From cac175b4b7038d3c7d83b71b48d2391ee52d4065 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 25 Jul 2023 15:07:01 +0200
Subject: [PATCH 01/18] add `ReversibleScale` type - simplify `LogFunctions`

---
 src/colorsampler.jl             |  4 ++--
 src/layouting/transformation.jl |  8 ++++----
 src/makielayout/blocks/axis.jl  |  2 +-
 src/makielayout/lineaxis.jl     | 23 ++++++++++++-----------
 src/types.jl                    | 15 +++++++++++++++
 5 files changed, 34 insertions(+), 18 deletions(-)

diff --git a/src/colorsampler.jl b/src/colorsampler.jl
index e0c728b6d8a..c8c36900bbb 100644
--- a/src/colorsampler.jl
+++ b/src/colorsampler.jl
@@ -179,7 +179,7 @@ end
 struct ColorMap{N,T<:AbstractArray{<:Number,N},T2<:AbstractArray{<:Number,N}}
     color::Observable{T}
     colormap::Observable{Vector{RGBAf}}
-    scale::Observable{Function}
+    scale::Observable{Union{ReversibleScale,Function}}
     mapping::Observable{Union{Nothing, Vector{Float64}}}
     colorrange::Observable{Vec{2,Float64}}
 
@@ -198,7 +198,7 @@ function assemble_colors(::T, @nospecialize(color), @nospecialize(plot)) where {
     color_tight = convert(Observable{T}, color)
     colormap = Observable(RGBAf[]; ignore_equal_values=true)
     categorical = Observable(false)
-    colorscale = convert(Observable{Function}, plot.colorscale)
+    colorscale = convert(Observable, plot.colorscale)
     mapping = Observable{Union{Nothing, Vector{Float64}}}(nothing)
 
     function update_colors(cmap, a)
diff --git a/src/layouting/transformation.jl b/src/layouting/transformation.jl
index 7ab943e16f9..3ed36c6dd7c 100644
--- a/src/layouting/transformation.jl
+++ b/src/layouting/transformation.jl
@@ -400,12 +400,11 @@ end
 
 const REVERSIBLE_SCALES = Union{
     # typeof(identity),  # no, this is a noop
-    typeof(log10),
-    typeof(log),
-    typeof(log2),
-    typeof(sqrt),
+    LogFunctions,
     typeof(pseudolog10),
     typeof(logit),
+    typeof(sqrt),
+    ReversibleScale,
     Symlog10,
 }
 
@@ -417,6 +416,7 @@ inverse_transform(::typeof(sqrt)) = x -> x ^ 2
 inverse_transform(::typeof(pseudolog10)) = inv_pseudolog10
 inverse_transform(F::Tuple) = map(inverse_transform, F)
 inverse_transform(::typeof(logit)) = logistic
+inverse_transform(s::ReversibleScale) = s.backward
 inverse_transform(s::Symlog10) = x -> inv_symlog10(x, s.low, s.high)
 inverse_transform(s) = nothing
 
diff --git a/src/makielayout/blocks/axis.jl b/src/makielayout/blocks/axis.jl
index 8656998749a..cd1f3e2ad83 100644
--- a/src/makielayout/blocks/axis.jl
+++ b/src/makielayout/blocks/axis.jl
@@ -1360,7 +1360,7 @@ defaultlimits(::typeof(Makie.pseudolog10)) = (0.0, 100.0)
 defaultlimits(::Makie.Symlog10) = (0.0, 100.0)
 
 defined_interval(::typeof(identity)) = OpenInterval(-Inf, Inf)
-defined_interval(::Union{typeof(log2), typeof(log10), typeof(log)}) = OpenInterval(0.0, Inf)
+defined_interval(::LogFunctions) = OpenInterval(0.0, Inf)
 defined_interval(::typeof(sqrt)) = Interval{:closed,:open}(0, Inf)
 defined_interval(::typeof(Makie.logit)) = OpenInterval(0.0, 1.0)
 defined_interval(::typeof(Makie.pseudolog10)) = OpenInterval(-Inf, Inf)
diff --git a/src/makielayout/lineaxis.jl b/src/makielayout/lineaxis.jl
index d8dbcd3b6a9..8edbb27394b 100644
--- a/src/makielayout/lineaxis.jl
+++ b/src/makielayout/lineaxis.jl
@@ -556,12 +556,12 @@ end
 get_tickvalues(::Automatic, ::typeof(identity), vmin, vmax) = get_tickvalues(WilkinsonTicks(5, k_min = 3), vmin, vmax)
 
 # fall back to identity if not overloaded scale function is used with automatic
-get_tickvalues(::Automatic, F, vmin, vmax) = get_tickvalues(automatic, identity, vmin, vmax)
+get_tickvalues(::Automatic, _, vmin, vmax) = get_tickvalues(automatic, identity, vmin, vmax)
 
 # fall back to non-scale aware behavior if no special version is overloaded
-get_tickvalues(ticks, scale, vmin, vmax) = get_tickvalues(ticks, vmin, vmax)
+get_tickvalues(ticks, _, vmin, vmax) = get_tickvalues(ticks, vmin, vmax)
 
-function get_ticks(ticks_and_labels::Tuple{Any, Any}, any_scale, ::Automatic, vmin, vmax)
+function get_ticks(ticks_and_labels::Tuple{Any, Any}, _, ::Automatic, vmin, vmax)
     n1 = length(ticks_and_labels[1])
     n2 = length(ticks_and_labels[2])
     if n1 != n2
@@ -570,7 +570,7 @@ function get_ticks(ticks_and_labels::Tuple{Any, Any}, any_scale, ::Automatic, vm
     ticks_and_labels
 end
 
-function get_ticks(tickfunction::Function, any_scale, formatter, vmin, vmax)
+function get_ticks(tickfunction::Function, _, formatter, vmin, vmax)
     result = tickfunction(vmin, vmax)
     if result isa Tuple{Any, Any}
         tickvalues, ticklabels = result
@@ -581,18 +581,20 @@ function get_ticks(tickfunction::Function, any_scale, formatter, vmin, vmax)
     return tickvalues, ticklabels
 end
 
+_logbase(s::ReversibleScale) = s.logbase
 _logbase(::typeof(log10)) = "10"
 _logbase(::typeof(log2)) = "2"
 _logbase(::typeof(log)) = "e"
+_logbase(::Any) = ""
 
-
-function get_ticks(::Automatic, scale::Union{typeof(log10), typeof(log2), typeof(log)},
-        any_formatter, vmin, vmax)
-    get_ticks(LogTicks(WilkinsonTicks(5, k_min = 3)), scale, any_formatter, vmin, vmax)
+function get_ticks(::Automatic, scale::Union{LogFunctions,ReversibleScale}, any_formatter, vmin, vmax)
+    wt = WilkinsonTicks(5, k_min = 3)
+    ticks = isempty(_logbase(scale)) ? wt : LogTicks(wt)
+    get_ticks(ticks, scale, any_formatter, vmin, vmax)
 end
 
 # log ticks just use the normal pipeline but with log'd limits, then transform the labels
-function get_ticks(l::LogTicks, scale::Union{typeof(log10), typeof(log2), typeof(log)}, ::Automatic, vmin, vmax)
+function get_ticks(l::LogTicks, scale::Union{LogFunctions,ReversibleScale}, ::Automatic, vmin, vmax)
     ticks_scaled = get_tickvalues(l.linear_ticks, identity, scale(vmin), scale(vmax))
 
     ticks = Makie.inverse_transform(scale).(ticks_scaled)
@@ -727,8 +729,7 @@ function get_minor_tickvalues(i::IntervalsBetween, scale, tickvalues, vmin, vmax
 end
 
 # for log scales, we need to step in log steps at the edges
-function get_minor_tickvalues(i::IntervalsBetween, scale::Union{typeof(log),typeof(log2),typeof(log10)},
-                              tickvalues, vmin, vmax)
+function get_minor_tickvalues(i::IntervalsBetween, scale::LogFunctions, tickvalues, vmin, vmax)
     vals = Float64[]
     length(tickvalues) < 2 && return vals
     n = i.n
diff --git a/src/types.jl b/src/types.jl
index c28e74df6a8..b562fd1ca3d 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -378,3 +378,18 @@ end
 
