Add logarithmic plot axes

This commit is an initial implementation for adding logarithmic plotting
axis.

This very much needs more testing!

The basic idea is, that everything stays the same, but PlotTransform
does the much needed coordinate transformation for us.

That is, unfortunatley not all of the story.

 * In a lot of places, we need estimates of "how many pixels does 1 plot
   space unit take" and the likes, either for overdraw reduction, or
   generally to size things. PlotTransform has been modifed for that for
   now, so this should work.
 * While the normal grid spacer renders just fine, it will also casually
   try to generate 100s of thousands of lines for a bigger range log
   plot. So GridInput has been made aware if there is a log axis
   present. The default spacer has also been modified to work initially.
 * All of the PlotBound transformations within PlotTransform need to be
   aware and handle the log scaling properly. This is done and works
   well, but its a bit.. icky, for lack of a better word. If someone has
   a better idea how to handle this, be my guest :D
 * PlotPoint generation from generator functions has to become aware of
   logarithmic plotting, otherwise the resolution of the plotted points
   will suffer.

Especially the spacer generation is still kinda WIP; it is messy at best
right now. Especially for zooming in, it currently only adds lines on the
lower bound due to the way the generator function works right now.

I will address this in a follow up commit/--amend (or someone else will).

demo/src/plot_demo.rs

@@ -2,13 +2,13 @@ use std::f64::consts::TAU;
 use std::ops::RangeInclusive;
 
 use egui::{
-    remap, vec2, Color32, ComboBox, NumExt, Pos2, Response, ScrollArea, Stroke, TextWrapMode, Vec2b,
+    remap, vec2, Color32, ComboBox, DragValue, NumExt, Pos2, Response, ScrollArea, Stroke,
+    TextWrapMode, Vec2b,
 };
-
 use egui_plot::{
-    Arrows, AxisHints, Bar, BarChart, BoxElem, BoxPlot, BoxSpread, CoordinatesFormatter, Corner,
-    GridInput, GridMark, HLine, Legend, Line, LineStyle, MarkerShape, Plot, PlotImage, PlotPoint,
-    PlotPoints, PlotResponse, Points, Polygon, Text, VLine,
+    Arrows, AxisHints, AxisTransform, AxisTransforms, Bar, BarChart, BoxElem, BoxPlot, BoxSpread,
+    CoordinatesFormatter, Corner, GridInput, GridMark, HLine, Legend, Line, LineStyle, MarkerShape,
+    Plot, PlotBounds, PlotImage, PlotPoint, PlotPoints, PlotResponse, Points, Polygon, Text, VLine,
 };
 
 // ----------------------------------------------------------------------------
@@ -23,6 +23,7 @@ enum Panel {
     Interaction,
     CustomAxes,
     LinkedAxes,
+    LogAxes,
 }
 
 impl Default for Panel {
@@ -43,6 +44,7 @@ pub struct PlotDemo {
     interaction_demo: InteractionDemo,
     custom_axes_demo: CustomAxesDemo,
     linked_axes_demo: LinkedAxesDemo,
+    log_axes_demo: LogAxesDemo,
     open_panel: Panel,
 }
 
@@ -74,6 +76,7 @@ impl PlotDemo {
             ui.selectable_value(&mut self.open_panel, Panel::Interaction, "Interaction");
             ui.selectable_value(&mut self.open_panel, Panel::CustomAxes, "Custom Axes");
             ui.selectable_value(&mut self.open_panel, Panel::LinkedAxes, "Linked Axes");
+            ui.selectable_value(&mut self.open_panel, Panel::LogAxes, "Log Axes");
         });
         ui.separator();
 
@@ -102,6 +105,9 @@ impl PlotDemo {
             Panel::LinkedAxes => {
                 self.linked_axes_demo.ui(ui);
             }
+            Panel::LogAxes => {
+                self.log_axes_demo.ui(ui);
+            }
         }
     }
 }
@@ -691,6 +697,111 @@ impl LinkedAxesDemo {
     }
 }
 
