Higher-Dimensional Spaces using Hyperbolic Geometry скачать в хорошем качестве

Higher-Dimensional Spaces using Hyperbolic Geometry

A novel method of interactive visualization of higher-dimensional grids, based on hyperbolic geometry. In our approach, visualized objects are adjacent on the screen if and only if they are in adjacent cells of the grid. Previous attempts do not show the whole higher-dimensional space at once, put close objects in distant parts of the screen, or map multiple locations to the same point on the screen; our solution lacks these disadvantages, making it applicable in data visualization, user interfaces, and game design. Four dimensions: 0:00 a 4x4x4x4 cage with a golden point in the center 0:15 one-dimensional tunnel (bright red) 0:35 the 1-skeleton of the tessellation of ℤ⁴ with cubes of edge 2 1:12 two-dimensional tunnel 1:30 two hyperplanes in distance 2 (blue and green), i.e., three-dimensional tunnel 2:00 two hyperplanes in distance 3 (cyan and green) 2:20 two orthogonal hyperplanes (red and yellow) 2:45 four quarterspaces (red, yellow, cyan, blue) 3:00 diagonal tunnel in all coordinates except one (golden and silver) 3:45 diagonal tunnel (purple and gray) Six dimensions: 4:10 a 4x4x4x4x4x4 cage with a golden point in the center 4:30 one-dimensional tunnel (bright red) 5:00 the 1-skeleton of the tessellation of ℤ⁶ with cubes of edge 2 5:20 two-dimensional tunnel 5:40 four-dimensional tunnel 6:00 two hyperplanes in distance 3 (cyan and green) 6:20 two orthogonal hyperplanes (red and yellow) 6:45 four quarterspaces (red, yellow, cyan, blue) 7:05 diagonal tunnel in all coordinates except one (golden and silver) 7:30 diagonal tunnel (purple and gray) other: 7:50 time-sliced visualization of the visualization of ℤ⁴ using {3,4,4} Paper: https://arxiv.org/abs/2110.00327