Merge pull request #6955 from dotCooCoo/fix/blend-profiles-follow-key-start

Blend: stroke profiles turn with a key path started at another anchor

crates/doc/src/blend.rs

@@ -236,7 +236,8 @@ fn lcm(a: usize, b: usize) -> usize {
     a.checked_div(x).map_or(0, |q| q * b)
 }
 
-/// Interpolate width profiles (none is uniform) at every position either has a width point.
+/// Interpolate width profiles (none is uniform) at every position either has a width point,
+/// keeping their discontinuous points (a position where either steps gives two points).
 fn lerp_profile(x: Option<&WidthProfile>, y: Option<&WidthProfile>, t: f64) -> Option<WidthProfile> {
     if x.is_none() && y.is_none() {
         return None;
@@ -245,22 +246,45 @@ fn lerp_profile(x: Option<&WidthProfile>, y: Option<&WidthProfile>, t: f64) -> O
     let (x, y) = (x.unwrap_or(&uniform), y.unwrap_or(&uniform));
     let mut at: Vec<f64> = x.points.iter().chain(&y.points).map(|p| p.0).filter(|p| p.is_finite()).collect();
     at.sort_by(f64::total_cmp);
-    at.dedup_by(|a, b| (*a - *b).abs() < 1e-6);
-    let points = at
-        .into_iter()
-        .map(|p| {
-            let ((l1, r1), (l2, r2)) = (x.at(p), y.at(p));
-            (p, lerp_f64(l1, l2, t), lerp_f64(r1, r2, t))
-        })
-        .collect();
+    // Within the distance `around` reads a discontinuous point at, so a point near one keeps it.
+    at.dedup_by(|a, b| (*a - *b).abs() <= 1e-7);
+    // Each profile is a smooth curve through its own points: samples between the positions keep
+    // both curves' shapes where the other profile's points and steps change the tangents. Two
+    // profiles with points at the same positions need none (so a preset on both keys stays it).
+    let same_positions = x.points.len() == y.points.len() && x.points.iter().zip(&y.points).all(|(p, q)| (p.0 - q.0).abs() <= 1e-7);
+    let per_span = if same_positions { 1 } else { (4096 / at.len().max(1)).clamp(1, 8) };
+    let mut points = Vec::with_capacity(at.len() * per_span + 2);
+    let mix = |p: f64, (l1, r1): (f64, f64), (l2, r2): (f64, f64)| (p, lerp_f64(l1, l2, t), lerp_f64(r1, r2, t));
+    for (k, &p) in at.iter().enumerate() {
+        let ((xb, xa), (yb, ya)) = (x.around(p), y.around(p));
+        points.push(mix(p, xb, yb));
+        // A discontinuous point ends the curve on each side even where both widths match.
+        if steps_at(x, p) || steps_at(y, p) {
+            points.push(mix(p, xa, ya));
+        }
+        if let Some(&q) = at.get(k + 1) {
+            for j in 1..per_span {
+                let f = p + (q - p) * j as f64 / per_span as f64;
+                points.push(mix(f, x.at(f), y.at(f)));
+            }
+        }
+    }
     Some(WidthProfile { points })
 }
 
+/// Whether width profile `w` has a discontinuous point at `p` (two points there, within `1e-7`,
+/// as [`WidthProfile::around`] reads them).
+fn steps_at(w: &WidthProfile, p: f64) -> bool {
+    let i = w.points.partition_point(|q| q.0 < p - 1e-7);
+    w.points.get(i..).unwrap_or_default().iter().take_while(|q| q.0 <= p + 1e-7).count() > 1
+}
+
 /// The positions along the stroke where either of two pen recordings has a sample, in order.
 fn sample_positions(x: Option<&[(f64, f64)]>, y: Option<&[(f64, f64)]>) -> Vec<f64> {
     let mut at: Vec<f64> = x.unwrap_or_default().iter().chain(y.unwrap_or_default()).map(|p| p.0).filter(|p| p.is_finite()).collect();
     at.sort_by(f64::total_cmp);
-    at.dedup_by(|a, b| (*a - *b).abs() < 1e-6);
+    // Within the distance `step_after` reads a step at, so a sample near a step keeps the step.
+    at.dedup_by(|a, b| (*a - *b).abs() <= 1e-9);
     if at.is_empty() {
         at = vec![0.0, 1.0];
     }
@@ -487,6 +511,161 @@ fn reverse_closed(sp: &mut SubPath) {
     sp.anchors.rotate_right(1);
 }
 
