diff --git a/CHANGELOG.md b/CHANGELOG.md
index 440fa8fc..b5c892fd 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,7 +5,9 @@ NOTE: [`epaint`](epaint/CHANGELOG.md), [`eframe`](eframe/CHANGELOG.md), [`egui-w
 
 
 ## Unreleased
-* Add `*_released` & `*_clicked` methods for `PointerState`.
+* Add `*_released` & `*_clicked` methods for `PointerState` ([#1582](https://github.com/emilk/egui/pull/1582)).
+* Optimize painting of filled circles (e.g. for scatter plots) by 10x or more ([#1616](https://github.com/emilk/egui/pull/1616)).
+
 
 ## 0.18.1 - 2022-05-01
 * Change `Shape::Callback` from `&dyn Any` to `&mut dyn Any` to support more backends.
diff --git a/egui/src/context.rs b/egui/src/context.rs
index 63e1a240..38cdbcab 100644
--- a/egui/src/context.rs
+++ b/egui/src/context.rs
@@ -830,14 +830,17 @@ impl Context {
 
         let pixels_per_point = self.pixels_per_point();
         let tessellation_options = *self.tessellation_options();
-        let font_image_size = self.fonts().font_image_size();
+        let texture_atlas = self.fonts().texture_atlas();
+        let font_tex_size = texture_atlas.lock().size();
+        let prepared_discs = texture_atlas.lock().prepared_discs();
 
         let paint_stats = PaintStats::from_shapes(&shapes);
         let clipped_primitives = tessellator::tessellate_shapes(
             pixels_per_point,
             tessellation_options,
+            font_tex_size,
+            prepared_discs,
             shapes,
-            font_image_size,
         );
         self.write().paint_stats = paint_stats.with_clipped_primitives(&clipped_primitives);
         clipped_primitives
diff --git a/egui/src/introspection.rs b/egui/src/introspection.rs
index 91a1a8a4..c0003695 100644
--- a/egui/src/introspection.rs
+++ b/egui/src/introspection.rs
@@ -142,6 +142,7 @@ impl Widget for &mut epaint::TessellationOptions {
                 feathering,
                 feathering_size_in_pixels,
                 coarse_tessellation_culling,
+                prerasterized_discs,
                 round_text_to_pixels,
                 debug_paint_clip_rects,
                 debug_paint_text_rects,
@@ -158,6 +159,8 @@ impl Widget for &mut epaint::TessellationOptions {
                 .text("Feathering size in pixels");
             ui.add_enabled(*feathering, feathering_slider);
 
+            ui.checkbox(prerasterized_discs, "Speed up filled circles with pre-rasterization");
+
             ui.add(
                 crate::widgets::Slider::new(bezier_tolerance, 0.0001..=10.0)
                     .logarithmic(true)
diff --git a/egui_demo_lib/benches/benchmark.rs b/egui_demo_lib/benches/benchmark.rs
index 0dceba6a..9e9f52ad 100644
--- a/egui_demo_lib/benches/benchmark.rs
+++ b/egui_demo_lib/benches/benchmark.rs
@@ -124,8 +124,13 @@ pub fn criterion_benchmark(c: &mut Criterion) {
 
         let galley = fonts.layout(LOREM_IPSUM_LONG.to_owned(), font_id, color, wrap_width);
         let font_image_size = fonts.font_image_size();
-        let mut tessellator =
-            egui::epaint::Tessellator::new(1.0, Default::default(), font_image_size);
+        let prepared_discs = fonts.texture_atlas().lock().prepared_discs();
+        let mut tessellator = egui::epaint::Tessellator::new(
+            1.0,
+            Default::default(),
+            font_image_size,
+            prepared_discs,
+        );
         let mut mesh = egui::epaint::Mesh::default();
         let text_shape = TextShape::new(egui::Pos2::ZERO, galley);
         c.bench_function("tessellate_text", |b| {
diff --git a/egui_demo_lib/src/demo/misc_demo_window.rs b/egui_demo_lib/src/demo/misc_demo_window.rs
index 85262e54..b379239c 100644
--- a/egui_demo_lib/src/demo/misc_demo_window.rs
+++ b/egui_demo_lib/src/demo/misc_demo_window.rs
@@ -158,6 +158,20 @@ impl View for MiscDemoWindow {
                     painter.line_segment([c, c + r * Vec2::angled(TAU * 3.0 / 8.0)], stroke);
                 });
             });
+
+        CollapsingHeader::new("Many circles of different sizes")
+            .default_open(false)
+            .show(ui, |ui| {
+                ui.horizontal_wrapped(|ui| {
+                    for i in 0..100 {
+                        let r = i as f32 * 0.5;
+                        let size = Vec2::splat(2.0 * r + 5.0);
+                        let (rect, _response) = ui.allocate_at_least(size, Sense::hover());
+                        ui.painter()
+                            .circle_filled(rect.center(), r, ui.visuals().text_color());
+                    }
+                });
+            });
     }
 }
 