 # The color type we ideally use for most color attributes
 const RGBColors = Union{RGBAf, Vector{RGBAf}, Vector{Float32}}
+
+const LogFunctions = Union{typeof(log10), typeof(log2), typeof(log)}
+
+struct ReversibleScale{F <: Function, B <: Function}
+    forward::F
+    backward::B
+    logbase::String
+    function ReversibleScale(forward, backward, logbase = "")
+        new{typeof(forward),typeof(backward)}(forward, backward, logbase)
+    end
+end
+
+function (s::ReversibleScale)(args...)  # functor
+    s.forward(args...)
+end

From f26d8163e0eef1860db2c4d6d2dd1fbcd5dc118f Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 25 Jul 2023 18:35:25 +0200
Subject: [PATCH 02/18] fix `scaled_steps`

---
 ReferenceTests/src/tests/examples2d.jl |  9 +++++++++
 src/makielayout/blocks/axis.jl         |  8 ++++----
 src/makielayout/blocks/colorbar.jl     | 23 ++++++++++++-----------
 3 files changed, 25 insertions(+), 15 deletions(-)

diff --git a/ReferenceTests/src/tests/examples2d.jl b/ReferenceTests/src/tests/examples2d.jl
index f79c4416ae7..0256f0d3e75 100644
--- a/ReferenceTests/src/tests/examples2d.jl
+++ b/ReferenceTests/src/tests/examples2d.jl
@@ -597,6 +597,15 @@ end
     fig
 end
 
+@reference_test "custom colorscale (heatmap)" begin
+    x = 10.0.^(1:0.1:4)
+    y = 1.0:0.1:5.0
+    scale = Makie.ReversibleScale(x -> log10(x + 2), x -> exp10(x) - 2, "10")
+    fig, ax, hm = heatmap(x, y, (x, y) -> x; axis = (; xscale = scale), colorscale = scale)
+    Colorbar(fig[1, 2], hm)
+    fig
+end
+
 @reference_test "colorscale (lines)" begin
     xs = 0:0.01:10
     ys = 2 .* (1 .+ sin.(xs))
diff --git a/src/makielayout/blocks/axis.jl b/src/makielayout/blocks/axis.jl
index cd1f3e2ad83..bc21a0c1502 100644
--- a/src/makielayout/blocks/axis.jl
+++ b/src/makielayout/blocks/axis.jl
@@ -1349,10 +1349,9 @@ defaultlimits(limits::Tuple{Real, Nothing}, scale) = (limits[1], defaultlimits(s
 defaultlimits(limits::Tuple{Nothing, Real}, scale) = (defaultlimits(scale)[1], limits[2])
 defaultlimits(limits::Tuple{Nothing, Nothing}, scale) = defaultlimits(scale)
 
-
-defaultlimits(::typeof(log10)) = (1.0, 1000.0)
-defaultlimits(::typeof(log2)) = (1.0, 8.0)
-defaultlimits(::typeof(log)) = (1.0, exp(3.0))
+defaultlimits(scale::Union{LogFunctions,ReversibleScale}) = let inv_scale = inverse_transform(scale)
+    (inv_scale(0.0), inv_scale(3.0))
+end
 defaultlimits(::typeof(identity)) = (0.0, 10.0)
 defaultlimits(::typeof(sqrt)) = (0.0, 100.0)
 defaultlimits(::typeof(Makie.logit)) = (0.01, 0.99)
@@ -1360,6 +1359,7 @@ defaultlimits(::typeof(Makie.pseudolog10)) = (0.0, 100.0)
 defaultlimits(::Makie.Symlog10) = (0.0, 100.0)
 
 defined_interval(::typeof(identity)) = OpenInterval(-Inf, Inf)
+defined_interval(::ReversibleScale) = OpenInterval(-Inf, Inf)
 defined_interval(::LogFunctions) = OpenInterval(0.0, Inf)
 defined_interval(::typeof(sqrt)) = Interval{:closed,:open}(0, Inf)
 defined_interval(::typeof(Makie.logit)) = OpenInterval(0.0, 1.0)
diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index 6ccbc928238..f8fc60d1788 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -68,7 +68,12 @@ function Colorbar(fig_or_scene, contourf::Union{Contourf, Tricontourf}; kwargs..
 
 end
 
-colorbar_range(start, stop, length, _) = LinRange(start, stop, length)  # noop
+colorbar_range(start, stop, length, _::typeof(identity)) = LinRange(start, stop, length)
+function colorbar_range(start, stop, length, _)
+    @warn "cannot determine inverse_transform"
+    colorbar_range(start, stop, length, identity)  # noop (nothing we can do, bailing out)
+end
+
 function colorbar_range(start, stop, length, scale::REVERSIBLE_SCALES)
     inverse_transform(scale).(range(start, stop; length))
 end
@@ -146,7 +151,7 @@ function initialize_block!(cb::Colorbar)
     map_is_categorical = lift(x -> x isa PlotUtils.CategoricalColorGradient, blockscene, cgradient)
 
     steps = lift(blockscene, cgradient, cb.nsteps, cb.scale) do cgradient, n, scale
-        s = if cgradient isa PlotUtils.CategoricalColorGradient
+        if cgradient isa PlotUtils.CategoricalColorGradient
             cgradient.values
         else
             collect(colorbar_range(0, 1, n, scale))
@@ -363,17 +368,13 @@ end
 
 Sets the space allocated for the ticklabels of the `Colorbar` to the minimum that is needed and returns that value.
 """
-function tight_ticklabel_spacing!(cb::Colorbar)
-    space = tight_ticklabel_spacing!(cb.axis)
-    return space
-end
+tight_ticklabel_spacing!(cb::Colorbar) = tight_ticklabel_spacing!(cb.axis)
 
 function scaled_steps(steps, scale, lims)
-    # first scale to limits so we can actually apply the scale to the values
-    # (log(0) doesn't work etc.)
-    s_limits = steps .* (lims[2] - lims[1]) .+ lims[1]
     # scale with scaling function
-    s_limits_scaled = scale.(s_limits)
+    steps_scaled = scale.(steps)
+    # normalize to lims range
+    steps_lim_scaled = @. steps_scaled * (scale(lims[2]) -  scale(lims[1])) + scale(lims[1])
     # then rescale to 0 to 1
-    s_scaled = (s_limits_scaled .- s_limits_scaled[1]) ./ (s_limits_scaled[end] - s_limits_scaled[1])
+    @. (steps_lim_scaled - steps_lim_scaled[begin]) / (steps_lim_scaled[end] - steps_lim_scaled[begin])
 end

From bed582386068024ad8150dcc3dcb84a5db04484f Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 25 Jul 2023 19:45:42 +0200
Subject: [PATCH 03/18] add news entry

---
 NEWS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/NEWS.md b/NEWS.md
index ba55a509260..04973beed26 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -2,6 +2,7 @@
 
 ## master
 
+- Allow arbitrary reversible scale functions through `Makie.ReversibleScale`.
 - Fix automatic normal generation for meshes with shading and no normals [#3041](https://github.com/MakieOrg/Makie.jl/pull/3041).
 
