4-D Visualization of Minkowski Quaternionic Point Set Operations

TL;DR

This paper explores 4D visualization of Minkowski quaternionic point set operations, demonstrating how to generate and visualize complex sets like Clifford torus and 3-sphere using projections.

Contribution

It specifies the Minkowski product as a quaternionic product and visualizes selected point sets in 4D to 3D projections, highlighting geometric modeling techniques.

Findings

Generated sets containing circles, lines, or both.

Visualized complex 4D point sets using projections.

Demonstrated the generation of Clifford torus and 3-sphere.

Abstract

The contribution emphasizes the geometric modeling point of view on Minkowski point set operations. In this paper, the Minkowski product is specified as the quaternionic product. Selected point sets are visualized using double orthogonal projection and perspective projection from four-dimensional to three-dimensional space. In particular, we demonstrate the generation of sets containing circles (Clifford torus, 3-sphere), lines (quadratic cone), or both.