diff --git a/egui/src/containers/area.rs b/egui/src/containers/area.rs
index f4c1f27b..054d30ff 100644
--- a/egui/src/containers/area.rs
+++ b/egui/src/containers/area.rs
@@ -139,7 +139,7 @@ impl Area {
         let state = ctx.memory().areas.get(id).cloned();
         let mut state = state.unwrap_or_else(|| State {
             pos: default_pos.unwrap_or_else(|| automatic_area_position(ctx)),
-            size: Vec2::zero(),
+            size: Vec2::ZERO,
             interactable,
         });
         state.pos = new_pos.unwrap_or(state.pos);
@@ -198,7 +198,7 @@ impl Prepared {
     }
 
     pub(crate) fn content_ui(&self, ctx: &CtxRef) -> Ui {
-        let max_rect = Rect::from_min_size(self.state.pos, Vec2::infinity());
+        let max_rect = Rect::from_min_size(self.state.pos, Vec2::INFINITY);
         let shadow_radius = ctx.style().visuals.window_shadow.extrusion; // hacky
         let mut clip_rect = max_rect
             .expand(ctx.style().visuals.clip_rect_margin)
@@ -241,7 +241,7 @@ impl Prepared {
         };
 
         let move_response = ctx.interact(
-            Rect::everything(),
+            Rect::EVERYTHING,
             ctx.style().spacing.item_spacing,
             layer_id,
             interact_id,
diff --git a/egui/src/containers/popup.rs b/egui/src/containers/popup.rs
index 4c17f367..e0beffd4 100644
--- a/egui/src/containers/popup.rs
+++ b/egui/src/containers/popup.rs
@@ -37,7 +37,7 @@ pub fn show_tooltip(ctx: &CtxRef, add_contents: impl FnOnce(&mut Ui)) {
     let id = Id::tooltip();
     let response = show_tooltip_area(ctx, id, window_pos, add_contents);
 
-    let tooltip_rect = tooltip_rect.unwrap_or_else(Rect::nothing);
+    let tooltip_rect = tooltip_rect.unwrap_or(Rect::NOTHING);
     ctx.frame_state().tooltip_rect = Some(tooltip_rect.union(response.rect));
 }
 
@@ -114,7 +114,7 @@ pub fn popup_below_widget(
                 let frame = Frame::popup(ui.style());
                 let frame_margin = frame.margin;
                 frame.show(ui, |ui| {
-                    ui.with_layout(Layout::top_down_justified(Align::left()), |ui| {
+                    ui.with_layout(Layout::top_down_justified(Align::LEFT), |ui| {
                         ui.set_width(widget_response.rect.width() - 2.0 * frame_margin.x);
                         add_contents(ui)
                     });
diff --git a/egui/src/containers/resize.rs b/egui/src/containers/resize.rs
index 7ba84f7e..712d4f4d 100644
--- a/egui/src/containers/resize.rs
+++ b/egui/src/containers/resize.rs
@@ -124,7 +124,7 @@ impl Resize {
     /// Not manually resizable, just takes the size of its contents.
     /// Text will not wrap, but will instead make your window width expand.
     pub fn auto_sized(self) -> Self {
-        self.min_size(Vec2::zero())
+        self.min_size(Vec2::ZERO)
             .default_size(Vec2::splat(f32::INFINITY))
             .resizable(false)
     }
diff --git a/egui/src/containers/scroll_area.rs b/egui/src/containers/scroll_area.rs
index e9e44f6e..117dcd82 100644
--- a/egui/src/containers/scroll_area.rs
+++ b/egui/src/containers/scroll_area.rs
@@ -19,9 +19,9 @@ pub(crate) struct State {
 impl Default for State {
     fn default() -> Self {
         Self {
-            offset: Vec2::zero(),
+            offset: Vec2::ZERO,
             show_scroll: false,
-            vel: Vec2::zero(),
+            vel: Vec2::ZERO,
             scroll_start_offset_from_top: None,
         }
     }
@@ -222,7 +222,7 @@ impl Prepared {
 
                 let friction = friction_coeff * dt;
                 if friction > state.vel.length() || state.vel.length() < stop_speed {
-                    state.vel = Vec2::zero();
+                    state.vel = Vec2::ZERO;
                 } else {
                     state.vel -= friction * state.vel.normalized();
                     // Offset has an inverted coordinate system compared to
@@ -244,7 +244,7 @@ impl Prepared {
             if scrolling_up || scrolling_down {
                 state.offset.y -= scroll_delta.y;
                 // Clear scroll delta so no parent scroll will use it.
-                frame_state.scroll_delta = Vec2::zero();
+                frame_state.scroll_delta = Vec2::ZERO;
             }
         }
 
