What’s a knot?

The first of a series of videos for Numberphile about mathematical knots.

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The work flow was quite complicated, but luckily I found a piece of specialist software called knotplot which contained a catalogue of the knots of crossing numbers 1-10, saving me days of work making knot models. I had to build a custom script to export these as mesh data so they could be imported to blender and rendered with appropriate texturing. I gave everything bold outlines using the freestyle renderer to suit the Numberphile style of looking a bit handmade and rough round the edges and to make what could have easily become spaghetti clearer and more readable.

I used Blenders python scripting functionality to import all the knots in one go and render each knot out in sequence.

Sequences like the road, where the knots had non-uniform cross-sections had to be imported as a list of points to form a bezier and then beveled, textured and animated in Blender.

Everything was rendered as transparent pngs and brought into After Effects to be composited with the ubiquitous numberphile brown paper then sequenced and animated to the audio.

Oh and I made my own custom font, SloPPy (mostly) Sans in font-forge to make life easier and keep things consistent through numberphile projects, it’s a bit janky but it works for my purposes.