Geodesic Structures

  • November 30, 2023

Construction of 3D surfaces using grids

In mathematics, surface models are a fascinating way to visualize and understand complex geometric shapes. Here we look at the surface models of sphere, torus and torus node.

Sphere

The sphere, as the simplest three-dimensional object, can be viewed as a closed surface that is equidistant from all points in a space to a fixed point at its center. Its surface is homogeneous and has no corners or edges.

Torus

The torus, on the other hand, is an interesting geometry that is created when a circle rotates around an axis that is not in its plane. The resulting object resembles a tire or donut. The surface of a torus consists of two parts - the outer cylindrical surface and the inner tube surface.

Torus Knot

Torus nodes are a specific class of nodes that run on the surface of a torus. They are created by a complex interweaving of lines on the surface of the torus and create aesthetically pleasing patterns. These nodes are often explored in mathematics, physics, and computer graphics, and provide a rich playing field for exploring topology and geometry.
The surface models of sphere, torus and torus nodes are not only mathematical concepts, but also aesthetically pleasing representations that expand our understanding of the diversity and beauty of geometric shapes.