@@ -310,7 +310,7 @@ impl Prepared {
             state.offset.y = state.offset.y.min(max_offset);
             #[allow(clippy::float_cmp)]
             if state.offset.y != unbounded_offset_y {
-                state.vel = Vec2::zero();
+                state.vel = Vec2::ZERO;
             }
 
             // Avoid frame-delay by calculating a new handle rect:
diff --git a/egui/src/containers/window.rs b/egui/src/containers/window.rs
index a60cc70d..398287d9 100644
--- a/egui/src/containers/window.rs
+++ b/egui/src/containers/window.rs
@@ -705,7 +705,7 @@ fn show_title_bar(
             title_label,
             title_galley,
             min_rect,
-            rect: Rect::invalid(), // Will be filled in later
+            rect: Rect::NAN, // Will be filled in later
         }
     });
 
diff --git a/egui/src/context.rs b/egui/src/context.rs
index 6980c9df..3884f840 100644
--- a/egui/src/context.rs
+++ b/egui/src/context.rs
@@ -51,11 +51,11 @@ impl Default for FrameState {
     fn default() -> Self {
         Self {
             used_ids: Default::default(),
-            available_rect: Rect::invalid(),
-            unused_rect: Rect::invalid(),
-            used_by_panels: Rect::invalid(),
+            available_rect: Rect::NAN,
+            unused_rect: Rect::NAN,
+            used_by_panels: Rect::NAN,
             tooltip_rect: None,
-            scroll_delta: Vec2::zero(),
+            scroll_delta: Vec2::ZERO,
             scroll_target: None,
         }
     }
@@ -76,7 +76,7 @@ impl FrameState {
         used_ids.clear();
         *available_rect = input.screen_rect();
         *unused_rect = input.screen_rect();
-        *used_by_panels = Rect::nothing();
+        *used_by_panels = Rect::NOTHING;
         *tooltip_rect = None;
         *scroll_delta = input.scroll_delta;
         *scroll_target = None;
@@ -118,7 +118,7 @@ impl FrameState {
     pub(crate) fn allocate_central_panel(&mut self, panel_rect: Rect) {
         // Note: we do not shrink `available_rect`, because
         // we allow windows to cover the CentralPanel.
-        self.unused_rect = Rect::nothing(); // Nothing left unused after this
+        self.unused_rect = Rect::NOTHING; // Nothing left unused after this
         self.used_by_panels = self.used_by_panels.union(panel_rect);
     }
 }
diff --git a/egui/src/data/input.rs b/egui/src/data/input.rs
index caa22cc2..e6f44665 100644
--- a/egui/src/data/input.rs
+++ b/egui/src/data/input.rs
@@ -49,7 +49,7 @@ impl Default for RawInput {
     fn default() -> Self {
         #![allow(deprecated)] // for screen_size
         Self {
-            scroll_delta: Vec2::zero(),
+            scroll_delta: Vec2::ZERO,
             screen_size: Default::default(),
             screen_rect: None,
             pixels_per_point: None,
diff --git a/egui/src/experimental/easy_mark_viewer.rs b/egui/src/experimental/easy_mark_viewer.rs
index 91a1748a..dbc6c356 100644
--- a/egui/src/experimental/easy_mark_viewer.rs
+++ b/egui/src/experimental/easy_mark_viewer.rs
@@ -8,7 +8,7 @@ pub fn easy_mark(ui: &mut Ui, easy_mark: &str) {
 