 ## v0.19.7

From 56d597ac8d1f77a772ea6a4e942c199ccdb0a1e2 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 8 Aug 2023 13:02:22 +0200
Subject: [PATCH 04/18] add more flexibility

---
 ReferenceTests/src/tests/examples2d.jl | 2 +-
 src/makielayout/blocks/axis.jl         | 5 +++--
 src/types.jl                           | 8 +++++---
 3 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/ReferenceTests/src/tests/examples2d.jl b/ReferenceTests/src/tests/examples2d.jl
index 0256f0d3e75..cb845e8f889 100644
--- a/ReferenceTests/src/tests/examples2d.jl
+++ b/ReferenceTests/src/tests/examples2d.jl
@@ -600,7 +600,7 @@ end
 @reference_test "custom colorscale (heatmap)" begin
     x = 10.0.^(1:0.1:4)
     y = 1.0:0.1:5.0
-    scale = Makie.ReversibleScale(x -> log10(x + 2), x -> exp10(x) - 2, "10")
+    scale = Makie.ReversibleScale(x -> log10(x + 2), x -> exp10(x) - 2; logbase = "10")
     fig, ax, hm = heatmap(x, y, (x, y) -> x; axis = (; xscale = scale), colorscale = scale)
     Colorbar(fig[1, 2], hm)
     fig
diff --git a/src/makielayout/blocks/axis.jl b/src/makielayout/blocks/axis.jl
index bc21a0c1502..b4b120bce6d 100644
--- a/src/makielayout/blocks/axis.jl
+++ b/src/makielayout/blocks/axis.jl
@@ -1349,7 +1349,8 @@ defaultlimits(limits::Tuple{Real, Nothing}, scale) = (limits[1], defaultlimits(s
 defaultlimits(limits::Tuple{Nothing, Real}, scale) = (defaultlimits(scale)[1], limits[2])
 defaultlimits(limits::Tuple{Nothing, Nothing}, scale) = defaultlimits(scale)
 
-defaultlimits(scale::Union{LogFunctions,ReversibleScale}) = let inv_scale = inverse_transform(scale)
+defaultlimits(scale::ReversibleScale) = inverse_transform(scale).(scale.limits)
+defaultlimits(scale::LogFunctions) = let inv_scale = inverse_transform(scale)
     (inv_scale(0.0), inv_scale(3.0))
 end
 defaultlimits(::typeof(identity)) = (0.0, 10.0)
@@ -1358,8 +1359,8 @@ defaultlimits(::typeof(Makie.logit)) = (0.01, 0.99)
 defaultlimits(::typeof(Makie.pseudolog10)) = (0.0, 100.0)
 defaultlimits(::Makie.Symlog10) = (0.0, 100.0)
 
+defined_interval(scale::ReversibleScale) = scale.interval
 defined_interval(::typeof(identity)) = OpenInterval(-Inf, Inf)
-defined_interval(::ReversibleScale) = OpenInterval(-Inf, Inf)
 defined_interval(::LogFunctions) = OpenInterval(0.0, Inf)
 defined_interval(::typeof(sqrt)) = Interval{:closed,:open}(0, Inf)
 defined_interval(::typeof(Makie.logit)) = OpenInterval(0.0, 1.0)
diff --git a/src/types.jl b/src/types.jl
index b562fd1ca3d..d6629cc4d93 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -381,12 +381,14 @@ const RGBColors = Union{RGBAf, Vector{RGBAf}, Vector{Float32}}
 
 const LogFunctions = Union{typeof(log10), typeof(log2), typeof(log)}
 
-struct ReversibleScale{F <: Function, B <: Function}
+struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     forward::F
     backward::B
     logbase::String
-    function ReversibleScale(forward, backward, logbase = "")
-        new{typeof(forward),typeof(backward)}(forward, backward, logbase)
+    limits::NTuple{2,Float32}
+    interval::I
+    function ReversibleScale(forward, backward; logbase = "", limits = (0f0, 10f0), interval = OpenInterval(-Inf32, Inf32))
+        new{typeof(forward),typeof(backward),typeof(interval)}(forward, backward, logbase, limits, interval)
     end
 end
 

From ec9ed8489e0109e4d9210a792b600f1c67ffda79 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Fri, 11 Aug 2023 12:19:54 +0200
Subject: [PATCH 05/18] simplify `interval` kw

---
 src/makielayout/blocks/axis.jl | 2 +-
 src/types.jl                   | 6 +++++-
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/src/makielayout/blocks/axis.jl b/src/makielayout/blocks/axis.jl
index b4b120bce6d..5f2ca8b3806 100644
--- a/src/makielayout/blocks/axis.jl
+++ b/src/makielayout/blocks/axis.jl
@@ -499,7 +499,7 @@ function initialize_block!(ax::Axis; palette = nothing)
     register_events!(ax, scene)
 
     # these are the user defined limits
-    on(blockscene, ax.limits) do mlims
+    on(blockscene, ax.limits) do _
         reset_limits!(ax)
     end
 
diff --git a/src/types.jl b/src/types.jl
index d6629cc4d93..74b1463d79a 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -387,7 +387,11 @@ struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     logbase::String
     limits::NTuple{2,Float32}
     interval::I
-    function ReversibleScale(forward, backward; logbase = "", limits = (0f0, 10f0), interval = OpenInterval(-Inf32, Inf32))
+    function ReversibleScale(forward, backward; logbase = "", limits = (0f0, 10f0), interval = (-Inf32, Inf32))
+        if !(interval isa AbstractInterval)
+            interval = OpenInterval(Float32.(interval)...)
+        end
+        limits = Tuple(Float32.(limits))
         new{typeof(forward),typeof(backward),typeof(interval)}(forward, backward, logbase, limits, interval)
     end
 end

From 93a4af3dc8f73a01cff057977619c7248933aee7 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Fri, 11 Aug 2023 12:34:42 +0200
Subject: [PATCH 06/18] add docstring

---
 src/types.jl | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/src/types.jl b/src/types.jl
index 74b1463d79a..bf4907169b5 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -200,6 +200,9 @@ end
 
 Struct to hold all relevant matrices and additional parameters, to let backends
 apply camera based transformations.
+
+## Fields
+$(TYPEDFIELDS)
 """
 struct Camera
     """
@@ -381,11 +384,34 @@ const RGBColors = Union{RGBAf, Vector{RGBAf}, Vector{Float32}}
 
 const LogFunctions = Union{typeof(log10), typeof(log2), typeof(log)}
 
+"""
+    ReversibleScale
+
+Custom scale struct, taking a scaling (forward) and an inverse (backward) arbitrary scale function.
+
+## Fields
+$(TYPEDFIELDS)
+"""
 struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
+    """
+    forward transformation (e.g. `log10`)
+    """
     forward::F
+    """
+    inverse transformation (e.g. `exp10` for `log10` such that backward ∘ forward ≡ identity)
+    """
     backward::B
+    """
+    ticks base (e.g. "10" for pseudo `log10` ticks) (optional)
+    """
     logbase::String
+    """
+    default limits (optional)
+    """
     limits::NTuple{2,Float32}
+    """
+    valid limits interval (optional)
+    """
     interval::I
     function ReversibleScale(forward, backward; logbase = "", limits = (0f0, 10f0), interval = (-Inf32, Inf32))
         if !(interval isa AbstractInterval)

From 82c68d4a873a9c4c27955dc6a9f3e0c597dede3b Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Sun, 20 Aug 2023 14:22:24 +0200
Subject: [PATCH 07/18] apply sugestions - clarify warnings

---
 src/makielayout/blocks/colorbar.jl | 2 +-
 src/makielayout/lineaxis.jl        | 4 ++--
 src/types.jl                       | 4 ++--
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index f8fc60d1788..0f15019f686 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -70,7 +70,7 @@ end
 
 colorbar_range(start, stop, length, _::typeof(identity)) = LinRange(start, stop, length)
 function colorbar_range(start, stop, length, _)
-    @warn "cannot determine inverse_transform"
+    @warn "Cannot determine inverse transform: maybe use `Makie.ReverseibleScale` instead ? "
     colorbar_range(start, stop, length, identity)  # noop (nothing we can do, bailing out)
 end
 
diff --git a/src/makielayout/lineaxis.jl b/src/makielayout/lineaxis.jl
index 8edbb27394b..a540eb7157a 100644
--- a/src/makielayout/lineaxis.jl
+++ b/src/makielayout/lineaxis.jl
@@ -585,11 +585,11 @@ _logbase(s::ReversibleScale) = s.logbase
 _logbase(::typeof(log10)) = "10"
 _logbase(::typeof(log2)) = "2"
 _logbase(::typeof(log)) = "e"
-_logbase(::Any) = ""
+_logbase(::Any) = nothing
 
 function get_ticks(::Automatic, scale::Union{LogFunctions,ReversibleScale}, any_formatter, vmin, vmax)
     wt = WilkinsonTicks(5, k_min = 3)
-    ticks = isempty(_logbase(scale)) ? wt : LogTicks(wt)
+    ticks = isnothing(_logbase(scale)) ? wt : LogTicks(wt)
     get_ticks(ticks, scale, any_formatter, vmin, vmax)
 end
 
diff --git a/src/types.jl b/src/types.jl
index bf4907169b5..763968da018 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -404,7 +404,7 @@ struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     """
     ticks base (e.g. "10" for pseudo `log10` ticks) (optional)
     """
-    logbase::String
+    logbase::Union{Nothing,String}
     """
     default limits (optional)
     """
@@ -413,7 +413,7 @@ struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     valid limits interval (optional)
     """
     interval::I
-    function ReversibleScale(forward, backward; logbase = "", limits = (0f0, 10f0), interval = (-Inf32, Inf32))
+    function ReversibleScale(forward, backward; logbase = nothing, limits = (0f0, 10f0), interval = (-Inf32, Inf32))
         if !(interval isa AbstractInterval)
             interval = OpenInterval(Float32.(interval)...)
         end