+// ----------------------------------------------------------------------------
+#[derive(PartialEq, serde::Deserialize, serde::Serialize, Default)]
+struct LogAxesDemo {
+    axis_transforms: AxisTransforms,
+}
+
+/// Helper function showing how to do arbitrary transform picking
+fn transform_edit(id: &str, old_transform: AxisTransform, ui: &mut egui::Ui) -> AxisTransform {
+    ui.horizontal(|ui| {
+        ui.label(format!("Transform for {id}"));
+        if ui
+            .radio(matches!(old_transform, AxisTransform::Linear), "Linear")
+            .clicked()
+        {
+            return AxisTransform::Linear;
+        }
+        if ui
+            .radio(
+                matches!(old_transform, AxisTransform::Logarithmic(_)),
+                "Logarithmic",
+            )
+            .clicked()
+        {
+            let reuse_base = if let AxisTransform::Logarithmic(base) = old_transform {
+                base
+            } else {
+                10.0
+            };
+            return AxisTransform::Logarithmic(reuse_base);
+        }
+
+        // no change, but perhaps additional things?
+        match old_transform {
+            // Nah?
+            AxisTransform::Logarithmic(mut base) => {
+                ui.label("Base:");
+                ui.add(DragValue::new(&mut base).range(2.0..=100.0));
+                AxisTransform::Logarithmic(base)
+            }
+            _ => old_transform,
+        }
+    })
+    .inner
+}
+
+impl LogAxesDemo {
+    fn line_exp() -> Line {
+        Line::new(PlotPoints::from_explicit_callback(
+            move |x| 10.0_f64.powf(x / 200.0),
+            0.1..=1000.0,
+            1000,
+        ))
+        .name("y = 10^(x/200)")
+        .color(Color32::RED)
+    }
+
+    fn line_lin() -> Line {
+        Line::new(PlotPoints::from_explicit_callback(
+            move |x| -5.0 + x,
+            0.1..=1000.0,
+            1000,
+        ))
+        .name("y = -5 + x")
+        .color(Color32::GREEN)
+    }
+
+    fn line_log() -> Line {
+        Line::new(PlotPoints::from_explicit_callback(
+            move |x| x.log10(),
+            0.1..=1000.0,
+            1000,
+        ))
+        .name("y = log10(x)")
+        .color(Color32::BLUE)
+    }
+
+    fn ui(&mut self, ui: &mut egui::Ui) -> Response {
+        let old_transforms = self.axis_transforms;
+        self.axis_transforms.horizontal =
+            transform_edit("horizontal axis", self.axis_transforms.horizontal, ui);
+        self.axis_transforms.vertical =
+            transform_edit("vertical axis", self.axis_transforms.vertical, ui);
+        let just_changed = old_transforms != self.axis_transforms;
+        Plot::new("log_demo")
+            .axis_transforms(self.axis_transforms)
+            .x_axis_label("x")
+            .y_axis_label("y")
+            .show_axes(Vec2b::new(true, true))
+            .legend(Legend::default())
+            .show(ui, |ui| {
+                if just_changed {
+                    if let AxisTransform::Logarithmic(_) = self.axis_transforms.horizontal {
+                        ui.set_plot_bounds(PlotBounds::from_min_max([0.1, 0.1], [1e3, 1e4]));
+                    } else {
+                        ui.set_plot_bounds(PlotBounds::from_min_max([0.0, 0.0], [3.0, 1000.0]));
+                    }
+                }
+                ui.line(Self::line_exp());
+                ui.line(Self::line_lin());
+                ui.line(Self::line_log());
+            })
+            .response
+    }
+}
+
 // ----------------------------------------------------------------------------
 
 #[derive(Default, PartialEq, serde::Deserialize, serde::Serialize)]

egui_plot/src/axis.rs

@@ -339,8 +339,11 @@ impl<'a> AxisWidget<'a> {
         for step in self.steps.iter() {
             let text = (self.hints.formatter)(*step, &self.range);
             if !text.is_empty() {
-                let spacing_in_points =
-                    (transform.dpos_dvalue()[usize::from(axis)] * step.step_size).abs() as f32;
+                let spacing_in_points = transform.points_at_pos_range(
+                    [step.value, step.value],
+                    [step.step_size, step.step_size],
+                )[usize::from(axis)]
+                .abs();
 
                 if spacing_in_points <= label_spacing.min {
                     // Labels are too close together - don't paint them.

egui_plot/src/items/bar.rs

@@ -186,7 +186,7 @@ impl RectElement for Bar {
     }
 
     fn default_values_format(&self, transform: &PlotTransform) -> String {
-        let scale = transform.dvalue_dpos();
+        let scale = transform.smallest_distance_per_point();
         let scale = match self.orientation {
             Orientation::Horizontal => scale[0],
             Orientation::Vertical => scale[1],

egui_plot/src/items/box_elem.rs

@@ -271,7 +271,7 @@ impl RectElement for BoxElem {
     }
 
     fn default_values_format(&self, transform: &PlotTransform) -> String {
-        let scale = transform.dvalue_dpos();
+        let scale = transform.smallest_distance_per_point();
         let scale = match self.orientation {
             Orientation::Horizontal => scale[0],
             Orientation::Vertical => scale[1],

egui_plot/src/items/mod.rs

@@ -41,7 +41,7 @@ pub trait PlotItem {
     fn shapes(&self, ui: &Ui, transform: &PlotTransform, shapes: &mut Vec<Shape>);
 
     /// For plot-items which are generated based on x values (plotting functions).
-    fn initialize(&mut self, x_range: RangeInclusive<f64>);
+    fn initialize(&mut self, x_range: RangeInclusive<f64>, log_base: Option<f64>);
 
     fn name(&self) -> &str;
 