+/// How a key's subpaths were turned for its blend, so that its stroke's profiles, pen
+/// recordings and arrowheads turn with it: position `u` along the turned subpath is position
+/// `start + u` (`start - u` when `reversed`) along the key's own, wrapping round a closed one.
+#[derive(Clone, Copy, Debug, Default, PartialEq)]
+struct Orient {
+    start: f64,
+    reversed: bool,
+    closed: bool,
+}
+
+impl Orient {
+    fn of(sp: &SubPath) -> Self {
+        Self { closed: sp.closed, ..Self::default() }
+    }
+
+    /// The subpath now starts at the fraction `f` of its length.
+    fn rotate(&mut self, f: f64) {
+        self.start += if self.reversed { -f } else { f };
+    }
+
+    /// The subpath now runs the other way.
+    fn reverse(&mut self) {
+        self.start += if self.reversed { -1.0 } else { 1.0 };
+        self.reversed = !self.reversed;
+    }
+
+    /// As [`start_at`] turns `sp` (call it before).
+    fn start_at(&mut self, sp: &SubPath, i: usize) {
+        let n = sp.anchors.len();
+        if i >= n {
+            return;
+        }
+        if sp.closed {
+            self.rotate(arc_fraction(sp, i));
+        } else if i + 1 == n && n > 1 {
+            self.reverse();
+        }
+    }
+
+    /// Where a closed subpath now starts, as a fraction of its length; 0 for an open one.
+    fn seam(&self) -> f64 {
+        let s = if self.closed { self.start.rem_euclid(1.0) } else { 0.0 };
+        if s > 1e-9 && s < 1.0 - 1e-9 { s } else { 0.0 }
+    }
+
+    fn is_identity(&self) -> bool {
+        !self.reversed && self.seam() == 0.0
+    }
+
+    /// Whether two subpaths were turned alike, so one stroke along both turns the same way.
+    fn same_turn(&self, o: &Self) -> bool {
+        self.reversed == o.reversed && (self.seam() - o.seam()).abs() < 1e-9
+    }
+}
+
+/// How far along `sp` its anchor `i` sits, as a fraction of its length.
+fn arc_fraction(sp: &SubPath, i: usize) -> f64 {
+    let pos = sp.anchor_arc_positions();
+    match (pos.get(i), pos.last()) {
+        (Some(&at), Some(&total)) if total.is_finite() && total > 1e-12 => (at / total).clamp(0.0, 1.0),
+        _ => 0.0,
+    }
+}
+
+/// Samples (position, value) along a key's subpath, read along the subpath turned as `o` says.
+/// A closed subpath starting elsewhere starts the samples there too: the ones before it move
+/// past the seam (`wrap` applied), which keeps any step the seam makes, and a value between
+/// samples is read with `at`. A reversed subpath then reads them backwards (`flip` applied).
+fn reoriented<V: Copy>(points: &[(f64, V)], o: Orient, at: impl Fn(f64) -> V, wrap: impl Fn(V) -> V, flip: impl Fn(V) -> V) -> Vec<(f64, V)> {
+    let s = o.seam();
+    let mut out = points.to_vec();
+    if s > 0.0
+        && let (Some(&(_, first)), Some(&(_, last))) = (points.first(), points.last())
+    {
+        let i = points.partition_point(|q| q.0 < s - 1e-9);
+        let j = points.partition_point(|q| q.0 <= s + 1e-9).max(i);
+        let (before, after) = match points.get(i..j) {
+            Some([p, .., q]) => (p.1, q.1),
+            Some([p]) => (p.1, p.1),
+            _ => (at(s), at(s)),
+        };
+        out = Vec::with_capacity(points.len() + 4);
+        out.push((0.0, after));
+        out.extend(points.get(j..).unwrap_or_default().iter().map(|&(t, v)| (t - s, v)));
+        out.push((1.0 - s, last));
+        out.push((1.0 - s, wrap(first)));
+        out.extend(points.get(..i).unwrap_or_default().iter().map(|&(t, v)| (t + 1.0 - s, wrap(v))));
+        out.push((1.0, wrap(before)));
+    }
+    if o.reversed {
+        out = out.into_iter().rev().map(|(t, v)| (1.0 - t, flip(v))).collect();
+    }
+    out
+}
+
+/// A key's stroke read along its subpath turned as `o` says: its width profile (whose sides swap
+/// when reversed), pen pressure, tilt, bearing and rotation, and on a reversed open path its
+/// arrowheads.
+fn reorient_stroke(s: &mut StrokeLayer, o: Orient) {
+    if o.is_identity() {
+        return;
+    }
+    let same = |v: f64| v;
+    if let Some(p) = &mut s.profile {
+        let mut pts: Vec<(f64, (f64, f64))> = p.points.iter().map(|&(t, l, r)| (t, (l, r))).collect();
+        // A width profile is a smooth curve through its points: where the new start splits a span,
+        // samples of that span keep its curve once its ends become ends of the profile.
+        let seam = o.seam();
+        let i = p.points.partition_point(|q| q.0 < seam);
+        if seam > 0.0
+            && let (Some(a), Some(b)) = (i.checked_sub(1).and_then(|j| p.points.get(j)), p.points.get(i))
+            && seam - a.0 > 1e-9
+            && b.0 - seam > 1e-9
+        {
+            const SAMPLES: usize = 32;
+            let (a, b) = (a.0, b.0);
+            let extra: Vec<(f64, (f64, f64))> =
+                (1..SAMPLES).map(|k| a + (b - a) * k as f64 / SAMPLES as f64).filter(|f| (f - seam).abs() > 1e-9).map(|f| (f, p.at(f))).collect();
+            pts.splice(i..i, extra);
+        }
+        let out = reoriented(&pts, o, |f| p.at(f), |v| v, |(l, r)| (r, l));
+        p.points = out.into_iter().map(|(t, (l, r))| (t, l, r)).collect();
+    }
+    for p in [&mut s.pressure, &mut s.tilt].into_iter().flatten() {
+        let out = reoriented(&p.points, o, |f| p.at(f), same, same);
+        p.points = out;
+    }
+    for p in [&mut s.bearing, &mut s.rotation].into_iter().flatten() {
+        // The samples moved past the seam carry the whole turns the recording makes along the
+        // stroke, so the angle does not jump by them there.
+        let turns = match (p.points.first(), p.points.last()) {
+            (Some(a), Some(b)) if (b.1 - a.1).is_finite() => ((b.1 - a.1) / 360.0).round() * 360.0,
+            _ => 0.0,
+        };
+        let out = reoriented(&p.points, o, |f| p.unwrapped_at(f), |v| v + turns, same);
+        p.points = out;
+    }
+    if o.reversed && !o.closed {
+        std::mem::swap(&mut s.start_arrow, &mut s.end_arrow);
+        s.arrow_scale = (s.arrow_scale.1, s.arrow_scale.0);
+    }
+}
+
+/// `n` with every stroke read along its subpaths turned as `o` says.
+fn reorient_strokes(n: &mut Node, o: Orient) {
+    if o.is_identity() {
+        return;
+    }
+    for it in n.appearance.items.iter_mut() {
+        if let AppearanceItem::Stroke(s) = it {
+            reorient_stroke(s, o);
+        }
+    }
+}
+
 /// Anchor positions of a subpath relative to its box, scaled to unit size.
 fn normalised(sp: &SubPath) -> Vec<Vec2> {
     let pts = sp.anchors.iter().map(|a| a.p);
@@ -524,6 +703,8 @@ fn best_rotation(a: &SubPath, b: &SubPath) -> usize {
 pub struct PathPair {
     a: Vec<SubPath>,
     b: Vec<SubPath>,
+    /// How each path's subpaths were turned, where all of them turned alike (else unturned).
+    orient: (Orient, Orient),
 }
 
