heatmap mark?

[Fil]

I sometimes see users trying to make heatmaps with Plot.cell, which results in incorrect charts when x and y are continuous. The recommended approach (until now) was to use Plot.bin to create the small squares (or rather, rectangles), as x/y bins. However with projections, this is now incomplete, and we should have a solution for heatmaps in the projected space. Like hexbin, but based on squares (or any other tessellation?). There's probably a lot of code to share with hexbin, the most difficult part to decide might be the API?

[mbostock]

Related or duplicate of #984?

Also not sure I follow why the recommended approach of rect + bin is “incomplete” with re. to projections, since we support projecting rects now (at least for cylindrical projections under the normal aspect).

I used rect for this recently for Advent of Code:

Plot.plot({
    grid: true,
    round: true,
    x: {domain: [grid.x1 - 0.5, grid.x2 + 0.5]},
    y: {domain: [grid.y2 + 0.5, -0.5]},
    color: {
      domain: ["rock", "sand", "source"],
      range: ["#5a4d41", "#c2b280", "red"]
    },
    marks: [
      Plot.rect(grid.values, {
        x1: (d, i) => grid.x1 + i % grid.m - 0.5,
        y1: (d, i) => grid.y1 + Math.floor(i / grid.m) - 0.5,
        x2: (d, i) => grid.x1 + i % grid.m + 0.5,
        y2: (d, i) => grid.y1 + Math.floor(i / grid.m) + 0.5,
        fill: (d) => d
      })
    ]
  })

I originally used the interval option (1) but for the smaller grids I wanted the rects to be centered on their value rather than between values.

[mbostock]

I would like to better understand how continuous heatmaps are commonly expressed. Do we want a sparse sample-based approach as with the pixel mark in #1185 (which is really just an optimization of the existing rect mark + interval transform)? Or does the user want to supply a continuous function of xy that is them sampled automatically (in a grid) by Plot? Or maybe the user supplies dense samples in a grid (similar to ImageData) so that the x and y channels can be implicit? Or all of the above?

[Fil]

matplotlib has a funky interpolation method
https://matplotlib.org/stable/gallery/images_contours_and_fields/interpolation_methods.html

[mbostock]

Fixed in #1196.