From 4ec2f989f2878fd45bb766537346222b7f969b7d Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Sun, 20 Aug 2023 17:13:42 +0200
Subject: [PATCH 08/18] remove space

---
 src/colorsampler.jl                | 4 ++--
 src/makielayout/blocks/colorbar.jl | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/colorsampler.jl b/src/colorsampler.jl
index 929a26ea84d..47a16029f98 100644
--- a/src/colorsampler.jl
+++ b/src/colorsampler.jl
@@ -179,7 +179,7 @@ end
 struct ColorMap{N,T<:AbstractArray{<:Number,N},T2<:AbstractArray{<:Number,N}}
     color::Observable{T}
     colormap::Observable{Vector{RGBAf}}
-    scale::Observable{Union{ReversibleScale,Function}}
+    scale::Observable{Union{ReversibleScale, Function}}
     mapping::Observable{Union{Nothing, Vector{Float64}}}
     colorrange::Observable{Vec{2,Float64}}
 
@@ -198,7 +198,7 @@ function assemble_colors(::T, @nospecialize(color), @nospecialize(plot)) where {
     color_tight = convert(Observable{T}, color)
     colormap = Observable(RGBAf[]; ignore_equal_values=true)
     categorical = Observable(false)
-    colorscale = convert(Observable, plot.colorscale)
+    colorscale = convert(Observable{Union{ReversibleScale, Function}}, plot.colorscale)
     mapping = Observable{Union{Nothing, Vector{Float64}}}(nothing)
 
     function update_colors(cmap, a)
diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index 0f15019f686..979f0f1eadc 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -70,7 +70,7 @@ end
 
 colorbar_range(start, stop, length, _::typeof(identity)) = LinRange(start, stop, length)
 function colorbar_range(start, stop, length, _)
-    @warn "Cannot determine inverse transform: maybe use `Makie.ReverseibleScale` instead ? "
+    @warn "Cannot determine inverse transform: maybe use `Makie.ReverseibleScale` instead ?"
     colorbar_range(start, stop, length, identity)  # noop (nothing we can do, bailing out)
 end
 

From 7befef13d965b3e21356b680b8a933a3806d4d49 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 22 Aug 2023 19:03:53 +0200
Subject: [PATCH 09/18] simplify `colorbar_range`

---
 src/layouting/transformation.jl    | 10 ----------
 src/makielayout/blocks/colorbar.jl | 16 ++++++++--------
 2 files changed, 8 insertions(+), 18 deletions(-)

diff --git a/src/layouting/transformation.jl b/src/layouting/transformation.jl
index 86195495856..be9edbab9a4 100644
--- a/src/layouting/transformation.jl
+++ b/src/layouting/transformation.jl
@@ -399,16 +399,6 @@ function inv_symlog10(x, low, high)
     end
 end
 
-const REVERSIBLE_SCALES = Union{
-    # typeof(identity),  # no, this is a noop
-    LogFunctions,
-    typeof(pseudolog10),
-    typeof(logit),
-    typeof(sqrt),
-    ReversibleScale,
-    Symlog10,
-}
-
 inverse_transform(::typeof(identity)) = identity
 inverse_transform(::typeof(log10)) = exp10
 inverse_transform(::typeof(log)) = exp
diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index 8aa4be14438..374a933099c 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -90,14 +90,14 @@ function Colorbar(fig_or_scene, voronoi::Voronoiplot; kwargs...)
     )
 end
 
-colorbar_range(start, stop, length, _::typeof(identity)) = LinRange(start, stop, length)
-function colorbar_range(start, stop, length, _)
-    @warn "Cannot determine inverse transform: maybe use `Makie.ReverseibleScale` instead ?"
-    colorbar_range(start, stop, length, identity)  # noop (nothing we can do, bailing out)
-end
-
-function colorbar_range(start, stop, length, scale::REVERSIBLE_SCALES)
-    inverse_transform(scale).(range(start, stop; length))
+function colorbar_range(start, stop, length, colorscale)
+    rev = inverse_transform(colorscale)
+    if isnothing(rev)
+        @warn "Cannot determine inverse transform: you can use `colorscale=Makie.ReversibleScale($(colorscale), reverse($(colorscale)))` instead.
+Falling back to `identity`, which leads to sub optimal ticks!"
+        return LinRange(start, stop, length)
+    end
+    rev.(range(start, stop; length))
 end
 
 function initialize_block!(cb::Colorbar)

From 70113ca781739f48ecb2619825bd4073abe0d703 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Wed, 23 Aug 2023 18:03:12 +0200
Subject: [PATCH 10/18] add inverse transform checks

---
 src/layouting/transformation.jl    |  6 +++---
 src/makielayout/blocks/colorbar.jl | 14 +++++++-------
 src/types.jl                       | 26 +++++++++++++++++---------
 test/makielayout.jl                | 12 ++++++++++++
 4 files changed, 39 insertions(+), 19 deletions(-)

diff --git a/src/layouting/transformation.jl b/src/layouting/transformation.jl
index be9edbab9a4..b1541407ad8 100644
--- a/src/layouting/transformation.jl
+++ b/src/layouting/transformation.jl
@@ -401,15 +401,15 @@ end
 
 inverse_transform(::typeof(identity)) = identity
 inverse_transform(::typeof(log10)) = exp10
-inverse_transform(::typeof(log)) = exp
 inverse_transform(::typeof(log2)) = exp2
+inverse_transform(::typeof(log)) = exp
 inverse_transform(::typeof(sqrt)) = x -> x ^ 2
 inverse_transform(::typeof(pseudolog10)) = inv_pseudolog10
 inverse_transform(F::Tuple) = map(inverse_transform, F)
 inverse_transform(::typeof(logit)) = logistic
-inverse_transform(s::ReversibleScale) = s.backward
+inverse_transform(s::ReversibleScale) = s.reverse
 inverse_transform(s::Symlog10) = x -> inv_symlog10(x, s.low, s.high)
-inverse_transform(s) = nothing
+inverse_transform(::Any) = nothing
 
 function is_identity_transform(t)
     return t === identity || t isa Tuple && all(x-> x === identity, t)
diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index 374a933099c..a23240397c9 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -91,13 +91,13 @@ function Colorbar(fig_or_scene, voronoi::Voronoiplot; kwargs...)
 end
 
 function colorbar_range(start, stop, length, colorscale)
-    rev = inverse_transform(colorscale)
-    if isnothing(rev)
-        @warn "Cannot determine inverse transform: you can use `colorscale=Makie.ReversibleScale($(colorscale), reverse($(colorscale)))` instead.
-Falling back to `identity`, which leads to sub optimal ticks!"
-        return LinRange(start, stop, length)
-    end
-    rev.(range(start, stop; length))
+    colorscale === identity && return LinRange(start, stop, length)
+
+    reverse = inverse_transform(colorscale)
+    isnothing(reverse) && throw(ArgumentError(
+        "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(colorscale), reverse($(colorscale)))` instead."
+    ))
+    reverse.(range(start, stop; length))
 end
 
 function initialize_block!(cb::Colorbar)
diff --git a/src/types.jl b/src/types.jl
index 763968da018..53e9e1316a7 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -387,7 +387,7 @@ const LogFunctions = Union{typeof(log10), typeof(log2), typeof(log)}
 """
     ReversibleScale
 
-Custom scale struct, taking a scaling (forward) and an inverse (backward) arbitrary scale function.
+Custom scale struct, taking a forward and reverse arbitrary scale function.
 
