4DPolytopes Documentation
This plugin is a collection of 10 Parametric Objects and an Geometry Generator.
All objects are inherently 4-dimentional. The extra dimension is called W.
There are 2 ways to view a 4D object on a 3D world:
Projection - Projects the 4D object on the 3D plane like we can project a 3D object on a 2D plane using a spotlight. This method has the advantage of exposing all points and edges at the same time but creates perspective distortions making difficult to conceive the real object.
Slice - Creates a 3D section of the 4D object as it passes through the 3D plane. This method creates accurate volume representations with no intersecting surfaces of convex objects but the drawback is that any polygon/edge/point that has a 4th coordinate less or greater than 0 is completely invisible. Seeing the whole object with this method is impossible. To understand the full object one must move it gradually on the W axis until it passes completely through the 3D space.
The Extrude 4D works like the Poke geometry Modifier by connecting all points of a polygon to a single offset point away from it on the W axis.
Future plans:
Select Axis Facets option for the Hypercube. To automatically color opposite set of cubes for better visualization.
Better icons for 4D toruses.
A second Klein Bottle that is closer to the one depicted on the internet.
Notice
The Slice mode requires to install the Scipy and Numpy Python libraries to your C4D Pytthon311 folder.
If those are not found the algorithm will fallback to a custom-made Hull implementation that is buggy and provides poor results. I've included a TXT file inside the plugin folder with links to the appropriate .whl files and how to install them.
The plugin produces an extensive registration output on the Python Console. If the Scipy and Numpy Python libraries are found you will see a check-mark on every object.
Do you want to contribute to the development of this plugin? If yes, contact me.