diff --git a/epaint/CHANGELOG.md b/epaint/CHANGELOG.md
index e0a42144..9612e77b 100644
--- a/epaint/CHANGELOG.md
+++ b/epaint/CHANGELOG.md
@@ -3,6 +3,7 @@ All notable changes to the epaint crate will be documented in this file.
 
 
 ## Unreleased
+* Optimize tessellation of filled circles by 10x or more ([#1616](https://github.com/emilk/egui/pull/1616)).
 
 
 ## 0.18.1 - 2022-05-01
diff --git a/epaint/benches/benchmark.rs b/epaint/benches/benchmark.rs
index 3ae5d901..126ec2bf 100644
--- a/epaint/benches/benchmark.rs
+++ b/epaint/benches/benchmark.rs
@@ -1,6 +1,6 @@
 use criterion::{black_box, criterion_group, criterion_main, Criterion};
 
-use epaint::{pos2, Color32, Shape, Stroke};
+use epaint::*;
 
 fn single_dashed_lines(c: &mut Criterion) {
     c.bench_function("single_dashed_lines", move |b| {
@@ -39,5 +39,43 @@ fn many_dashed_lines(c: &mut Criterion) {
     });
 }
 
-criterion_group!(benches, single_dashed_lines, many_dashed_lines);
+fn tessellate_circles(c: &mut Criterion) {
+    c.bench_function("tessellate_circles_100k", move |b| {
+        let radii: [f32; 10] = [1.0, 2.0, 3.6, 4.0, 5.7, 8.0, 10.0, 13.0, 15.0, 17.0];
+        let mut clipped_shapes = vec![];
+        for r in radii {
+            for _ in 0..10_000 {
+                let clip_rect = Rect::from_min_size(Pos2::ZERO, Vec2::splat(1024.0));
+                let shape = Shape::circle_filled(Pos2::new(10.0, 10.0), r, Color32::WHITE);
+                clipped_shapes.push(ClippedShape(clip_rect, shape));
+            }
+        }
+        assert_eq!(clipped_shapes.len(), 100_000);
+
+        let pixels_per_point = 2.0;
+        let options = TessellationOptions::default();
+
+        let atlas = TextureAtlas::new([4096, 256]);
+        let font_tex_size = atlas.size();
+        let prepared_discs = atlas.prepared_discs();
+
+        b.iter(|| {
+            let clipped_primitive = tessellate_shapes(
+                pixels_per_point,
+                options,
+                font_tex_size,
+                prepared_discs.clone(),
+                clipped_shapes.clone(),
+            );
+            black_box(clipped_primitive);
+        });
+    });
+}
+
+criterion_group!(
+    benches,
+    single_dashed_lines,
+    many_dashed_lines,
+    tessellate_circles
+);
 criterion_main!(benches);
diff --git a/epaint/src/shadow.rs b/epaint/src/shadow.rs
index c6590aca..efbb2e50 100644
--- a/epaint/src/shadow.rs
+++ b/epaint/src/shadow.rs
@@ -73,6 +73,7 @@ impl Shadow {
                 ..Default::default()
             },
             font_tex_size,
+            vec![],
         );
         let mut mesh = Mesh::default();
         tessellator.tessellate_rect(&rect, &mut mesh);
diff --git a/epaint/src/tessellator.rs b/epaint/src/tessellator.rs
index f6e84a5d..a3e9d8a7 100644
--- a/epaint/src/tessellator.rs
+++ b/epaint/src/tessellator.rs
@@ -5,6 +5,7 @@
 