 impl PathPair {
@@ -535,6 +716,7 @@ impl PathPair {
         let cb = b.bounds().map(|r| r.center()).unwrap_or_default();
         let degenerate = |like: &SubPath, c: Point| SubPath::new(vec![Anchor::corner(c); like.anchors.len().max(1)], like.closed);
         let (mut va, mut vb) = (Vec::with_capacity(n), Vec::with_capacity(n));
+        let mut orient = (Orient::default(), Orient::default());
         for i in 0..n {
             let (mut sa, mut sb) = match (a.subpaths.get(i), b.subpaths.get(i)) {
                 (Some(x), Some(y)) => (x.clone(), y.clone()),
@@ -542,17 +724,21 @@ impl PathPair {
                 (None, Some(y)) => (degenerate(y, ca), y.clone()),
                 (None, None) => continue,
             };
+            let (mut oa, mut ob) = (Orient::of(&sa), Orient::of(&sb));
             let explicit = i == 0 && (starts.0.is_some() || starts.1.is_some());
             if explicit {
                 if let Some(s) = starts.0 {
+                    oa.start_at(&sa, s);
                     start_at(&mut sa, s);
                 }
                 if let Some(s) = starts.1 {
+                    ob.start_at(&sb, s);
                     start_at(&mut sb, s);
                 }
             }
             let closed = sa.closed && sb.closed && sa.anchors.len() > 2 && sb.anchors.len() > 2;
             if closed && (sa.area() * sb.area()) < 0.0 {
+                ob.reverse();
                 reverse_closed(&mut sb);
             }
             let m = sa.anchors.len().max(sb.anchors.len());
@@ -560,12 +746,26 @@ impl PathPair {
             grow(&mut sb, m);
             if closed && !explicit {
                 let r = best_rotation(&sa, &sb);
+                if r != 0 {
+                    ob.rotate(arc_fraction(&sb, r));
+                }
                 sb.anchors.rotate_left(r);
             }
+            // One stroke runs along every subpath of a key, each reading it by its own length, so
+            // it turns only when all of the key's subpaths turned alike.
+            if i == 0 {
+                orient = (oa, ob);
+            }
+            if i < a.subpaths.len() && !orient.0.same_turn(&oa) {
+                orient.0 = Orient::default();
+            }
+            if i < b.subpaths.len() && !orient.1.same_turn(&ob) {
+                orient.1 = Orient::default();
+            }
             va.push(sa);
             vb.push(sb);
         }
-        Self { a: va, b: vb }
+        Self { a: va, b: vb, orient }
     }
 
