Support non-identity axis scales in ablines

[jkrumbiegel]

ablines used to error on any non-identity axis scale (ABLines is only defined for the identity transform). But there's no real reason for that: f(x) = slope * x + intercept is defined in data coordinates, so under a transform it just becomes a curve in screen space. This draws it as a subdivided curve (256 points sampled evenly across the visible range), and keeps the cheap 2-point line for the identity transform.

A few details fall out of this:

• On log-log axes a zero-intercept line maps back to a straight line, as you'd expect; with a nonzero intercept it's genuinely curved.
• The line value can leave the y-scale domain (e.g. go negative on a log y axis) even when the axis limits are valid. Those points become NaN, so the line breaks there. Since the visible y-range is always inside the domain, the break is always off-screen.
• Per-line color/linewidth vectors still work, and it now draws with lines rather than linesegments.

f = Figure(size = (600, 500))

ax = Axis(f[1, 1], title = "identity")
ablines!(ax, [0.0, 1.0, 2.0], [1.0, -0.5, 0.25], color = [:orange, :red, :purple], linewidth = 3)
limits!(ax, 0, 10, -2, 6)

ax = Axis(f[1, 2], xscale = log10, title = "log x")
ablines!(ax, 0.0, 0.002, color = :orange, linewidth = 3)
limits!(ax, 1, 1000, 0, 3)

ax = Axis(f[1, 3], yscale = log10, title = "log y, crosses zero")
ablines!(ax, -50.0, 50.0, color = :orange, linewidth = 3)
limits!(ax, 1, 4, 1, 200)

ax = Axis(f[2, 1], xscale = log10, yscale = log10, title = "log-log, zero intercept")
ablines!(ax, [0.0, 0.0, 0.0], [1.0, 3.0, 0.3], color = [:orange, :red, :purple], linewidth = [2, 4, 6])
limits!(ax, 1, 100, 0.1, 1000)

ax = Axis(f[2, 2], xscale = log10, yscale = log10, title = "log-log, nonzero intercept")
ablines!(ax, [1.0, 10.0, 100.0], 1.0, color = [:orange, :red, :purple], linewidth = 3)
limits!(ax, 1, 100, 1, 1000)

ax = Axis(f[2, 3], xscale = sqrt, title = "sqrt x")
ablines!(ax, 0.0, 1.0, color = :orange, linewidth = 3)
limits!(ax, 0, 100, 0, 100)

f

[ffreyer]

This should probably be an attribute?

[jkrumbiegel]

Yeah good point!

[SimonDanisch]

At some point we wanted to make this work generically by adapting the apply_transform machinery to be able to add points to lines:

apply_transform(func, vector_of_points)::Vector{Point}

Maybe worth a shot with claude being able to do the annoying interface refactor?

[ffreyer]

Dendrogram has something specifically for Polar:

Makie.jl/Makie/src/stats/dendrogram.jl

Lines 93 to 136 in eff2c6f

	resample_for_transform(tf, args...; step = nothing) = args
	function resample_for_transform(tf::Polar, ps, args...; step = 2pi / 180)
	isempty(ps) && return (ps, args...)
	interpolated_points = similar(ps, 0)
	push!(interpolated_points, ps[1])
	interpolated_args = map(x -> similar(x, 0), args)
	for (old, new) in zip(args, interpolated_args)
	push!(new, old[1])
	end
	dim = ifelse(tf.theta_as_x, 1, 2)
	for i in 2:length(ps)
	p0 = ps[i - 1]
	p1 = ps[i]
	if isnan(p0) || isnan(p1)
	push!(interpolated_points, p1)
	for (old, new) in zip(args, interpolated_args)
	push!(new, old[i])
	end
	continue
	end
	N = 1 + max(1, round(Int, abs(p1[dim] - p0[dim]) / step))
	if N == 2
	push!(interpolated_points, p1)
	for (old, new) in zip(args, interpolated_args)
	push!(new, old[i])
	end
	else
	append!(interpolated_points, range(p0, p1, length = N)[2:N])
	for (old, new) in zip(args, interpolated_args)
	if isnan(old[i - 1]) || isnan(old[i])
	append!(new, (old[i - 1] for _ in 2:N))
	else
	append!(new, range(old[i - 1], old[i], length = N)[2:N])
	end
	end
	end
	end
	return (interpolated_points, interpolated_args...)
	end

If we added resampling in an automated way it would definitely need an on/off switch. Discrete plots like scatter definitely shouldn't resample. Something like lines may also have situations where it shouldn't. For example if you make a spider chart by reducing the number of points in a PolarAxis.

[SimonDanisch]

Yeah, it'd need to dispatch on the plot type as well...
We had a concept somewhere sometime I think, which thought this through a bit more than my comment 😅