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Tube Plots, Knots, and Braids

Mitchell A. Berger
Organization: Mathematics, UCL
Old MathSource #

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The basic function tube[curve, color, radius] draws a tube around curve.

Features: The central curve can be either a function or a list of data points. Closed or open curves are handled equally. The algorithm for drawing the surface of the tube can be chosen from three options, including Frenet normal and binormal. For the Frenet option, inflection points (where the curvature vanishes) are smoothly handled. Also, the differentiation is numerical, which can greatly speed up evaluation. Tubes can be coloured as a function of position. The radius of the tube can be a function of position. Twist can be added to the tube surface. There are functions which draw braids, either from a set of curves or from an Artin word. There is an arrow utility which draws a three dimensional arrow on the side of a tube. The arrow automatically positions itself to be in front, given the viewing angle.

*Mathematica Technology > Programming > 3D Graphics
*Mathematica Technology > Programming > Color
*Mathematics > Topology

Tubes, Knots, Links, Braids, Topology, Arrows
Downloads Download Wolfram CDF Player

Tuba.m (32.2 KB) - Mathematica Package
Tuba.nb (67.2 KB) - Mathematica Notebook
TubaExamples.nb (18.8 KB) - Mathematica Notebook

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