     /// The path at `t` (0 = `a`, 1 = `b`).
@@ -680,7 +880,12 @@ impl Lerp {
                 _ => Shape::Other,
             },
         };
-        Self { a: a.clone(), b: b.clone(), shape }
+        let (mut a, mut b) = (a.clone(), b.clone());
+        if let Shape::Path { pair, .. } = &shape {
+            reorient_strokes(&mut a, pair.orient.0);
+            reorient_strokes(&mut b, pair.orient.1);
+        }
+        Self { a, b, shape }
     }
 
     /// The object at `t` (0 = `a`, 1 = `b`), with id 0.
@@ -1597,6 +1802,7 @@ pub fn blend_expand(keys: &[Arc<Node>], spec: &BlendSpec) -> Vec<Node> {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use crate::appearance::Arrowhead;
     use vectorcraft_geom::{Rect, shapes};
 
     #[test]
@@ -1909,6 +2115,89 @@ mod tests {
         assert!(s.pressure.is_none() && s.tilt.is_none() && s.bearing.is_none() && s.rotation.is_none());
     }
 
+    #[test]
+    fn a_point_near_the_other_keys_step_keeps_the_step() {
+        let flat = PressureProfile { points: vec![(0.0, 0.0), (0.4999995, 0.0), (1.0, 0.0)] };
+        let stepped = PressureProfile { points: vec![(0.0, 0.0), (0.5, 0.0), (0.5, 1.0), (1.0, 1.0)] };
+        let p = lerp_pressure(Some(&flat), Some(&stepped), 1.0).unwrap_or_default();
+        assert!((p.at(0.75) - 1.0).abs() < 1e-9, "{p:?}");
+        let narrow = WidthProfile { points: vec![(0.0, 1.0, 1.0), (0.4999995, 1.0, 1.0), (1.0, 1.0, 1.0)] };
+        let stepped = WidthProfile { points: vec![(0.0, 1.0, 1.0), (0.5, 1.0, 1.0), (0.5, 0.0, 0.0), (1.0, 0.0, 0.0)] };
+        let w = lerp_profile(Some(&narrow), Some(&stepped), 1.0).unwrap_or_default();
+        assert!(w.at(0.75).0.abs() < 1e-9, "{w:?}");
+        // The other key's step doesn't reshape a smooth profile's curve.
+        let early = WidthProfile { points: vec![(0.0, 1.0, 1.0), (0.25, 1.0, 1.0), (0.25, 0.5, 0.5), (1.0, 0.5, 0.5)] };
+        let w = lerp_profile(Some(&WidthProfile::lens()), Some(&early), 0.0).unwrap_or_default();
+        for u in [0.1, 0.125, 0.2, 0.3, 0.4] {
+            let (got, want) = (w.at(u).0, WidthProfile::lens().at(u).0);
+            assert!((got - want).abs() < 5e-3, "at {u}: {got} for {want}: {w:?}");
+        }
+        let lens = WidthProfile::lens();
+        assert_eq!(lerp_profile(Some(&lens), Some(&lens), 0.5).and_then(|p| p.preset_id()), Some("lens"));
+    }
+
+    #[test]
+    fn stroke_profiles_turn_with_a_key_path_started_elsewhere() {
+        let keyed = |path: PathData, edit: &dyn Fn(&mut StrokeLayer)| {
+            let mut ap = Appearance::default();
+            ap.set_stroke(Paint::solid(Color::BLACK));
+            if let Some(s) = ap.stroke_mut() {
+                edit(s);
+            }
+            Node::path(NodeId(1), path, ap)
+        };
+        let stroke = |n: &Node| n.appearance.stroke().cloned().unwrap_or_else(|| panic!("a stroke"));
+        let pressure = |s: &StrokeLayer, f: f64| s.pressure.as_ref().map_or(PressureProfile::MID, |p| p.at(f));
+        // An open key clicked at its last anchor runs the other way, and so do its pressure, its
+        // width profile (whose sides swap) and its arrowheads.
+        let line = |x: f64| PathData::single(SubPath::polyline(&[Point::new(x, 0.0), Point::new(x + 10.0, 0.0)], false));
+        let light = keyed(line(0.0), &|s| s.pressure = Some(PressureProfile { points: vec![(0.0, 0.0), (1.0, 0.0)] }));
+        let ramp = keyed(line(100.0), &|s| {
+            s.pressure = Some(PressureProfile { points: vec![(0.0, 1.0), (1.0, 0.0)] });
