perf: simplify stroke outlines before PDF export

Each stroke mesh has about 16 points per pen sample, and every one of them
went into the PDF as a polygon point: a full handwritten page (1650 strokes)
took 2.9 s to export, and PNG export and copying a selection as an image
took as long, because both go through the PDF. The outline is now simplified
with a closed Douglas-Peucker that measures against segments, at most 0.01 mm
from the drawn outline. The same page now takes 0.44 s (PNG 0.55 s), the PDF
shrinks from 10.7 MB to 1.4 MB, and the rendered PNG differs only in edge
anti-aliasing (max 21/255). INK_NOTES_EXACT_OUTLINES=1 exports every point
as before.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/ARCHITECTURE.de.md

@@ -195,7 +195,7 @@ Jede Seite hat einen eigenen Verlauf (`history.rs`): Hinzufügen, Entfernen, Ers
 2. **PDF** (nur im Notfall): importierte PDF-Seite als Bild, falls sie sich nicht als Vektor übernehmen lässt.
 3. **Images:** eingefügte Bilder (höchstens 300 dpi).
 4. **Text:** Textfelder als echter Text mit eingebetteter Schrift (durchsuchbar, kopierbar). Jedes Feld liegt in einem eigenen Koordinatensystem, das eine Transformationsmatrix auf seine Ecken abbildet.
-5. **Ink:** Striche als gefüllte Polygone, Formen als Pfade. Halbtransparente Striche (Textmarker) bekommen einen Grafikzustand mit Deckkraft (`ca`/`CA`); printpdf kann solche Zustände nicht anlegen, deshalb trägt `add_alpha_states` sie nach dem Speichern mit `lopdf` in die Seitenressourcen ein. Jeder Strich ist ein einziger Pfad und deckt sich daher nicht selbst doppelt.
+5. **Ink:** Striche als gefüllte Polygone, Formen als Pfade. Halbtransparente Striche (Textmarker) bekommen einen Grafikzustand mit Deckkraft (`ca`/`CA`); printpdf kann solche Zustände nicht anlegen, deshalb trägt `add_alpha_states` sie nach dem Speichern mit `lopdf` in die Seitenressourcen ein. Jeder Strich ist ein einziger Pfad und deckt sich daher nicht selbst doppelt. Der Umriss eines Strichs wird vor dem Export vereinfacht (`geometry::simplify_closed_outline`, höchstens 0,01 mm vom gezeichneten entfernt): Das Netz hat etwa 16 Punkte je Stiftpunkt, und mit allen dauerte der Export einer vollen Seite Sekunden. `INK_NOTES_EXACT_OUTLINES=1` exportiert wie bisher jeden Punkt.
 
 Importierte PDF-Seiten werden anschließend als Form-XObject unter die Seite gelegt (`pdf_merge.rs`), bleiben also Vektorgrafik. Seitentitel werden zu Lesezeichen.
 

docs/ARCHITECTURE.md

@@ -195,7 +195,7 @@ Each page has its own history (`history.rs`): adding, removing, replacing and mo
 2. **PDF** (fallback only): imported PDF page as an image, if it cannot be taken over as vectors.
 3. **Images:** inserted images (at most 300 dpi).
 4. **Text:** text boxes as real text with embedded font (searchable, copyable). Each box lives in its own coordinate system that a transformation matrix maps onto its corners.
-5. **Ink:** strokes as filled polygons, shapes as paths. Semi-transparent strokes (highlighter) get a graphics state with opacity (`ca`/`CA`); printpdf cannot create such states, so `add_alpha_states` adds them to the page resources with `lopdf` after saving. Each stroke is a single path and therefore does not cover itself twice.
+5. **Ink:** strokes as filled polygons, shapes as paths. Semi-transparent strokes (highlighter) get a graphics state with opacity (`ca`/`CA`); printpdf cannot create such states, so `add_alpha_states` adds them to the page resources with `lopdf` after saving. Each stroke is a single path and therefore does not cover itself twice. The outline of a stroke is simplified before export (`geometry::simplify_closed_outline`, at most 0.01 mm away from the drawn one): the mesh has about 16 points per pen sample, and with all of them a full page took seconds to export. `INK_NOTES_EXACT_OUTLINES=1` exports every point as before.
 
