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

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

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

demo/src/plot_demo.rs

@@ -7,8 +7,8 @@ use egui::{
 
 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,
+    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 +697,76 @@ impl LinkedAxesDemo {
     }
 }
 
+// ----------------------------------------------------------------------------
+#[derive(PartialEq, serde::Deserialize, serde::Serialize)]
+struct LogAxesDemo {
+    log_axes: Vec2b,
+}
+
+impl Default for LogAxesDemo {
+    fn default() -> Self {
+        Self {
+            log_axes: Vec2b::new(false, true),
+        }
+    }
+}
+
+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 just_changed = ui.checkbox(&mut self.log_axes.x, "Log X-Axis").clicked();
+        ui.checkbox(&mut self.log_axes.y, "Log Y-Axis");
+        Plot::new("log_demo")
+            .log_axes(self.log_axes)
+            .x_axis_label("x")
+            .y_axis_label("y")
+            .show_axes(Vec2b::new(true, true))
+            .legend(Legend::default())
+            .show(ui, |ui| {
+                if just_changed {
+                    if self.log_axes.x {
+                        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

@@ -2069,7 +2069,7 @@ 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 {