Carpet plots

[etpinard]

References:

• https://www.mathworks.com/matlabcentral/fileexchange/40831-carpet-plot-toolkit/content/CarpetPlots/carpet.m
• https://en.wikipedia.org/wiki/Carpet_plot

[rreusser]

One challenge for this plot: contour lines. We need hash lines along a contour line in order to represent inequalities, which means we need to be able to construct continuous contour lines. simplicial-complex-contour, unless I'm wrong, needs triangle geometry in 2D and returns contour segments in cell order rather than as continuous lines.

Imagine a quad a-b-d-c which we need to split into triangles in order to get contours.

c ------- d
|  \      |
|    \    |
|      \  |
a ------- b

The first choice is a-b-c and b-d-c. When there's high frequency detail, this doesn't do so well:

a-d-c and a-b-d obviously gives similar results:

A switching function that minimizes the angle between the normals (imagining the data projecting into the third dimension) is better but not great:

Okay, so next I tried splitting it into four triangles by taking the centroid of the coordinates and data.

c ------- d
| \     / |
|    O    |
| /     \ |
a ------- b

This basically just adds a lot more noise to the contours since it's all based on linear interpolation. It does get the topology pretty good though. So at @alexcjohnson's suggestion, I filtered out the center points after using them to construct the geometry. Yay. This seems to work well:

Nothing will get it perfect when there's heavy aliasing, but this is at least way better. The code can hopefully be extracted, cleaned up just a bit (not worth heavy cleanup since 250 x 250 grids take about 300ms to construct pretty complicated contours), and used in the svg version. 😄

Current prototype at: https://rreusser.github.io/demos/carpet/

[etpinard]

done in #1595