@@ -228,7 +228,7 @@ impl PlotItem for HLine {
         style.style_line(points, *stroke, *highlight, shapes);
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {}
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, _log_base: Option<f64>) {}
 
     fn name(&self) -> &str {
         &self.name
@@ -371,7 +371,7 @@ impl PlotItem for VLine {
         style.style_line(points, *stroke, *highlight, shapes);
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {}
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, _log_base: Option<f64>) {}
 
     fn name(&self) -> &str {
         &self.name
@@ -581,8 +581,8 @@ impl PlotItem for Line {
         style.style_line(values_tf, *stroke, *highlight, shapes);
     }
 
-    fn initialize(&mut self, x_range: RangeInclusive<f64>) {
-        self.series.generate_points(x_range);
+    fn initialize(&mut self, x_range: RangeInclusive<f64>, log_base: Option<f64>) {
+        self.series.generate_points(x_range, log_base);
     }
 
     fn name(&self) -> &str {
@@ -737,8 +737,8 @@ impl PlotItem for Polygon {
         style.style_line(values_tf, *stroke, *highlight, shapes);
     }
 
-    fn initialize(&mut self, x_range: RangeInclusive<f64>) {
-        self.series.generate_points(x_range);
+    fn initialize(&mut self, x_range: RangeInclusive<f64>, log_base: Option<f64>) {
+        self.series.generate_points(x_range, log_base);
     }
 
     fn name(&self) -> &str {
@@ -879,7 +879,7 @@ impl PlotItem for Text {
         }
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {}
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, _log_base: Option<f64>) {}
 
     fn name(&self) -> &str {
         self.name.as_str()
@@ -1157,8 +1157,8 @@ impl PlotItem for Points {
             });
     }
 
-    fn initialize(&mut self, x_range: RangeInclusive<f64>) {
-        self.series.generate_points(x_range);
+    fn initialize(&mut self, x_range: RangeInclusive<f64>, log_base: Option<f64>) {
+        self.series.generate_points(x_range, log_base);
     }
 
     fn name(&self) -> &str {
@@ -1312,10 +1312,11 @@ impl PlotItem for Arrows {
             });
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, log_base: Option<f64>) {
         self.origins
-            .generate_points(f64::NEG_INFINITY..=f64::INFINITY);
-        self.tips.generate_points(f64::NEG_INFINITY..=f64::INFINITY);
+            .generate_points(f64::NEG_INFINITY..=f64::INFINITY, log_base);
+        self.tips
+            .generate_points(f64::NEG_INFINITY..=f64::INFINITY, log_base);
     }
 
     fn name(&self) -> &str {
@@ -1504,7 +1505,7 @@ impl PlotItem for PlotImage {
         }
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {}
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, _log_base: Option<f64>) {}
 
     fn name(&self) -> &str {
         self.name.as_str()
@@ -1699,7 +1700,7 @@ impl PlotItem for BarChart {
         }
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, _log_base: Option<f64>) {
         // nothing to do
     }
 
@@ -1873,7 +1874,7 @@ impl PlotItem for BoxPlot {
         }
     }
 
-    fn initialize(&mut self, _x_range: RangeInclusive<f64>) {
+    fn initialize(&mut self, _x_range: RangeInclusive<f64>, _log_base: Option<f64>) {
         // nothing to do
     }
 
@@ -2059,7 +2060,7 @@ pub(super) fn rulers_at_value(
     };
 
     let text = {
-        let scale = plot.transform.dvalue_dpos();
+        let scale = plot.transform.smallest_distance_per_point();
         let x_decimals = ((-scale[0].abs().log10()).ceil().at_least(0.0) as usize).clamp(1, 6);
         let y_decimals = ((-scale[1].abs().log10()).ceil().at_least(0.0) as usize).clamp(1, 6);
         if let Some(custom_label) = label_formatter {

egui_plot/src/items/values.rs

@@ -276,15 +276,28 @@ impl PlotPoints {
 
     /// If initialized with a generator function, this will generate `n` evenly spaced points in the
     /// given range.
-    pub(super) fn generate_points(&mut self, x_range: RangeInclusive<f64>) {
+    pub(super) fn generate_points(&mut self, x_range: RangeInclusive<f64>, log_base: Option<f64>) {
         if let Self::Generator(generator) = self {
             *self = Self::range_intersection(&x_range, &generator.x_range)
                 .map(|intersection| {
-                    let increment =
-                        (intersection.end() - intersection.start()) / (generator.points - 1) as f64;
+                    let increment = match log_base {
+                        Some(base) => {
+                            (intersection.end().log(base) - intersection.start().log(base))
+                                / (generator.points - 1) as f64
+                        }
+                        None => {
+                            (intersection.end() - intersection.start())
+                                / (generator.points - 1) as f64
+                        }
+                    };
                     (0..generator.points)
                         .map(|i| {
-                            let x = intersection.start() + i as f64 * increment;
+                            let x = match log_base {
+                                Some(base) => {
+                                    base.powf(intersection.start().log(base) + i as f64 * increment)
+                                }
+                                None => intersection.start() + i as f64 * increment,
+                            };
                             let y = (generator.function)(x);
                             [x, y]
                         })