 ## Fields
 $(TYPEDFIELDS)
@@ -398,9 +398,9 @@ struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     """
     forward::F
     """
-    inverse transformation (e.g. `exp10` for `log10` such that backward ∘ forward ≡ identity)
+    reverse transformation (e.g. `exp10` for `log10` such that reverse ∘ forward ≡ identity)
     """
-    backward::B
+    reverse::B
     """
     ticks base (e.g. "10" for pseudo `log10` ticks) (optional)
     """
@@ -413,12 +413,20 @@ struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     valid limits interval (optional)
     """
     interval::I
-    function ReversibleScale(forward, backward; logbase = nothing, limits = (0f0, 10f0), interval = (-Inf32, Inf32))
-        if !(interval isa AbstractInterval)
-            interval = OpenInterval(Float32.(interval)...)
-        end
-        limits = Tuple(Float32.(limits))
-        new{typeof(forward),typeof(backward),typeof(interval)}(forward, backward, logbase, limits, interval)
+    function ReversibleScale(forward, reverse = Automatic(); logbase = nothing, limits = (0f0, 10f0), interval = (-Inf32, Inf32))
+        reverse isa Automatic && (reverse = inverse_transform(forward))
+        isnothing(reverse) && throw(ArgumentError(
+            "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(forward), reverse($(forward)))` instead."
+        ))
+        interval isa AbstractInterval || (interval = OpenInterval(Float32.(interval)...))
+
+        lft, rgt = limits = Tuple(Float32.(limits))
+
+        Id = reverse ∘ forward
+        lft ≈ Id(lft) || throw(ArgumentError("Invalid inverse transform: $lft !≈ $(Id(lft))"))
+        rgt ≈ Id(rgt) || throw(ArgumentError("Invalid inverse transform: $rgt !≈ $(Id(rgt))"))
+
+        new{typeof(forward),typeof(reverse),typeof(interval)}(forward, reverse, logbase, limits, interval)
     end
 end
 
diff --git a/test/makielayout.jl b/test/makielayout.jl
index 8d0bd20d107..b8e67b3c86a 100644
--- a/test/makielayout.jl
+++ b/test/makielayout.jl
@@ -376,3 +376,15 @@ end
     @test_nowarn axislegend()
     f
 end
+
+@testset "ReversibleScale" begin
+    @test Makie.ReversibleScale(identity).reverse === identity
+    @test Makie.ReversibleScale(log).reverse === exp
+    @test_throws ArgumentError Makie.ReversibleScale(x -> log10(x))  # missing reverse scale
+    @test_throws ArgumentError Makie.ReversibleScale(sqrt, exp10)  # incorrect reverse scale
+end
+
+@testset "Invalid inverse transform" begin
+    f = Figure()
+    @test_throws ArgumentError Colorbar(f[1, 1], limits = (1, 100), scale = x -> log10(x))
+end

From 17454b5acfa381503edd92b074002bc7a738042d Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Wed, 23 Aug 2023 18:54:16 +0200
Subject: [PATCH 11/18] renames

---
 src/layouting/transformation.jl    |  2 +-
 src/makielayout/blocks/colorbar.jl |  9 +++++----
 src/types.jl                       | 24 ++++++++++++------------
 test/makielayout.jl                |  8 ++++----
 4 files changed, 22 insertions(+), 21 deletions(-)

diff --git a/src/layouting/transformation.jl b/src/layouting/transformation.jl
index b1541407ad8..19b25aaa250 100644
--- a/src/layouting/transformation.jl
+++ b/src/layouting/transformation.jl
@@ -407,7 +407,7 @@ inverse_transform(::typeof(sqrt)) = x -> x ^ 2
 inverse_transform(::typeof(pseudolog10)) = inv_pseudolog10
 inverse_transform(F::Tuple) = map(inverse_transform, F)
 inverse_transform(::typeof(logit)) = logistic
-inverse_transform(s::ReversibleScale) = s.reverse
+inverse_transform(s::ReversibleScale) = s.inverse
 inverse_transform(s::Symlog10) = x -> inv_symlog10(x, s.low, s.high)
 inverse_transform(::Any) = nothing
 
diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index a23240397c9..7a4accf7deb 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -93,11 +93,12 @@ end
 function colorbar_range(start, stop, length, colorscale)
     colorscale === identity && return LinRange(start, stop, length)
 
-    reverse = inverse_transform(colorscale)
-    isnothing(reverse) && throw(ArgumentError(
-        "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(colorscale), reverse($(colorscale)))` instead."
+    inverse = inverse_transform(colorscale)
+    isnothing(inverse) && throw(ArgumentError(
+        "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(colorscale), inverse($(colorscale)))` instead."
     ))
-    reverse.(range(start, stop; length))
+
+    inverse.(range(start, stop; length))
 end
 
 function initialize_block!(cb::Colorbar)
diff --git a/src/types.jl b/src/types.jl
index 53e9e1316a7..95bba20cf8c 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -387,22 +387,22 @@ const LogFunctions = Union{typeof(log10), typeof(log2), typeof(log)}
 """
     ReversibleScale
 
-Custom scale struct, taking a forward and reverse arbitrary scale function.
+Custom scale struct, taking a forward and inverse arbitrary scale function.
 
 ## Fields
 $(TYPEDFIELDS)
 """
-struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
+struct ReversibleScale{F <: Function, I <: Function, T <: AbstractInterval}
     """
     forward transformation (e.g. `log10`)
     """
     forward::F
     """
-    reverse transformation (e.g. `exp10` for `log10` such that reverse ∘ forward ≡ identity)
+    inverse transformation (e.g. `exp10` for `log10` such that inverse ∘ forward ≡ identity)
     """
-    reverse::B
+    inverse::I
     """
-    ticks base (e.g. "10" for pseudo `log10` ticks) (optional)
+    LogTicks base (e.g. "10" for pseudo log ticks) (optional)
     """
     logbase::Union{Nothing,String}
     """
@@ -412,21 +412,21 @@ struct ReversibleScale{F <: Function, B <: Function, I <: AbstractInterval}
     """
     valid limits interval (optional)
     """
-    interval::I
-    function ReversibleScale(forward, reverse = Automatic(); logbase = nothing, limits = (0f0, 10f0), interval = (-Inf32, Inf32))
-        reverse isa Automatic && (reverse = inverse_transform(forward))
-        isnothing(reverse) && throw(ArgumentError(
-            "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(forward), reverse($(forward)))` instead."
+    interval::T
+    function ReversibleScale(forward, inverse = Automatic(); logbase = nothing, limits = (0f0, 10f0), interval = (-Inf32, Inf32))
+        inverse isa Automatic && (inverse = inverse_transform(forward))
+        isnothing(inverse) && throw(ArgumentError(
+            "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(forward), inverse($(forward)))` instead."
         ))
         interval isa AbstractInterval || (interval = OpenInterval(Float32.(interval)...))
 
         lft, rgt = limits = Tuple(Float32.(limits))
 
-        Id = reverse ∘ forward
+        Id = inverse ∘ forward
         lft ≈ Id(lft) || throw(ArgumentError("Invalid inverse transform: $lft !≈ $(Id(lft))"))
         rgt ≈ Id(rgt) || throw(ArgumentError("Invalid inverse transform: $rgt !≈ $(Id(rgt))"))
 
-        new{typeof(forward),typeof(reverse),typeof(interval)}(forward, reverse, logbase, limits, interval)
+        new{typeof(forward),typeof(inverse),typeof(interval)}(forward, inverse, logbase, limits, interval)
     end
 end
 
diff --git a/test/makielayout.jl b/test/makielayout.jl
index b8e67b3c86a..32e5ea2cde7 100644
--- a/test/makielayout.jl
+++ b/test/makielayout.jl
@@ -378,10 +378,10 @@ end
 end
 