 Imported PDF pages are then placed under the page as a form XObject (`pdf_merge.rs`), so they stay vector graphics. Page titles become bookmarks.
 

src/export.rs

@@ -1222,21 +1222,25 @@ fn render_stroke_polygon(layer: &printpdf::PdfLayerReference, stroke: &Stroke) {
 
     // Geschlossener Pfad um den Ribbon-Rand:
     // Left[0] -> Left[1] -> ... -> Left[n-1] -> Right[n-1] -> Right[n-2] -> ... -> Right[0]
-    let mut ring = Vec::with_capacity(n * 2);
-
-    // 1. Linke Hüllkurve vorwärts
-    for i in 0..n {
-        let v = stroke.vertices[i * 2];
-        let (x, y) = page_to_pdf_mm(v.position[0], v.position[1]);
-        ring.push((Point::new(Mm(x), Mm(y)), false));
-    }
-
-    // 2. Rechte Hüllkurve rückwärts
-    for i in (0..n).rev() {
-        let v = stroke.vertices[i * 2 + 1];
-        let (x, y) = page_to_pdf_mm(v.position[0], v.position[1]);
-        ring.push((Point::new(Mm(x), Mm(y)), false));
-    }
+    let outline: Vec<glam::Vec2> = (0..n)
+        .map(|i| stroke.vertices[i * 2].position)
+        .chain((0..n).rev().map(|i| stroke.vertices[i * 2 + 1].position))
+        .map(glam::Vec2::from)
+        .collect();
+    // The mesh has about 16 points per pen sample, far more than the eye (or a printer) can
+    // tell apart; fewer points make the PDF, PNG export and copying as an image much faster
+    let outline = if exact_outlines() {
+        outline
+    } else {
+        crate::geometry::simplify_closed_outline(&outline, OUTLINE_TOLERANCE)
+    };
+    let ring: Vec<(Point, bool)> = outline
+        .iter()
+        .map(|p| {
+            let (x, y) = page_to_pdf_mm(p.x, p.y);
+            (Point::new(Mm(x), Mm(y)), false)
+        })
+        .collect();
 
     let fill_color = Color::Rgb(Rgb::new(
         stroke.color[0],
@@ -1254,6 +1258,17 @@ fn render_stroke_polygon(layer: &printpdf::PdfLayerReference, stroke: &Stroke) {
     layer.add_polygon(poly);
 }
 
+/// Largest deviation of an exported stroke outline from the drawn one, in page units
+/// (0.01 mm: a tenth of a pixel at 200 dpi).
+pub const OUTLINE_TOLERANCE: f32 = 0.1;
+
+/// `INK_NOTES_EXACT_OUTLINES=1` exports every point of the stroke outlines, as before this change
+/// (fallback in case the simplified outlines ever look wrong).
+fn exact_outlines() -> bool {
+    static EXACT: std::sync::OnceLock<bool> = std::sync::OnceLock::new();
+    *EXACT.get_or_init(|| std::env::var_os("INK_NOTES_EXACT_OUTLINES").is_some_and(|v| v != "0"))
+}
+
 /// Strategie B: Kubische Bézier-Kurven aus den Abtastpunkten via printpdf::Line.
 fn render_stroke_bezier(layer: &printpdf::PdfLayerReference, stroke: &Stroke) {
     if stroke.points.is_empty() {

src/geometry.rs

@@ -352,6 +352,63 @@ fn rdp_recursive(points: &[Vec2], epsilon: f32) -> Vec<Vec2> {
     }
 }
 
+/// Simplifies a closed outline (the last point connects back to the first) so that no point
+/// of the original lies farther than `tolerance` from the result. Unlike
+/// [`ramer_douglas_peucker`], it measures the distance to the segment, not to the infinite
+/// line, so stroke tips that turn back are kept. Works without recursion, so long strokes
+/// cannot overflow the stack.
+pub fn simplify_closed_outline(points: &[Vec2], tolerance: f32) -> Vec<Vec2> {
+    if points.len() <= 3 {
+        return points.to_vec();
+    }
+    // Two chains between the first point and the point farthest from it: the start of an
+    // outline often lies on top of its end (round cap), which would leave no chord to measure
+    let far = (1..points.len())
+        .max_by(|&i, &j| {
+            points[i]
+                .distance_squared(points[0])
+                .total_cmp(&points[j].distance_squared(points[0]))
+        })
+        .unwrap_or(1);
+    let mut keep = vec![false; points.len()];
+    keep[0] = true;
+    keep[far] = true;
+    let mut stack = vec![(0, far), (far, points.len())];
+    while let Some((start, end)) = stack.pop() {
+        // `end == points.len()` closes the ring back to the first point
+        let (a, b) = (points[start], points[end % points.len()]);
+        let mut worst = (0.0_f32, start);
+        for (i, &p) in points.iter().enumerate().take(end).skip(start + 1) {
+            let d = point_to_segment_dist(p, a, b);
+            if d > worst.0 {
+                worst = (d, i);
+            }
+        }
+        if worst.0 > tolerance {
+            keep[worst.1] = true;
+            stack.push((start, worst.1));
+            stack.push((worst.1, end));
+        }
+    }
+    points
+        .iter()
+        .zip(keep)
+        .filter_map(|(&p, keep)| keep.then_some(p))
+        .collect()
+}
+
+/// Abstand eines Punktes `p` zur Strecke von `a` nach `b`.
+#[inline]
+pub fn point_to_segment_dist(p: Vec2, a: Vec2, b: Vec2) -> f32 {
+    let ab = b - a;
+    let len_sq = ab.length_squared();
+    if len_sq < 1e-12 {
+        return p.distance(a);
+    }
+    let t = ((p - a).dot(ab) / len_sq).clamp(0.0, 1.0);
+    p.distance(a + ab * t)
+}
+
 /// Abstand eines Punktes `p` zur Geraden durch `a` und `b`.
 #[inline]
 pub fn point_to_line_dist(p: Vec2, a: Vec2, b: Vec2) -> f32 {
@@ -2327,6 +2384,78 @@ pub fn shape_to_stroke(
 mod tests {
     use super::*;
 
