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arXiv · 2007.13470

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

Michal Zamboj
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Abstract

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.

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Michal Zamboj. 2020-07-07. Interactive 4-D Visualization of Stereographic Images From the Double Orthogonal Projection. https://doi.org/10.1007/978-3-030-63403-2_11

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