colors and contours in luametafun

* colors and contours in luametafun
@ 2021-09-01  7:54 Jacob Kauffmann via ntg-context
  2022-06-20 16:29 ` Jacob Kauffmann via ntg-context
  0 siblings, 1 reply; 3+ messages in thread
From: Jacob Kauffmann via ntg-context @ 2021-09-01  7:54 UTC (permalink / raw)
  To: mailing list for ConTeXt users; +Cc: Jacob Kauffmann

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Dear list,

I am a huge fan of the new metafun interface.
Hans asked for luametafun requests, so here are a few.

 - color by value in lmt_surface
We want to show a surface plot of a function where the color indicates the function value (instead, or in addition to a light source).
The easiest would be to have variable cf for the brightness factor (as it is), and in addition variables such as zt, minz, maxz, akin to the color formatter for lmt_contour.
This becomes handy when colors are to be aligned with function values (e.g. negative = blue, zero = white, positive = red, see MWE attached).

 - controlling line levels in lmt_contour
It would be convenient if certain levels could be set by the user. E.g. to make sure the zero level contour line is included.
The user interface could potentially take a list, levels = { -1, -.5, 0, .5, 1 }, of contour level lines. See MWE attached.
From my understanding marching squares can do that. A possible reference implementation could be QuadContourGenerator [1] in matplotlib, a bit of description can be found in [2].

 - colormaps
Contour plots often use rather complex colormaps, such as jet, rainbow or veridis. They are optimized for perceptual resolution, color blindness, screen/print or certain use cases.
The functionality is already there, but from a user's perspective, it would be much easier if some of these were provided by the interface.
The interface could be color = "colormap('jet')(l/n)". Indeed, these are useful in other use cases as well, such as bar charts, surface plots or shades.
One rudimentary example is in the attached file.

 - number of levels in lmt_contour (potential bug)
The number of levels is different from the user's input. Depending on the output range it can be lower or higher (see MWE attached).

Cheers,
Jacob Kauffmann

[1] https://github.com/matplotlib/matplotlib/blob/96ff1146ad053c5c7481efd9de039c879a595968/src/_contour.cpp
[2] https://github.com/matplotlib/matplotlib/blob/96ff1146ad053c5c7481efd9de039c879a595968/src/_contour.h

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\starttext

\setupMPpage[
	offset=10pt,
	instance=doublefun]

\startluacode
-- function used in the examples
function fun(x,y)
	local exp = math.exp
	return 1.5*exp(-1.5*((x + 1.1)^2 + (y - 1.1)^2)) 
		 + 0.5*exp(-1.0*((x + 1)^2 + (y + 1)^2))
		 - 0.5*exp(-0.9*((x - 1)^2 + (y - 0)^2))
end

-- example of a simple blue-gray-red colormap
function colormap(f)
	local abs, min = math.abs, math.min
	local r, g, b = min(1, 2*f), 1-2*abs(f-.5), min(1,2-2*f)
	return .85*r, .85*g, .85*b
end
\stopluacode

\startMPpage
draw lmt_surface [
	code = "fun(x,y)",
	% here, I'd like to use something like
	% color = "colormap( 0.5 * fun(xt,yt) / max(abs(minz),abs(maxz)) + 0.5 )
	color = "colormap(f)",
	xmin = -3,
	xmax = 3,
	ymin = -3,
	ymax = 3,
	xstep = .3,
	ystep = .3,
	xvector = { -0.3, -0.5 },
	linecolor = 0
] xsized 10cm;
\stopMPpage

\startMPpage
label.rt(textext("all three plots are specified with {\tt levels = 7}"), (0, 4cm));

picture SixLevels;
SixLevels := lmt_contour [
	xmin = -3, xmax = 3, xstep = .05,
	ymin = -3, ymax = 3, ystep = .05,
	% would be nice to do something like
	% levels = {-1, -.5, 0, .5, 1}
	levels = 7,
	height = 3cm,
	function = "fun(x,y)",
	color = "colormap(l/n + .21)",
	linecolor = "black",
	legend = false,
	cache = true
];
draw SixLevels;
label.top(textext("six levels"), .5[ulcorner SixLevels, urcorner SixLevels]);

picture SevenLevels;
SevenLevels := lmt_contour [
	xmin = -3, xmax = 3, xstep = .05,
	ymin = -3, ymax = 3, ystep = .05,
	levels = 7,
	height = 3cm,
	function = "fun(x, y)*5",
	color = "colormap(l/n + .08)",
	linecolor = "black",
	legend = false,
	cache = true,
] xshifted 3.5cm;
draw SevenLevels;
label.top(textext("seven levels"), .5[ulcorner SevenLevels, urcorner SevenLevels]);

picture EightLevels;
EightLevels := lmt_contour [
	xmin = -3, xmax = 3, xstep = .05,
	ymin = -3, ymax = 3, ystep = .05,
	levels = 7,
	height = 3cm,
	function = "fun(x,y)*10",
	color = "colormap(l/n + .08)",
	linecolor = "black",
	legend = false,
	cache = true,
] xshifted 7cm;
draw EightLevels;
label.top(textext("eight levels"), .5[ulcorner EightLevels, urcorner EightLevels]);
\stopMPpage

\stoptext

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