 pub fn easy_mark_it<'em>(ui: &mut Ui, items: impl Iterator<Item = easy_mark::Item<'em>>) {
     ui.horizontal_wrapped(|ui| {
-        ui.spacing_mut().item_spacing = Vec2::zero();
+        ui.spacing_mut().item_spacing = Vec2::ZERO;
         for item in items {
             item_ui(ui, item);
         }
diff --git a/egui/src/input_state.rs b/egui/src/input_state.rs
index a853df49..7d5ee657 100644
--- a/egui/src/input_state.rs
+++ b/egui/src/input_state.rs
@@ -114,7 +114,7 @@ impl InputState {
     }
 
     pub fn wants_repaint(&self) -> bool {
-        self.pointer.wants_repaint() || self.scroll_delta != Vec2::zero() || !self.events.is_empty()
+        self.pointer.wants_repaint() || self.scroll_delta != Vec2::ZERO || !self.events.is_empty()
     }
 
     /// Was the given key pressed this frame?
@@ -259,8 +259,8 @@ impl Default for PointerState {
         Self {
             latest_pos: None,
             interact_pos: None,
-            delta: Vec2::zero(),
-            velocity: Vec2::zero(),
+            delta: Vec2::ZERO,
+            velocity: Vec2::ZERO,
             pos_history: History::new(1000, 0.1),
             down: Default::default(),
             press_origin: None,
@@ -357,7 +357,7 @@ impl PointerState {
         self.delta = if let (Some(old_pos), Some(new_pos)) = (old_pos, self.latest_pos) {
             new_pos - old_pos
         } else {
-            Vec2::zero()
+            Vec2::ZERO
         };
 
         if let Some(pos) = self.latest_pos {
@@ -380,7 +380,7 @@ impl PointerState {
     }
 
     fn wants_repaint(&self) -> bool {
-        !self.pointer_events.is_empty() || self.delta != Vec2::zero()
+        !self.pointer_events.is_empty() || self.delta != Vec2::ZERO
     }
 
     /// How much the pointer moved compared to last frame, in points.
@@ -429,7 +429,7 @@ impl PointerState {
     /// Is the pointer currently moving?
     /// This is smoothed so a few frames of stillness is required before this returns `true`.
     pub fn is_moving(&self) -> bool {
-        self.velocity != Vec2::zero()
+        self.velocity != Vec2::ZERO
     }
 
     /// Was any pointer button pressed (`!down -> down`) this frame?
diff --git a/egui/src/layout.rs b/egui/src/layout.rs
index 70661cba..b03d14ca 100644
--- a/egui/src/layout.rs
+++ b/egui/src/layout.rs
@@ -133,7 +133,7 @@ impl Default for Layout {
         Self {
             main_dir: Direction::TopDown,
             main_wrap: false,
-            cross_align: Align::left(),
+            cross_align: Align::LEFT,
             cross_justify: false,
         }
     }
@@ -253,7 +253,7 @@ impl Layout {
 
     fn horizontal_align(&self) -> Align {
         match self.main_dir {
-            // Direction::LeftToRight => Align::left(),
+            // Direction::LeftToRight => Align::LEFT,
             // Direction::RightToLeft => Align::right(),
             Direction::LeftToRight | Direction::RightToLeft => Align::Center, // looks better to e.g. center text within a button
 
@@ -263,8 +263,8 @@ impl Layout {
 
     fn vertical_align(&self) -> Align {
         match self.main_dir {
-            // Direction::TopDown => Align::top(),
-            // Direction::BottomUp => Align::bottom(),
+            // Direction::TopDown => Align::TOP,
+            // Direction::BottomUp => Align::BOTTOM,
             Direction::TopDown | Direction::BottomUp => Align::Center, // looks better to e.g. center text within a button
 