 #![allow(clippy::identity_op)]
 
+use crate::texture_atlas::PreparedDisc;
 use crate::*;
 use emath::*;
 
@@ -618,6 +619,10 @@ pub struct TessellationOptions {
     /// This likely makes
     pub coarse_tessellation_culling: bool,
 
+    /// If `true`, small filled circled will be optimized by using pre-rasterized circled
+    /// from the font atlas.
+    pub prerasterized_discs: bool,
+
     /// If `true` (default) align text to mesh grid.
     /// This makes the text sharper on most platforms.
     pub round_text_to_pixels: bool,
@@ -644,6 +649,7 @@ impl Default for TessellationOptions {
             feathering: true,
             feathering_size_in_pixels: 1.0,
             coarse_tessellation_culling: true,
+            prerasterized_discs: true,
             round_text_to_pixels: true,
             debug_paint_text_rects: false,
             debug_paint_clip_rects: false,
@@ -968,6 +974,8 @@ pub struct Tessellator {
     pixels_per_point: f32,
     options: TessellationOptions,
     font_tex_size: [usize; 2],
+    /// See [`TextureAtlas::prepared_discs`].
+    prepared_discs: Vec<PreparedDisc>,
     /// size of feathering in points. normally the size of a physical pixel. 0.0 if disabled
     feathering: f32,
     /// Only used for culling
@@ -980,10 +988,12 @@ impl Tessellator {
     /// Create a new [`Tessellator`].
     ///
     /// * `font_tex_size`: size of the font texture. Required to normalize glyph uv rectangles when tessellating text.
+    /// * `prepared_discs`: What [`TextureAtlas::prepared_discs`] returns. Can safely be set to an empty vec.
     pub fn new(
         pixels_per_point: f32,
         options: TessellationOptions,
         font_tex_size: [usize; 2],
+        prepared_discs: Vec<PreparedDisc>,
     ) -> Self {
         let feathering = if options.feathering {
             let pixel_size = 1.0 / pixels_per_point;
@@ -995,6 +1005,7 @@ impl Tessellator {
             pixels_per_point,
             options,
             font_tex_size,
+            prepared_discs,
             feathering,
             clip_rect: Rect::EVERYTHING,
             scratchpad_points: Default::default(),
@@ -1137,7 +1148,7 @@ impl Tessellator {
         let CircleShape {
             center,
             radius,
-            fill,
+            mut fill,
             stroke,
         } = shape;
 
@@ -1154,6 +1165,30 @@ impl Tessellator {
             return;
         }
 
+        if self.options.prerasterized_discs && fill != Color32::TRANSPARENT {
+            let radius_px = radius * self.pixels_per_point;
+            // strike the right balance between some circles becoming too blurry, and some too sharp.
+            let cutoff_radius = radius_px * 2.0_f32.powf(0.25);
+
+            // Find the right disc radius for a crisp edge:
+            // TODO: perhaps we can do something faster than this linear search.
+            for disc in &self.prepared_discs {
+                if cutoff_radius <= disc.r {
+                    let side = radius_px * disc.w / (self.pixels_per_point * disc.r);
+                    let rect = Rect::from_center_size(center, Vec2::splat(side));
+                    out.add_rect_with_uv(rect, disc.uv, fill);
+
+                    if stroke.is_empty() {
+                        return; // we are done
+                    } else {
+                        // we still need to do the stroke
+                        fill = Color32::TRANSPARENT; // don't fill again below
+                        break;
+                    }
+                }
+            }
+        }
+
         self.scratchpad_path.clear();
         self.scratchpad_path.add_circle(center, radius);
         self.scratchpad_path.fill(self.feathering, fill, out);
@@ -1476,7 +1511,8 @@ impl Tessellator {
 /// * `pixels_per_point`: number of physical pixels to each logical point
 /// * `options`: tessellation quality
 /// * `shapes`: what to tessellate
-/// * `font_tex_size`: size of the font texture (required to normalize glyph uv rectangles)
+/// * `font_tex_size`: size of the font texture. Required to normalize glyph uv rectangles when tessellating text.
+/// * `prepared_discs`: What [`TextureAtlas::prepared_discs`] returns. Can safely be set to an empty vec.
 ///
 /// The implementation uses a [`Tessellator`].
 ///
@@ -1485,10 +1521,12 @@ impl Tessellator {
 pub fn tessellate_shapes(
     pixels_per_point: f32,
     options: TessellationOptions,
-    shapes: Vec<ClippedShape>,
     font_tex_size: [usize; 2],
+    prepared_discs: Vec<PreparedDisc>,
+    shapes: Vec<ClippedShape>,
 ) -> Vec<ClippedPrimitive> {
-    let mut tessellator = Tessellator::new(pixels_per_point, options, font_tex_size);
+    let mut tessellator =
+        Tessellator::new(pixels_per_point, options, font_tex_size, prepared_discs);
 