+    /// Largest distance of any point of `original` from the closed outline `simplified`.
+    fn outline_deviation(original: &[Vec2], simplified: &[Vec2]) -> f32 {
+        original
+            .iter()
+            .map(|&p| {
+                (0..simplified.len())
+                    .map(|i| {
+                        point_to_segment_dist(
+                            p,
+                            simplified[i],
+                            simplified[(i + 1) % simplified.len()],
+                        )
+                    })
+                    .fold(f32::INFINITY, f32::min)
+            })
+            .fold(0.0, f32::max)
+    }
+
+    #[test]
+    fn test_simplified_stroke_outline_stays_within_tolerance() {
+        // A handwritten loop like a letter, as the pen delivers it
+        let samples: Vec<StylusSample> = (0..30)
+            .map(|i| {
+                let t = i as f32 / 29.0 * std::f32::consts::TAU * 1.3;
+                StylusSample {
+                    position: Vec2::new(500.0 + 12.0 * t.cos() + t * 4.0, 800.0 + 20.0 * t.sin()),
+                    pressure: 0.4 + 0.3 * (t * 0.7).sin().abs(),
+                    timestamp: i as f64 * 0.008,
+                }
+            })
+            .collect();
+        let vertices = crate::storage::reconstruct_stroke_vertices(
+            &samples,
+            [0.0, 0.0, 0.0, 1.0],
+            5.0,
+            Default::default(),
+            true,
+        );
+        let n = vertices.len() / 2;
+        let outline: Vec<Vec2> = (0..n)
+            .map(|i| vertices[i * 2].position)
+            .chain((0..n).rev().map(|i| vertices[i * 2 + 1].position))
+            .map(Vec2::from)
+            .collect();
+        let tolerance = 0.1;
+        let simplified = simplify_closed_outline(&outline, tolerance);
+        let deviation = outline_deviation(&outline, &simplified);
+        assert!(deviation <= tolerance + 1e-4, "{deviation}");
+        assert!(
+            simplified.len() * 4 < outline.len(),
+            "{} -> {} points",
+            outline.len(),
+            simplified.len()
+        );
+    }
+
+    #[test]
+    fn test_simplified_outline_keeps_tips_that_turn_back() {
+        // Thin hairpin: out along y = 0 to x = 20, back along y = 0.05. Measured against the
+        // infinite line, the tip would vanish.
+        let mut outline: Vec<Vec2> = (0..=20).map(|x| Vec2::new(x as f32, 0.0)).collect();
+        outline.extend((0..20).rev().map(|x| Vec2::new(x as f32, 0.05)));
+        let simplified = simplify_closed_outline(&outline, 0.1);
+        let reach = simplified.iter().map(|p| p.x).fold(f32::MIN, f32::max);
+        assert_eq!(reach, 20.0, "{simplified:?}");
+        assert!(outline_deviation(&outline, &simplified) <= 0.1);
+        assert!(simplified.len() <= 4, "{simplified:?}");
+        // Tiny outlines stay as they are
+        let dot = [Vec2::ZERO, Vec2::X, Vec2::Y];
+        assert_eq!(simplify_closed_outline(&dot, 0.1), dot.to_vec());
+    }
+
     #[test]
     fn test_detect_line() {
         // Leicht zittrige diagonale Punktfolge