Figures for paper

[raphlinus]

This issue is to propose the figures for the paper.

1. A conceptual pipeline. First stage contains a number of encoded path segments, maybe one highlighted for expansion in subsequent stages (the others thinner/grayer). Next: approximation of the cubic with a sequence of Euler spirals (each a different color). Then maybe show the (exact) parallel curves of those spirals, colors matching. Finally show the flattening.

2. Images to show the stroke encoding. Slide 6 from RustLab2023 talk may be a starting point, but it doesn't show caps/joins.

3. Cubic to Euler error metric
   a. Probably a diagram showing cubic and ES superimposed, with common thetas, and an arrow showing the point of maximum distance.
   b. Double-parabola construction (see Cleaner parallel curves with Euler spirals
   c. Fit of double-parabola over theta_0, theta_1 space (same link as above)
   d. Heatmap plot of actual Fréchet distance vs estimate, for d_0, d_1 slice of parameter space, theta_0 and theta_1 fixed

4. Maybe a figure to support unrolled recursion? Not obvious what this should look like

5. Handling of cusp case. Show cubic w/cusp, highlight ES with 180 degree turn, likely also show parallel curves

6. Subdivision density
   a. Supporting figure for subdivision density, maybe the one from Flattening quadratic Béziers
   b. sqrt(|1-x^2|) (this figure is already in the paper) - it can be smaller though
   c. Exact and approximate integral of above (this figure is already in the paper)

7. Evolutes
   a. Euler spiral and its evolute (see wiki page), plus subdivisions for flattening
   b. Simplified Fig 11 from Nehab

8. Triangle strip as alternate output

9. Performance figures; follow Fig 15 from Nehab

[raphlinus]

Sketch for 3a:

[raphlinus]

Sketch for 5:

Also see image generated from raphlinus#100:

[raphlinus]

Sketch for 7b. I really love the way the watercolor looks for the winding number regions and am inclined to keep it. Obviously these curves need to be drawn mathematically.

[armansito]

Adding to the list above: renderings of scenes with strokes for the results section.