Full Text: DOI arXiv