             Direction::LeftToRight | Direction::RightToLeft => self.cross_align,
@@ -300,7 +300,7 @@ impl Layout {
 
     pub(crate) fn region_from_max_rect(&self, max_rect: Rect) -> Region {
         let cursor = self.initial_cursor(max_rect);
-        let min_rect = Rect::from_min_size(cursor, Vec2::zero());
+        let min_rect = Rect::from_min_size(cursor, Vec2::ZERO);
         Region {
             min_rect,
             max_rect,
diff --git a/egui/src/menu.rs b/egui/src/menu.rs
index d64ad056..a6f6119a 100644
--- a/egui/src/menu.rs
+++ b/egui/src/menu.rs
@@ -111,7 +111,7 @@ fn menu_impl<'c>(
                 style.visuals.widgets.inactive.bg_fill = Color32::TRANSPARENT;
                 style.visuals.widgets.inactive.bg_stroke = Stroke::none();
                 ui.set_style(style);
-                ui.with_layout(Layout::top_down_justified(Align::left()), add_contents);
+                ui.with_layout(Layout::top_down_justified(Align::LEFT), add_contents);
             })
         });
 
diff --git a/egui/src/placer.rs b/egui/src/placer.rs
index d56a41f4..120ad89c 100644
--- a/egui/src/placer.rs
+++ b/egui/src/placer.rs
@@ -127,7 +127,7 @@ impl Placer {
         self.layout.advance_cursor(&mut self.region.cursor, amount);
 
         self.region
-            .expand_to_include_rect(Rect::from_min_size(self.cursor(), Vec2::zero()));
+            .expand_to_include_rect(Rect::from_min_size(self.cursor(), Vec2::ZERO));
     }
 
     /// Advance cursor after a widget was added to a specific rectangle
diff --git a/egui/src/ui.rs b/egui/src/ui.rs
index d7eaf8ac..616a1702 100644
--- a/egui/src/ui.rs
+++ b/egui/src/ui.rs
@@ -625,7 +625,7 @@ impl Ui {
     ///     }
     ///
     ///     if scroll_bottom {
-    ///         ui.scroll_to_cursor(Align::bottom());
+    ///         ui.scroll_to_cursor(Align::BOTTOM);
     ///     }
     /// });
     /// ```
@@ -1223,7 +1223,7 @@ impl Ui {
                     pos2(pos.x + column_width, self.max_rect().right_bottom().y),
                 );
                 let mut column_ui =
-                    self.child_ui(child_rect, Layout::top_down_justified(Align::left()));
+                    self.child_ui(child_rect, Layout::top_down_justified(Align::LEFT));
                 column_ui.set_width(column_width);
                 column_ui
             })
diff --git a/egui_demo_lib/src/apps/demo/scrolling.rs b/egui_demo_lib/src/apps/demo/scrolling.rs
index ac146e02..80e65afa 100644
--- a/egui_demo_lib/src/apps/demo/scrolling.rs
+++ b/egui_demo_lib/src/apps/demo/scrolling.rs
@@ -90,7 +90,7 @@ impl super::View for Scrolling {
 
         let (current_scroll, max_scroll) = scroll_area.show(ui, |ui| {
             if scroll_top {
-                ui.scroll_to_cursor(Align::top());
+                ui.scroll_to_cursor(Align::TOP);
             }
             ui.vertical(|ui| {
                 for item in 1..=50 {
@@ -104,7 +104,7 @@ impl super::View for Scrolling {
             });
 
             if scroll_bottom {
-                ui.scroll_to_cursor(Align::bottom());
+                ui.scroll_to_cursor(Align::BOTTOM);
             }
 
             let margin = ui.visuals().clip_rect_margin;
diff --git a/emath/src/align.rs b/emath/src/align.rs
index 7f9aef02..991e57c2 100644
--- a/emath/src/align.rs
+++ b/emath/src/align.rs
@@ -19,20 +19,29 @@ pub enum Align {
 
 impl Align {
     /// Convenience for [`Self::Min`]
-    pub fn left() -> Self {
-        Self::Min
-    }
+    pub const LEFT: Self = Self::Min;
     /// Convenience for [`Self::Max`]
-    pub fn right() -> Self {
-        Self::Max
-    }
+    pub const RIGHT: Self = Self::Max;
     /// Convenience for [`Self::Min`]
-    pub fn top() -> Self {
-        Self::Min
-    }
+    pub const TOP: Self = Self::Min;
     /// Convenience for [`Self::Max`]
+    pub const BOTTOM: Self = Self::Max;
+
+    #[deprecated = "Use Self::LEFT"]
+    pub fn left() -> Self {
+        Self::LEFT
+    }
+    #[deprecated = "Use Self::RIGHT"]
+    pub fn right() -> Self {
+        Self::RIGHT
+    }
+    #[deprecated = "Use Self::TOP"]
+    pub fn top() -> Self {
+        Self::TOP
+    }
+    #[deprecated = "Use Self::BOTTOM"]
     pub fn bottom() -> Self {
-        Self::Max
+        Self::BOTTOM
     }
 