     let mut clipped_primitives: Vec<ClippedPrimitive> = Vec::default();
 
@@ -1562,6 +1600,15 @@ fn test_tessellator() {
     let shape = Shape::Vec(shapes);
     let clipped_shapes = vec![ClippedShape(rect, shape)];
 
-    let primitives = tessellate_shapes(1.0, Default::default(), clipped_shapes, [100, 100]);
+    let font_tex_size = [1024, 1024]; // unused
+    let prepared_discs = vec![]; // unused
+
+    let primitives = tessellate_shapes(
+        1.0,
+        Default::default(),
+        font_tex_size,
+        prepared_discs,
+        clipped_shapes,
+    );
     assert_eq!(primitives.len(), 2);
 }
diff --git a/epaint/src/text/fonts.rs b/epaint/src/text/fonts.rs
index d699e101..611a4931 100644
--- a/epaint/src/text/fonts.rs
+++ b/epaint/src/text/fonts.rs
@@ -394,6 +394,12 @@ impl Fonts {
         self.lock().fonts.max_texture_side
     }
 
+    /// The font atlas.
+    /// Pass this to [`crate::Tessellator`].
+    pub fn texture_atlas(&self) -> Arc<Mutex<TextureAtlas>> {
+        self.lock().fonts.atlas.clone()
+    }
+
     /// Current size of the font image.
     /// Pass this to [`crate::Tessellator`].
     pub fn font_image_size(&self) -> [usize; 2] {
@@ -535,14 +541,7 @@ impl FontsImpl {
 
         let texture_width = max_texture_side.at_most(8 * 1024);
         let initial_height = 64;
-        let mut atlas = TextureAtlas::new([texture_width, initial_height]);
-
-        {
-            // Make the top left pixel fully white:
-            let (pos, image) = atlas.allocate((1, 1));
-            assert_eq!(pos, (0, 0));
-            image[pos] = 1.0;
-        }
+        let atlas = TextureAtlas::new([texture_width, initial_height]);
 
         let atlas = Arc::new(Mutex::new(atlas));
 
diff --git a/epaint/src/text/text_layout_types.rs b/epaint/src/text/text_layout_types.rs
index 3af4069d..a0d04566 100644
--- a/epaint/src/text/text_layout_types.rs
+++ b/epaint/src/text/text_layout_types.rs
@@ -401,7 +401,7 @@ pub struct Glyph {
     pub pos: Pos2,
     /// Advance width and font row height.
     pub size: Vec2,
-    /// Position of the glyph in the font texture.
+    /// Position of the glyph in the font texture, in texels.
     pub uv_rect: UvRect,
     /// Index into [`LayoutJob::sections`]. Decides color etc.
     pub section_index: u32,
diff --git a/epaint/src/texture_atlas.rs b/epaint/src/texture_atlas.rs
index 0b8fe4dd..96d1f8b3 100644
--- a/epaint/src/texture_atlas.rs
+++ b/epaint/src/texture_atlas.rs
@@ -1,6 +1,8 @@
+use emath::{remap_clamp, Rect};
+
 use crate::{FontImage, ImageDelta};
 
-#[derive(Clone, Copy, Eq, PartialEq)]
+#[derive(Clone, Copy, Debug, Eq, PartialEq)]
 struct Rectu {
     /// inclusive
     min_x: usize,
@@ -27,6 +29,26 @@ impl Rectu {
     };
 }
 
