论文标题
互动4-D可视化的立体图像来自双正交投影的立体图像
Interactive 4-D Visualization of Stereographic Images From the Double Orthogonal Projection
论文作者
论文摘要
四个空间对两个相互垂直3空间的双重正交投影是在三维空间中可视化四维对象的一种方法。我们提出了一个互动动画，该动画是在4个空间中嵌入的3个球体上的超球形六角体的立体投影。所描述的是从双方正交投影中的三个球体上的点，超球形四面体的立体图像的合成结构。因此，徒手曲线在3速曲线上的双交投影是由其立体图像成反比的。此外，我们展示了一个应用的应用，并在2个球面上从Clelia曲线产生的3杆透中，对Hopf Tori的双向音调和立体图像的可视化构造和可视化。
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.
