# Sections and Shadows of Four-Dimensional Objects

@article{Zamboj2018SectionsAS, title={Sections and Shadows of Four-Dimensional Objects}, author={Michal Zamboj}, journal={Nexus Network Journal}, year={2018}, volume={20}, pages={475-487} }

Methods of constructions of sections and shadows of four-dimensional objects are explained. We visualize images of an object and its section or shadow at the same time in a double orthogonal projection on two perpendicular three-dimensional spaces. Our techniques are similar to the methods used in Monge’s projection of the three-dimensional space. Constructions are created in the interactive 3D modeling software GeoGebra 5, in which the user can freely move some input elements. We focus on a…

## 5 Citations

### Quadric Sections of Four-Dimensional Cones

- MathematicsAdvances in Intelligent Systems and Computing
- 2018

Graphic constructions of real three-dimensional quadrics as cuts of four-dimensional cones with three-dimensional spaces are described. All the constructions are presented on interactive models in…

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

- Art, Mathematics
- 2020

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…

### Synthetic construction of the Hopf fibration in a double orthogonal projection of 4-space

- ArtJ. Comput. Des. Eng.
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The recently introduced method of visualization of 4-space by its double orthogonal projection onto two mutually perpendicular 3-spaces is applied to investigate the Hopf fibration as a four-dimensional relation without analogy in lower dimensions.

### M ay 2 02 1 Synthetic construction of the Hopf fibration in a double orthogonal projection of 4-space

- Art
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The Hopf fibration mapping circles on a 3-sphere to points on a 2-sphere is well known to topologists. While the 2-sphere is embedded in 3-space, 4-dimensional Euclidean space is needed to visualize…

### Enabling four-dimensional conformal hybrid meshing with cubic pyramids

- Computer ScienceNumer. Algorithms
- 2022

A novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids and a new class of fully symmetric quadrature rules with positive weights are generated for the cubic pyramid.

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