     /// Convert `Min => 0.0`, `Center => 0.5` or `Max => 1.0`.
diff --git a/emath/src/pos2.rs b/emath/src/pos2.rs
index 21342dfe..ba9d47aa 100644
--- a/emath/src/pos2.rs
+++ b/emath/src/pos2.rs
@@ -82,8 +82,11 @@ impl Pos2 {
     /// The zero position, the origin.
     /// The top left corner in a GUI.
     /// Same as `Pos2::default()`.
+    pub const ZERO: Self = Self { x: 0.0, y: 0.0 };
+
+    #[deprecated = "Use Pos2::ZERO instead"]
     pub const fn zero() -> Self {
-        Self { x: 0.0, y: 0.0 }
+        Self::ZERO
     }
 
     pub const fn new(x: f32, y: f32) -> Self {
diff --git a/emath/src/rect.rs b/emath/src/rect.rs
index 12606874..177b6ba5 100644
--- a/emath/src/rect.rs
+++ b/emath/src/rect.rs
@@ -1,3 +1,4 @@
+use std::f32::INFINITY;
 use std::ops::RangeInclusive;
 
 use crate::*;
@@ -13,7 +14,37 @@ pub struct Rect {
 }
 
 impl Rect {
-    /// Infinite rectangle that contains everything
+    /// Infinite rectangle that contains everything.
+    pub const EVERYTHING: Self = Self {
+        min: pos2(-INFINITY, -INFINITY),
+        max: pos2(INFINITY, INFINITY),
+    };
+
+    /// The inverse of [`Self::EVERYTHING`]: streches from positive infinity to negative infinity.
+    /// Contains no points.
+    ///
+    /// This is useful as the seed for boulding bounding boxes.
+    ///
+    /// # Example:
+    /// ```
+    /// # use emath::*;
+    /// let mut rect = Rect::NOTHING;
+    /// rect.extend_with(pos2(2.0, 1.0));
+    /// rect.extend_with(pos2(0.0, 3.0));
+    /// assert_eq!(rect, Rect::from_min_max(pos2(0.0, 1.0), pos2(2.0, 3.0)))
+    /// ```
+    pub const NOTHING: Self = Self {
+        min: pos2(INFINITY, INFINITY),
+        max: pos2(-INFINITY, -INFINITY),
+    };
+
+    /// An invalid `Rect` filled with [`f32::NAN`];
+    pub const NAN: Self = Self {
+        min: pos2(f32::NAN, f32::NAN),
+        max: pos2(-f32::NAN, -f32::NAN),
+    };
+
+    #[deprecated = "Use Rect::EVERYTHING"]
     pub fn everything() -> Self {
         let inf = f32::INFINITY;
         Self {
@@ -22,6 +53,7 @@ impl Rect {
         }
     }
 
+    #[deprecated = "Use Rect::NOTHING"]
     pub fn nothing() -> Self {
         let inf = f32::INFINITY;
         Self {
@@ -30,15 +62,12 @@ impl Rect {
         }
     }
 
-    /// invalid, NAN filled Rect.
+    #[deprecated = "Use Rect::NAN"]
     pub fn invalid() -> Self {
-        Self {
-            min: pos2(f32::NAN, f32::NAN),
-            max: pos2(f32::NAN, f32::NAN),
-        }
+        Self::NAN
     }
 
