flatsurf/ipyvue-flatsurf

Visualize cylinders for two different directions

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  • Visualize on a smaller surface, e.g., make a picture of a genus 4 quadratic differential rather than a genus 8 abelian differential.
  • Visualize a generic surface and not the billiard.
  • Find two non-parallel directions on the surface that are different in some qualitative way, e.g., different ratio of moduli.
  • Apply GL(2,R) to make one direction horizontal and the other vertical and so that they have roughly the same length.
  • Visualize the components for both directions in the same triangulation and with the same layout in the plane.
  • Relabel half edges so inner edges get high numbers.
  • Label half edges without sign.
  • Hide half edges which are in the interior of cylinders.
  • Replace cylinder patches with single polygons to remove some output artifacts.
  • Export from vue-flatsurf to SVG.

This is now essentially all implemented in the gluings notebook.