+#[derive(Copy, Clone, Debug)]
+struct PrerasterizedDisc {
+    r: f32,
+    uv: Rectu,
+}
+
+/// A pre-rasterized disc (filled circle), somewhere in the texture atlas.
+#[derive(Copy, Clone, Debug)]
+pub struct PreparedDisc {
+    /// The radius of this disc in texels.
+    pub r: f32,
+
+    /// Width in texels.
+    pub w: f32,
+
+    /// Where in the texture atlas the disc is.
+    /// Normalized in 0-1 range.
+    pub uv: Rect,
+}
+
 /// Contains font data in an atlas, where each character occupied a small rectangle.
 ///
 /// More characters can be added, possibly expanding the texture.
@@ -42,24 +64,98 @@ pub struct TextureAtlas {
 
     /// Set when someone requested more space than was available.
     overflowed: bool,
+
+    /// pre-rasterized discs of radii `2^i`, where `i` is the index.
+    discs: Vec<PrerasterizedDisc>,
 }
 
 impl TextureAtlas {
     pub fn new(size: [usize; 2]) -> Self {
         assert!(size[0] >= 1024, "Tiny texture atlas");
-        Self {
+        let mut atlas = Self {
             image: FontImage::new(size),
             dirty: Rectu::EVERYTHING,
             cursor: (0, 0),
             row_height: 0,
             overflowed: false,
+            discs: vec![], // will be filled in below
+        };
+
+        // Make the top left pixel fully white for `WHITE_UV`, i.e. painting something with solid color:
+        let (pos, image) = atlas.allocate((1, 1));
+        assert_eq!(pos, (0, 0));
+        image[pos] = 1.0;
+
+        // Allocate a series of anti-aliased discs used to render small filled circles:
+        // TODO: these circles can be packed A LOT better.
+        // In fact, the whole texture atlas could be packed a lot better.
+        // for r in [1, 2, 4, 8, 16, 32, 64] {
+        //     let w = 2 * r + 3;
+        //     let hw = w as i32 / 2;
+        const LARGEST_CIRCLE_RADIUS: f32 = 64.0;
+        for i in 0.. {
+            let r = 2.0_f32.powf(i as f32 / 2.0 - 1.0);
+            if r > LARGEST_CIRCLE_RADIUS {
+                break;
+            }
+            let hw = (r + 0.5).ceil() as i32;
+            let w = (2 * hw + 1) as usize;
+            let ((x, y), image) = atlas.allocate((w, w));
+            for dx in -hw..=hw {
+                for dy in -hw..=hw {
+                    let distance_to_center = ((dx * dx + dy * dy) as f32).sqrt();
+                    let coverage = remap_clamp(
+                        distance_to_center,
+                        (r as f32 - 0.5)..=(r as f32 + 0.5),
+                        1.0..=0.0,
+                    );
+                    image[((x as i32 + hw + dx) as usize, (y as i32 + hw + dy) as usize)] =
+                        coverage;
+                }
+            }
+            atlas.discs.push(PrerasterizedDisc {
+                r,
+                uv: Rectu {
+                    min_x: x,
+                    min_y: y,
+                    max_x: x + w,
+                    max_y: y + w,
+                },
+            });
         }
+
+        atlas
     }
 
     pub fn size(&self) -> [usize; 2] {
         self.image.size
     }
 
+    /// Returns the locations and sizes of pre-rasterized discs (filled circles) in this atlas.
+    pub fn prepared_discs(&self) -> Vec<PreparedDisc> {
+        let size = self.size();
+        let inv_w = 1.0 / size[0] as f32;
+        let inv_h = 1.0 / size[1] as f32;
+        self.discs
+            .iter()
+            .map(|disc| {
+                let r = disc.r;
+                let Rectu {
+                    min_x,
+                    min_y,
+                    max_x,
+                    max_y,
+                } = disc.uv;
+                let w = max_x - min_x;
+                let uv = Rect::from_min_max(
+                    emath::pos2(min_x as f32 * inv_w, min_y as f32 * inv_h),
+                    emath::pos2(max_x as f32 * inv_w, max_y as f32 * inv_h),
+                );
+                PreparedDisc { r, w: w as f32, uv }
+            })
+            .collect()
+    }
+
     fn max_height(&self) -> usize {
         // the initial width is likely the max texture side size
         self.image.width()