Draw Weighted Planar Tangle Trees

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Below is a tool designed to draw the tangle represented by a weighted planar tangle tree (Bonahon & Siebenmann, 2016).

The rendered image is an 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

I’ve given a good number of dials here to mess with. I’ve set some defaults that seem to work well.

  1. In the “Tangle” field, input a linearized weighted planar tangle tree (information found in my thesis link to come).
  2. Configure the tool:
    1. In the “Strand Color” field, set the color of the strands of the tangle. For print you almost certainly want #000000.
    2. In the “Crossing Color” field, set the color of the crossing for the tangle. When an overstrand is drawn, a 2×2\times-sized copy is placed underneath it. This gives the appearance of the understrand being broken. For print you almost certainly want #ffffff.
    3. 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 settings you like.
    4. 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 "String Size"⋅11\text{"String Size"}\cdot 11.
    5. 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.
  3. Press the “Draw” button to render the tangle as an svg.
  4. 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:

SVG size (in px):

Columns:


Bulk print tangles up to TCN 10:

(-1 is the ∞ tangle and bounds are inclusive)

From:

Up to:






References

Bonahon, F., & Siebenmann, L. C. (2016). 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.