+            s.profile = Some(WidthProfile { points: vec![(0.0, 1.0, 0.0), (1.0, 0.0, 0.0)] });
+            s.start_arrow = Some(Arrowhead::Triangle);
+            s.arrow_scale = (200.0, 100.0);
+        });
+        let blend = Lerp::new(&light, &ramp, (None, Some(1)));
+        let s = stroke(&blend.at(0.25));
+        assert!(pressure(&s, 0.0).abs() < 1e-9 && (pressure(&s, 1.0) - 0.25).abs() < 1e-9, "{:?}", s.pressure);
+        let s = stroke(&blend.at(1.0));
+        assert_eq!(s.profile.as_ref().map(|p| p.at(1.0)), Some((0.0, 1.0)), "{:?}", s.profile);
+        assert_eq!((s.start_arrow, s.end_arrow, s.arrow_scale), (None, Some(Arrowhead::Triangle), (100.0, 200.0)));
+        // A key whose other subpaths keep their direction keeps its one stroke as it is.
+        let two = |x: f64| {
+            let sub = |y: f64| SubPath::polyline(&[Point::new(x, y), Point::new(x + 10.0, y)], false);
+            PathData::new(vec![sub(0.0), sub(20.0)])
+        };
+        let ramps = keyed(two(100.0), &|s| s.pressure = Some(PressureProfile { points: vec![(0.0, 1.0), (1.0, 0.0)] }));
+        let s = stroke(&Lerp::new(&keyed(two(0.0), &|_| {}), &ramps, (None, Some(1))).at(1.0));
+        assert!((pressure(&s, 0.0) - 1.0).abs() < 1e-9, "{:?}", s.pressure);
+        // A closed key started half way round starts its recordings there too, keeping the step
+        // where its own start was and the whole turn its rotation makes.
+        let square = |x: f64| shapes::rectangle(Rect::new(x, 0.0, x + 10.0, 10.0));
+        let plain = keyed(square(0.0), &|_| {});
+        let turning = keyed(square(100.0), &|s| {
+            s.pressure = Some(PressureProfile { points: vec![(0.0, 0.0), (1.0, 1.0)] });
+            s.rotation = Some(AngleProfile { points: vec![(0.0, 0.0), (1.0, 360.0)] });
+            s.profile = Some(WidthProfile { points: vec![(0.0, 1.0, 1.0), (1.0, 0.0, 0.0)] });
+        });
+        let blend = Lerp::new(&plain, &turning, (Some(0), Some(2)));
+        let s = stroke(&blend.at(1.0));
+        assert!((pressure(&s, 0.25) - 0.75).abs() < 1e-9 && (pressure(&s, 0.75) - 0.25).abs() < 1e-9, "{:?}", s.pressure);
+        let width = s.profile.as_ref().map_or((1.0, 1.0), |p| p.at(0.75));
+        assert!((width.0 - 0.75).abs() < 1e-6 && (width.1 - 0.75).abs() < 1e-6, "the width steps where the key started: {:?}", s.profile);
+        // A width curve split by the new start keeps its shape.
+        let lensed = keyed(square(100.0), &|s| s.profile = Some(WidthProfile::lens()));
+        let s = stroke(&Lerp::new(&plain, &lensed, (Some(0), Some(1))).at(1.0));
+        for u in [0.05, 0.125, 0.2, 0.6, 0.7, 0.74, 0.76, 0.8, 0.875, 0.95] {
+            let (got, want) = (s.profile.as_ref().map_or(1.0, |p| p.at(u).0), WidthProfile::lens().at((u + 0.25) % 1.0).0);
+            assert!((got - want).abs() < 2e-3, "at {u}: {got} for {want}: {:?}", s.profile);
+        }
+        let rot = |t: f64, f: f64| stroke(&blend.at(t)).rotation.as_ref().map_or(0.0, |p| p.unwrapped_at(f));
+        assert!((vectorcraft_geom::normalize_deg(rot(1.0, 0.25)) + 90.0).abs() < 1e-6, "{:?}", s.rotation);
+        assert!((rot(0.5, 0.499) - rot(0.5, 0.501)).abs() < 1.0, "no jump where the key started: {:?}", stroke(&blend.at(0.5)).rotation);
+    }
+
     #[test]
     fn odd_dash_blends_to_solid_with_closed_gaps() {
         let d = lerp_dash(Some(&Dash { pattern: vec![2.0, 3.0, 4.0], ..Default::default() }), None, 1.0).unwrap();