 @testset "ReversibleScale" begin
-    @test Makie.ReversibleScale(identity).reverse === identity
-    @test Makie.ReversibleScale(log).reverse === exp
-    @test_throws ArgumentError Makie.ReversibleScale(x -> log10(x))  # missing reverse scale
-    @test_throws ArgumentError Makie.ReversibleScale(sqrt, exp10)  # incorrect reverse scale
+    @test Makie.ReversibleScale(identity).inverse === identity
+    @test Makie.ReversibleScale(log).inverse === exp
+    @test_throws ArgumentError Makie.ReversibleScale(x -> log10(x))  # missing inverse scale
+    @test_throws ArgumentError Makie.ReversibleScale(sqrt, exp10)  # incorrect inverse scale
 end
 
 @testset "Invalid inverse transform" begin

From ef8c387e9d06c355f1e4c3d2e7de667e2165d7a6 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Sun, 27 Aug 2023 15:29:32 +0200
Subject: [PATCH 12/18] drop `LogTicks` - rework `Symlog10` and `pseudolog10`

---
 src/layouting/transformation.jl | 49 +++++++++++----------------------
 src/makielayout/blocks/axis.jl  |  8 +++---
 src/makielayout/lineaxis.jl     | 12 +++-----
 src/types.jl                    |  8 ++----
 test/makielayout.jl             | 14 ++++++++++
 5 files changed, 40 insertions(+), 51 deletions(-)

diff --git a/src/layouting/transformation.jl b/src/layouting/transformation.jl
index 19b25aaa250..8859ff918cd 100644
--- a/src/layouting/transformation.jl
+++ b/src/layouting/transformation.jl
@@ -339,7 +339,6 @@ function apply_transform(f, itr::ClosedInterval)
     return apply_transform(f, mini) .. apply_transform(f, maxi)
 end
 
-
 function apply_transform(f, r::Rect)
     mi = minimum(r)
     ma = maximum(r)
@@ -360,55 +359,39 @@ apply_transform(f::typeof(identity), r::Rect) = r
 apply_transform(f::NTuple{2, typeof(identity)}, r::Rect) = r
 apply_transform(f::NTuple{3, typeof(identity)}, r::Rect) = r
 
+const pseudolog10 = ReversibleScale(
+    x -> sign(x) * log10(abs(x) + 1),
+    x -> sign(x) * (exp10(abs(x)) - 1)
+)
 
-pseudolog10(x) = sign(x) * log10(abs(x) + 1)
-inv_pseudolog10(x) = sign(x) * (exp10(abs(x)) - 1)
-
-struct Symlog10
-    low::Float64
-    high::Float64
-    function Symlog10(low, high)
-        if !(low < 0 && high > 0)
-            error("Low bound needs to be smaller than 0 and high bound larger than 0. You gave $low, $high.")
-        end
-        new(Float64(low), Float64(high))
-    end
-end
-
-Symlog10(x) = Symlog10(-x, x)
-
-function (s::Symlog10)(x)
-    if x > 0
-        x <= s.high ? x / s.high * log10(s.high) : log10(x)
+Symlog10(hi) = Symlog10(-hi, hi)
+Symlog10(lo, hi) = ReversibleScale(
+    x -> if x > 0
+        x <= hi ? x / hi * log10(hi) : log10(x)
     elseif x < 0
-        x >= s.low ? x / abs(s.low) * log10(abs(s.low)) : sign(x) * log10(abs(x))
+        x >= lo ? x / abs(lo) * log10(abs(lo)) : -log10(abs(x))
     else
         x
-    end
-end
-
-function inv_symlog10(x, low, high)
-    if x > 0
-        l = log10(high)
-        x <= l ? x / l * high : exp10(x)
+    end,
+    x -> if x > 0
+        l = log10(hi)
+        x <= l ? x / l * hi : exp10(x)
     elseif x < 0
-        l = sign(x) * log10(abs(low))
-        x >= l ? x / l * abs(low) : sign(x) * exp10(abs(x))
+        l = -log10(abs(lo))
+        x >= l ? x / l * abs(lo) : -exp10(abs(x))
     else
         x
     end
-end
+)
 
 inverse_transform(::typeof(identity)) = identity
 inverse_transform(::typeof(log10)) = exp10
 inverse_transform(::typeof(log2)) = exp2
 inverse_transform(::typeof(log)) = exp
 inverse_transform(::typeof(sqrt)) = x -> x ^ 2
-inverse_transform(::typeof(pseudolog10)) = inv_pseudolog10
 inverse_transform(F::Tuple) = map(inverse_transform, F)
 inverse_transform(::typeof(logit)) = logistic
 inverse_transform(s::ReversibleScale) = s.inverse
-inverse_transform(s::Symlog10) = x -> inv_symlog10(x, s.low, s.high)
 inverse_transform(::Any) = nothing
 
 function is_identity_transform(t)
diff --git a/src/makielayout/blocks/axis.jl b/src/makielayout/blocks/axis.jl
index a8021f98ca9..e194faed532 100644
--- a/src/makielayout/blocks/axis.jl
+++ b/src/makielayout/blocks/axis.jl
@@ -1363,16 +1363,16 @@ end
 defaultlimits(::typeof(identity)) = (0.0, 10.0)
 defaultlimits(::typeof(sqrt)) = (0.0, 100.0)
 defaultlimits(::typeof(Makie.logit)) = (0.01, 0.99)
-defaultlimits(::typeof(Makie.pseudolog10)) = (0.0, 100.0)
-defaultlimits(::Makie.Symlog10) = (0.0, 100.0)
+# defaultlimits(::typeof(Makie.pseudolog10)) = (0.0, 100.0)
+# defaultlimits(::Makie.Symlog10) = (0.0, 100.0)
 
 defined_interval(scale::ReversibleScale) = scale.interval
 defined_interval(::typeof(identity)) = OpenInterval(-Inf, Inf)
 defined_interval(::LogFunctions) = OpenInterval(0.0, Inf)
 defined_interval(::typeof(sqrt)) = Interval{:closed,:open}(0, Inf)
 defined_interval(::typeof(Makie.logit)) = OpenInterval(0.0, 1.0)
-defined_interval(::typeof(Makie.pseudolog10)) = OpenInterval(-Inf, Inf)
-defined_interval(::Makie.Symlog10) = OpenInterval(-Inf, Inf)
+# defined_interval(::typeof(Makie.pseudolog10)) = OpenInterval(-Inf, Inf)
+# defined_interval(::Makie.Symlog10) = OpenInterval(-Inf, Inf)
 
 function update_state_before_display!(ax::Axis)
     reset_limits!(ax)
diff --git a/src/makielayout/lineaxis.jl b/src/makielayout/lineaxis.jl
index a540eb7157a..41ee1c9a100 100644
--- a/src/makielayout/lineaxis.jl
+++ b/src/makielayout/lineaxis.jl
@@ -581,20 +581,17 @@ function get_ticks(tickfunction::Function, _, formatter, vmin, vmax)
     return tickvalues, ticklabels
 end
 
-_logbase(s::ReversibleScale) = s.logbase
 _logbase(::typeof(log10)) = "10"
 _logbase(::typeof(log2)) = "2"
 _logbase(::typeof(log)) = "e"
-_logbase(::Any) = nothing
 
-function get_ticks(::Automatic, scale::Union{LogFunctions,ReversibleScale}, any_formatter, vmin, vmax)
-    wt = WilkinsonTicks(5, k_min = 3)
-    ticks = isnothing(_logbase(scale)) ? wt : LogTicks(wt)
+function get_ticks(::Automatic, scale::LogFunctions, any_formatter, vmin, vmax)
+    ticks = LogTicks(WilkinsonTicks(5, k_min = 3))
     get_ticks(ticks, scale, any_formatter, vmin, vmax)
 end
 
