interpolate between values instead of interpolating between colors

[SimonDanisch]

We've been interpolating between colors in the mesh shader...
TODO: We also still interpolate between colors in cairo at least for mesh.
Bug report: https://discourse.julialang.org/t/how-to-create-a-patch-shape-with-a-color-gradient-in-a-simple-2d-plot/62607/7?u=sdanisch

Before:

using GLMakie
vertices = Point2[
    (0.0, -1.0)
    (1.0, 0.0)
    (0.6, 1.0)
]
faces = [1, 2, 3]
colors = [1, 2, 3]
f, ax, p = mesh(vertices, faces, color = colors, shading = false, colormap = Reverse(:viridis))
Colorbar(f[1, 2], p)
f

With this PR:

[MakieBot]

Compile Times benchmark

Note, that these numbers may fluctuate on the CI servers, so take them with a grain of salt. All benchmark results are based on the mean time and negative percent mean faster than the base branch. Note, that GLMakie + WGLMakie run on an emulated GPU, so the runtime benchmark is much slower. Results are from running:

using_time = @ctime using Backend
# Compile time
create_time = @ctime fig = scatter(1:4; color=1:4, colormap=:turbo, markersize=20, visible=true)
display_time = @ctime Makie.colorbuffer(display(fig))
# Runtime
create_time = @benchmark fig = scatter(1:4; color=1:4, colormap=:turbo, markersize=20, visible=true)
display_time = @benchmark Makie.colorbuffer(display(fig))

	using	create	display	create	display
GLMakie	14.45s (14.40, 14.50) 0.03+-	20.42s (20.31, 20.55) 0.08+-	17.53s (17.44, 17.62) 0.07+-	15.12ms (15.04, 15.25) 0.07+-	77.63ms (76.89, 79.09) 0.71+-
master	14.41s (14.29, 14.49) 0.08+-	20.10s (19.97, 20.25) 0.08+-	17.53s (17.41, 17.72) 0.10+-	15.13ms (14.98, 15.24) 0.10+-	77.57ms (76.50, 78.82) 0.69+-
evaluation	+0.31%, 0.05s invariant (0.70d, 0.22p, 0.06std)	+1.58%, 0.32s slower X (3.91d, 0.00p, 0.08std)	-0.00%, -0.0s invariant (-0.00d, 1.00p, 0.08std)	-0.05%, -0.01ms invariant (-0.09d, 0.86p, 0.08std)	+0.08%, 0.06ms invariant (0.09d, 0.87p, 0.70std)
CairoMakie	11.64s (11.39, 12.75) 0.50+-	18.24s (17.84, 19.92) 0.75+-	2.25s (2.21, 2.47) 0.10+-	16.90ms (16.43, 18.11) 0.56+-	22.16ms (21.63, 24.18) 0.90+-
master	11.63s (11.37, 12.70) 0.48+-	17.63s (17.54, 17.84) 0.11+-	2.29s (2.26, 2.31) 0.01+-	17.11ms (16.83, 17.27) 0.16+-	21.86ms (21.72, 22.06) 0.11+-
evaluation	+0.04%, 0.0s invariant (0.01d, 0.99p, 0.49std)	+3.34%, 0.61s invariant (1.13d, 0.08p, 0.43std)	-1.51%, -0.03s invariant (-0.49d, 0.39p, 0.06std)	-1.21%, -0.2ms invariant (-0.49d, 0.39p, 0.36std)	+1.35%, 0.3ms invariant (0.46d, 0.42p, 0.51std)
WGLMakie	20.62s (20.34, 20.92) 0.20+-	40.51s (39.80, 41.16) 0.45+-	55.20s (54.41, 56.41) 0.78+-	27.03ms (26.03, 27.85) 0.61+-	2.05s (1.96, 2.12) 0.06+-
master	20.52s (20.05, 20.75) 0.22+-	39.91s (39.01, 40.96) 0.71+-	54.94s (53.50, 56.39) 0.94+-	26.96ms (26.07, 27.70) 0.52+-	2.05s (1.99, 2.11) 0.04+-
evaluation	+0.46%, 0.09s invariant (0.45d, 0.42p, 0.21std)	+1.47%, 0.6s invariant (1.00d, 0.09p, 0.58std)	+0.47%, 0.26s invariant (0.30d, 0.58p, 0.86std)	+0.29%, 0.08ms invariant (0.14d, 0.80p, 0.57std)	-0.08%, -0.0s invariant (-0.04d, 0.95p, 0.05std)

[jkrumbiegel]

Cairo can't do any other interpolation than between color. So to really support it we would need to software-render our own meshes to bitmaps directly.

[SimonDanisch]

Yeah, I've been wanting to do that... It's not even that hard, just need to find some time for it!

[asinghvi17]

Hmm...wouldn't that essentially lose the "vector" nature of the mesh (i.e., zoomability without pixelation)? Or are you proposing subdividing the mesh and interpolating along color gradients of smaller magnitude? Either way, it would probably be nice to be able to turn it on and off by some switch in CairoMakie.

Also, how would this affect large meshes like those generated by surface!?

[jkrumbiegel]

Mesh is already rasterized (at least in svgs). Could be that it's not in pdfs, not sure, but the mesh operator hasnt been added to the svg spec yet.

[asinghvi17]

Hmm, makes sense. I believe PDF does have a mesh gradient intrinsic, but in any case that would be a fixed color interpolation type. Would you be going along a route similar to this, or something else?

Edit: if we're doing this we could theoretically also allow the user to specify the mode of interpolation (linear, cubic, bilinear, etc)

[jkrumbiegel]

Capitalization here and above :)
It's not that good to paste the PR titles as those are usually not even complete sentences.