$\newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\LP}{\left(} \newcommand{\RP}{\right)} \newcommand{\LS}{\left\lbrace} \newcommand{\RS}{\right\rbrace} \newcommand{\LA}{\left\langle} \newcommand{\RA}{\right\rangle} \newcommand{\LB}{\left[} \newcommand{\RB}{\right]} \newcommand{\MM}{\ \middle|\ } \newcommand{\exp}{\text{exp}} \newcommand{\abs}[1]{\left\vert#1\right\vert} \newcommand{\msr}[1]{m\left(#1\right)} \newcommand{\inv}[1]{#1^{-1}} \newcommand{\bkt}[1]{\LA \img{#1}\RA} \require{color}$
Below is a tool designed to draw the tangle represented by a weighted planar tangle tree [1].
svg, a vector format. This means it can be scaled
infinitely. If you need to view it at a larger scale or would like to
postprocess the image, you can download it and use a tool such as Inkscape to
edit it.
I have done very little testing with this tool. I’m reasonably confident that valid input generates valid output. I have no idea what happens when invalid input is fed to the tool. If you find a bug, please report it.
Instructions
- In the “Tangle” field, input a linearized weighted planar tangle tree (information found in my thesis link to come).
- Configure the tool:
- In the “Strand Color” field, set the color of the strands of the tangle.
For print you almost certainly want
#000000. - In the “Crossing Color” field, set the color of the crossing for the
tangle. When an overstrand is drawn, a $2\times$-sized copy is placed
underneath it. This gives the appearance of the understrand being broken.
For print you almost certainly want
#ffffff. - In the “Eccentricity” field, select a number from 0 to 100. This will tell the tool how far away from a path vertex to place control points. Play around until you find a setting you like.
- In the “String Size” field, select a positive integer. This will be, in pixels, how large to make the strands of the tangle. A crossing will always have a height and width of $\text{“String Size”}\cdot 11$.
- In the “Gap Size” field, select a positive integer. This dictates how far apart units of a tangle should be placed. Play around until you find something you like.
- In the “Strand Color” field, set the color of the strands of the tangle.
For print you almost certainly want
- Press the “Draw” button to render the tangle as an
svg. - If you’re happy with the picture, you can download it by pressing the “Download” button.
Strand Color:
Crossing Color:
Eccentricity:
String Size:
Gap Size:
- F. Bonahon and L. Siebenmann,
New Geometric Splittings of Classical Knots and the Classification and Symmetries of Arborescent Knots,
https://dornsife.usc.edu/francis-bonahon/wp-content/uploads/sites/205/2023/06/BonSieb-compressed.pdf, 2016.