-    pub fn from_min_max(min: Pos2, max: Pos2) -> Self {
+    pub const fn from_min_max(min: Pos2, max: Pos2) -> Self {
         Rect { min, max }
     }
 
diff --git a/emath/src/rot2.rs b/emath/src/rot2.rs
index d8b9e687..2ec1783d 100644
--- a/emath/src/rot2.rs
+++ b/emath/src/rot2.rs
@@ -28,8 +28,12 @@ impl Default for Rot2 {
 }
 
 impl Rot2 {
+    /// The identity rotation: nothing rotates
+    pub const IDENTITY: Self = Self { s: 0.0, c: 1.0 };
+
+    #[deprecated = "Use Rot2::IDENTITY"]
     pub fn identity() -> Self {
-        Self { s: 0.0, c: 1.0 }
+        Self::IDENTITY
     }
 
     /// A 𝞃/4 = 90° rotation means rotating the X axis to the Y axis.
diff --git a/emath/src/vec2.rs b/emath/src/vec2.rs
index 9e2a42f0..65309381 100644
--- a/emath/src/vec2.rs
+++ b/emath/src/vec2.rs
@@ -81,23 +81,25 @@ impl Vec2 {
     pub const X: Vec2 = Vec2 { x: 1.0, y: 0.0 };
     pub const Y: Vec2 = Vec2 { x: 0.0, y: 1.0 };
 
+    pub const ZERO: Self = Self { x: 0.0, y: 0.0 };
+    pub const INFINITY: Self = Self::splat(f32::INFINITY);
+
+    #[deprecated = "Use Vec2::ZERO instead"]
     pub fn zero() -> Self {
-        Self { x: 0.0, y: 0.0 }
+        Self::ZERO
     }
 
+    #[deprecated = "Use Vec2::INFINITY instead"]
     pub fn infinity() -> Self {
-        Self {
-            x: f32::INFINITY,
-            y: f32::INFINITY,
-        }
+        Self::INFINITY
     }
 
-    pub fn new(x: f32, y: f32) -> Self {
+    pub const fn new(x: f32, y: f32) -> Self {
         Self { x, y }
     }
 
-    pub fn splat(v: impl Into<f32>) -> Self {
-        let v: f32 = v.into();
+    /// Set both `x` and `y` to the same value.
+    pub const fn splat(v: f32) -> Self {
         Self { x: v, y: v }
     }
 
diff --git a/epaint/src/tessellator.rs b/epaint/src/tessellator.rs
index b7e25e42..e2af6915 100644
--- a/epaint/src/tessellator.rs
+++ b/epaint/src/tessellator.rs
@@ -81,9 +81,9 @@ impl Path {
                 let mut n1 = (points[i + 1] - points[i]).normalized().rot90();
 
                 // Handle duplicated points (but not triplicated...):
-                if n0 == Vec2::zero() {
+                if n0 == Vec2::ZERO {
                     n0 = n1;
-                } else if n1 == Vec2::zero() {
+                } else if n1 == Vec2::ZERO {
                     n1 = n0;
                 }
 
@@ -121,9 +121,9 @@ impl Path {
             let mut n1 = (points[(i + 1) % n] - points[i]).normalized().rot90();
 
             // Handle duplicated points (but not triplicated...):
-            if n0 == Vec2::zero() {
+            if n0 == Vec2::ZERO {
                 n0 = n1;
-            } else if n1 == Vec2::zero() {
+            } else if n1 == Vec2::ZERO {
                 n1 = n0;
             }
 
@@ -461,7 +461,7 @@ impl Tessellator {
     pub fn from_options(options: TessellationOptions) -> Self {
         Self {
             options,
-            clip_rect: Rect::everything(),
+            clip_rect: Rect::EVERYTHING,
             scratchpad_points: Default::default(),
             scratchpad_path: Default::default(),
         }
@@ -744,7 +744,7 @@ pub fn tessellate_shapes(
 
     if options.debug_paint_clip_rects {
         for ClippedMesh(clip_rect, mesh) in &mut clipped_meshes {
-            tessellator.clip_rect = Rect::everything();
+            tessellator.clip_rect = Rect::EVERYTHING;
             tessellator.tessellate_shape(
                 fonts,
                 Shape::Rect {
@@ -760,7 +760,7 @@ pub fn tessellate_shapes(
 
     if options.debug_ignore_clip_rects {
         for ClippedMesh(clip_rect, _) in &mut clipped_meshes {
-            *clip_rect = Rect::everything();
+            *clip_rect = Rect::EVERYTHING;
         }
     }