 # log ticks just use the normal pipeline but with log'd limits, then transform the labels
-function get_ticks(l::LogTicks, scale::Union{LogFunctions,ReversibleScale}, ::Automatic, vmin, vmax)
+function get_ticks(l::LogTicks, scale::LogFunctions, ::Automatic, vmin, vmax)
     ticks_scaled = get_tickvalues(l.linear_ticks, identity, scale(vmin), scale(vmax))
 
     ticks = Makie.inverse_transform(scale).(ticks_scaled)
@@ -607,7 +604,7 @@ function get_ticks(l::LogTicks, scale::Union{LogFunctions,ReversibleScale}, ::Au
     )
     labels = rich.(_logbase(scale), superscript.(labels_scaled, offset = Vec2f(0.1f0, 0f0)))
 
-    (ticks, labels)
+    ticks, labels
 end
 
 # function get_ticks(::Automatic, scale::typeof(Makie.logit), any_formatter, vmin, vmax)
@@ -686,7 +683,6 @@ Gets tick labels by formatting each value in `values` according to a `Formatting
 """
 get_ticklabels(formatstring::AbstractString, values) = [Formatting.format(formatstring, v) for v in values]
 
-
 function get_ticks(m::MultiplesTicks, any_scale, ::Automatic, vmin, vmax)
     dvmin = vmin / m.multiple
     dvmax = vmax / m.multiple
diff --git a/src/types.jl b/src/types.jl
index 95bba20cf8c..d16d13fc561 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -402,10 +402,6 @@ struct ReversibleScale{F <: Function, I <: Function, T <: AbstractInterval}
     """
     inverse::I
     """
-    LogTicks base (e.g. "10" for pseudo log ticks) (optional)
-    """
-    logbase::Union{Nothing,String}
-    """
     default limits (optional)
     """
     limits::NTuple{2,Float32}
@@ -413,7 +409,7 @@ struct ReversibleScale{F <: Function, I <: Function, T <: AbstractInterval}
     valid limits interval (optional)
     """
     interval::T
-    function ReversibleScale(forward, inverse = Automatic(); logbase = nothing, limits = (0f0, 10f0), interval = (-Inf32, Inf32))
+    function ReversibleScale(forward, inverse = Automatic(); limits = (0f0, 10f0), interval = (-Inf32, Inf32))
         inverse isa Automatic && (inverse = inverse_transform(forward))
         isnothing(inverse) && throw(ArgumentError(
             "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(forward), inverse($(forward)))` instead."
@@ -426,7 +422,7 @@ struct ReversibleScale{F <: Function, I <: Function, T <: AbstractInterval}
         lft ≈ Id(lft) || throw(ArgumentError("Invalid inverse transform: $lft !≈ $(Id(lft))"))
         rgt ≈ Id(rgt) || throw(ArgumentError("Invalid inverse transform: $rgt !≈ $(Id(rgt))"))
 
-        new{typeof(forward),typeof(inverse),typeof(interval)}(forward, inverse, logbase, limits, interval)
+        new{typeof(forward),typeof(inverse),typeof(interval)}(forward, inverse, limits, interval)
     end
 end
 
diff --git a/test/makielayout.jl b/test/makielayout.jl
index 32e5ea2cde7..8cdd41ff8c9 100644
--- a/test/makielayout.jl
+++ b/test/makielayout.jl
@@ -388,3 +388,17 @@ end
     f = Figure()
     @test_throws ArgumentError Colorbar(f[1, 1], limits = (1, 100), scale = x -> log10(x))
 end
+
+@testset "Colorscales" begin
+    x = 10.0.^(1:0.1:4)
+    y = 1.0:0.1:5.0
+    z = broadcast((x, y) -> x, x, y')
+
+    scale = Makie.Symlog10(2)
+    fig, ax, hm = heatmap(x, y, z; colorscale = scale, axis = (; xscale = scale))
+    Colorbar(fig[1, 2], hm)
+
+    scale = Makie.pseudolog10
+    fig, ax, hm = heatmap(x, y, z; colorscale = scale, axis = (; xscale = scale))
+    Colorbar(fig[1, 2], hm)
+end

From 512d9f46b55d97e4cb416b62f3a54907f8191026 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Sun, 27 Aug 2023 16:08:42 +0200
Subject: [PATCH 13/18] add limits

---
 src/layouting/transformation.jl | 14 ++++++++------
 src/makielayout/blocks/axis.jl  |  4 ----
 2 files changed, 8 insertions(+), 10 deletions(-)

diff --git a/src/layouting/transformation.jl b/src/layouting/transformation.jl
index 8859ff918cd..c7a31c4deda 100644
--- a/src/layouting/transformation.jl
+++ b/src/layouting/transformation.jl
@@ -361,19 +361,20 @@ apply_transform(f::NTuple{3, typeof(identity)}, r::Rect) = r
 
 const pseudolog10 = ReversibleScale(
     x -> sign(x) * log10(abs(x) + 1),
-    x -> sign(x) * (exp10(abs(x)) - 1)
+    x -> sign(x) * (exp10(abs(x)) - 1);
+    limits=(0f0, 3f0)
 )
 
 Symlog10(hi) = Symlog10(-hi, hi)
-Symlog10(lo, hi) = ReversibleScale(
-    x -> if x > 0
+function Symlog10(lo, hi)
+    forward(x) = if x > 0
         x <= hi ? x / hi * log10(hi) : log10(x)
     elseif x < 0
         x >= lo ? x / abs(lo) * log10(abs(lo)) : -log10(abs(x))
     else
         x
-    end,
-    x -> if x > 0
+    end
+    inverse(x) = if x > 0
         l = log10(hi)
         x <= l ? x / l * hi : exp10(x)
     elseif x < 0
@@ -382,7 +383,8 @@ Symlog10(lo, hi) = ReversibleScale(
     else
         x
     end
-)
+    ReversibleScale(forward, inverse; limits=(0f0, 3f0))
+end
 
 inverse_transform(::typeof(identity)) = identity
 inverse_transform(::typeof(log10)) = exp10
diff --git a/src/makielayout/blocks/axis.jl b/src/makielayout/blocks/axis.jl
index e194faed532..ad179a11e3e 100644
--- a/src/makielayout/blocks/axis.jl
+++ b/src/makielayout/blocks/axis.jl
@@ -1363,16 +1363,12 @@ end
 defaultlimits(::typeof(identity)) = (0.0, 10.0)
 defaultlimits(::typeof(sqrt)) = (0.0, 100.0)
 defaultlimits(::typeof(Makie.logit)) = (0.01, 0.99)
-# defaultlimits(::typeof(Makie.pseudolog10)) = (0.0, 100.0)
-# defaultlimits(::Makie.Symlog10) = (0.0, 100.0)
 
 defined_interval(scale::ReversibleScale) = scale.interval
 defined_interval(::typeof(identity)) = OpenInterval(-Inf, Inf)
 defined_interval(::LogFunctions) = OpenInterval(0.0, Inf)
 defined_interval(::typeof(sqrt)) = Interval{:closed,:open}(0, Inf)
 defined_interval(::typeof(Makie.logit)) = OpenInterval(0.0, 1.0)
-# defined_interval(::typeof(Makie.pseudolog10)) = OpenInterval(-Inf, Inf)
-# defined_interval(::Makie.Symlog10) = OpenInterval(-Inf, Inf)
 
 function update_state_before_display!(ax::Axis)
     reset_limits!(ax)

From 774488337699fbf5a1e20e2a49475eb8948945d7 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Sun, 27 Aug 2023 16:58:50 +0200
Subject: [PATCH 14/18] remove test

---
 ReferenceTests/src/tests/examples2d.jl | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/ReferenceTests/src/tests/examples2d.jl b/ReferenceTests/src/tests/examples2d.jl
index e0a97ceaae8..1b60e466edb 100644
--- a/ReferenceTests/src/tests/examples2d.jl
+++ b/ReferenceTests/src/tests/examples2d.jl
@@ -597,15 +597,6 @@ end
     fig
 end
 
-@reference_test "custom colorscale (heatmap)" begin
-    x = 10.0.^(1:0.1:4)
-    y = 1.0:0.1:5.0
-    scale = Makie.ReversibleScale(x -> log10(x + 2), x -> exp10(x) - 2; logbase = "10")
-    fig, ax, hm = heatmap(x, y, (x, y) -> x; axis = (; xscale = scale), colorscale = scale)
-    Colorbar(fig[1, 2], hm)
-    fig
-end
-
 @reference_test "colorscale (lines)" begin
     xs = 0:0.01:10
     ys = 2 .* (1 .+ sin.(xs))

From 254f0a2cf075b929f63fb627af9d624e66a2ea47 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 29 Aug 2023 18:32:45 +0200
Subject: [PATCH 15/18] export `ReversibleScale`

---
 NEWS.md                            | 2 +-
 src/Makie.jl                       | 1 +
 src/makielayout/blocks/colorbar.jl | 2 +-
 src/types.jl                       | 2 +-
 test/makielayout.jl                | 8 ++++----
 5 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/NEWS.md b/NEWS.md
index 904d2bf94b2..e039f6e4f21 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,7 +1,7 @@
 # News
 
 ## master
-- Allow arbitrary reversible scale functions through `Makie.ReversibleScale`.
+- Allow arbitrary reversible scale functions through `ReversibleScale`.
 
 - Fixed some errors around dynamic changes of `ax.xscale` or `ax.yscale` [#3084](https://github.com/MakieOrg/Makie.jl/pull/3084)
 - Improved Barplot Label Alignment [#3160](https://github.com/MakieOrg/Makie.jl/issues/3160).
diff --git a/src/Makie.jl b/src/Makie.jl
index 11c719e6f70..3b954500da7 100644
--- a/src/Makie.jl
+++ b/src/Makie.jl
@@ -286,6 +286,7 @@ export save, colorbuffer
 export cgrad, available_gradients, showgradients
 
 export Pattern
+export ReversibleScale
 
 export assetpath
 # default icon for Makie
diff --git a/src/makielayout/blocks/colorbar.jl b/src/makielayout/blocks/colorbar.jl
index 7a4accf7deb..266d6efb049 100644
--- a/src/makielayout/blocks/colorbar.jl
+++ b/src/makielayout/blocks/colorbar.jl
@@ -95,7 +95,7 @@ function colorbar_range(start, stop, length, colorscale)
 
     inverse = inverse_transform(colorscale)
     isnothing(inverse) && throw(ArgumentError(
-        "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(colorscale), inverse($(colorscale)))` instead."
+        "Cannot determine inverse transform: you can use `ReversibleScale($(colorscale), inverse($(colorscale)))` instead."
     ))
 
     inverse.(range(start, stop; length))
diff --git a/src/types.jl b/src/types.jl
index d16d13fc561..fd8fb4078c6 100644
--- a/src/types.jl
+++ b/src/types.jl
@@ -412,7 +412,7 @@ struct ReversibleScale{F <: Function, I <: Function, T <: AbstractInterval}
     function ReversibleScale(forward, inverse = Automatic(); limits = (0f0, 10f0), interval = (-Inf32, Inf32))
         inverse isa Automatic && (inverse = inverse_transform(forward))
         isnothing(inverse) && throw(ArgumentError(
-            "Cannot determine inverse transform: you can use `Makie.ReversibleScale($(forward), inverse($(forward)))` instead."
+            "Cannot determine inverse transform: you can use `ReversibleScale($(forward), inverse($(forward)))` instead."
         ))
         interval isa AbstractInterval || (interval = OpenInterval(Float32.(interval)...))
 
diff --git a/test/makielayout.jl b/test/makielayout.jl
index 596251dbc01..54ebaec3f7c 100644
--- a/test/makielayout.jl
+++ b/test/makielayout.jl
@@ -378,10 +378,10 @@ end
 end
 
 @testset "ReversibleScale" begin
-    @test Makie.ReversibleScale(identity).inverse === identity
-    @test Makie.ReversibleScale(log).inverse === exp
-    @test_throws ArgumentError Makie.ReversibleScale(x -> log10(x))  # missing inverse scale
-    @test_throws ArgumentError Makie.ReversibleScale(sqrt, exp10)  # incorrect inverse scale
+    @test ReversibleScale(identity).inverse === identity
+    @test ReversibleScale(log).inverse === exp
+    @test_throws ArgumentError ReversibleScale(x -> log10(x))  # missing inverse scale
+    @test_throws ArgumentError ReversibleScale(sqrt, exp10)  # incorrect inverse scale
 end
 
 @testset "Invalid inverse transform" begin

From 2e6c03d1df250b91662e530e336d4554acc6f130 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 29 Aug 2023 18:38:17 +0200
Subject: [PATCH 16/18] add `ReversibleScale` docs to `heatmap`

---
 docs/examples/plotting_functions/heatmap.md | 22 +++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/docs/examples/plotting_functions/heatmap.md b/docs/examples/plotting_functions/heatmap.md
index fb6e8325774..989826c0eca 100644
--- a/docs/examples/plotting_functions/heatmap.md
+++ b/docs/examples/plotting_functions/heatmap.md
@@ -116,3 +116,25 @@ Colorbar(fig[:, end+1], colorrange = joint_limits)  # equivalent
 fig
 ```
 \end{examplefigure}
+
+
+### Using a custom colorscale
+
+One can define a custom (color)scale using the `ReversibleScale` type. When the transformation is simple enough (`log`, `sqrt`, ...), the reverse transform is automatically deduced.
+
+\begin{examplefigure}{}
+```julia
+using CairoMakie
+CairoMakie.activate!() # hide
+
+x = 10.0.^(1:0.1:4)
+y = 1.0:0.1:5.0
+z = broadcast((x, y) -> x, x, y')
+
+scale = ReversibleScale(log10)
+fig, ax, hm = heatmap(x, y, z; colorscale = scale, axis = (; xscale = scale))
+Colorbar(fig[1, 2], hm)
+
+fig
+```
+\end{examplefigure}

From 29f21bdd910f7a9d0a7c835c8449e6dbcd3c93e8 Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Tue, 5 Sep 2023 13:30:19 +0200
Subject: [PATCH 17/18] update `contour` docs

---
 docs/reference/plots/contour.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/reference/plots/contour.md b/docs/reference/plots/contour.md
index c1aa8231645..4c9d8fd5bdd 100644
--- a/docs/reference/plots/contour.md
+++ b/docs/reference/plots/contour.md
@@ -57,8 +57,8 @@ x = y = range(-6, 6; length=100)
 z = himmelblau.(x, y')
 
 levels = 10.0.^range(0.3, 3.5; length=10)
-colormap = Makie.sampler(:hsv, 100; scaling=Makie.Scaling(x -> x^(1 / 10), nothing))
-f, ax, ct = contour(x, y, z; labels=true, levels, colormap)
+colorscale = ReversibleScale(x -> x^(1 / 10), x -> x^10)
+f, ax, ct = contour(x, y, z; labels=true, levels, colormap=:hsv, colorscale)
 f
 ```
 \end{examplefigure}

From 07b26b0b5aadd199b380aef2ed2aa90ed49b3eee Mon Sep 17 00:00:00 2001
From: t-bltg <tf.bltg@gmail.com>
Date: Wed, 6 Sep 2023 16:37:06 +0200
Subject: [PATCH 18/18] enhance docs example

---
 docs/reference/plots/heatmap.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/reference/plots/heatmap.md b/docs/reference/plots/heatmap.md
index 87c06e0c86a..a7302c53b7b 100644
--- a/docs/reference/plots/heatmap.md
+++ b/docs/reference/plots/heatmap.md
@@ -129,9 +129,9 @@ CairoMakie.activate!() # hide
 
 x = 10.0.^(1:0.1:4)
 y = 1.0:0.1:5.0
-z = broadcast((x, y) -> x, x, y')
+z = broadcast((x, y) -> x - 10, x, y')
 
-scale = ReversibleScale(log10)
+scale = ReversibleScale(x -> asinh(x / 2) / log(10), x -> 2sinh(log(10) * x))
 fig, ax, hm = heatmap(x, y, z; colorscale = scale, axis = (; xscale = scale))
 Colorbar(fig[1, 2], hm)