docs/mcp.md

@@ -9150,7 +9150,8 @@ during it puts the value back:
 How blends interpolate: closed shapes start where they twist least unless `starts` picks the anchors; strokes
 interpolate weight, dashes (a solid stroke counts as the dashed one with its gaps closed), miter limit, arrowhead scale,
 width profiles and the pen pressure, tilt, bearing and rotation recorded with the Paintbrush (a stroke without a
-recording counts as half pressure, half tilt and 0°, as brushes read it; angles turn the shorter way round), while
+recording counts as half pressure, half tilt and 0°, as brushes read it; angles turn the shorter way round; a key's
+profiles, recordings and arrowheads turn with its path when the blend starts it at another anchor), while
 caps, joins, alignment, arrowheads and brushes switch halfway; gradients of one kind with
 different stop counts resample to a common set of stops. Groups pair their members in stacking order (members only
 one group has grow out of the other's centre), compound paths stay compound paths, and type, symbol instances and

docs/target-app-parity.md

@@ -1023,7 +1023,7 @@ Moved from the ROADMAP's "Shipped so far" on 2026-10-10. Update it when a featur
   - **Live Corners:** drag a live rectangle's corner widgets (Selection or Direct Selection) to round all corners, with a radius readout; with Direct Selection, select corner anchors to show and round just those corners (#381). Each corner keeps its own radius and kind (Round, Inverted Round, Chamfer): Alt-click a widget to cycle the kind, double-click it for the Corners dialog, and the Properties and Transform radius fields set the selected corners (`object.setLiveShape {corners, radius, kind}`). A link toggle behind Corner Radius (the `singleCornerRadius` preference) switches the panels to a field for each corner of a live rectangle: Top Left, Top Right, Bottom Right and Bottom Left. Corners stay circular when the rectangle is scaled unevenly or along its own sides when rotated (the radius keeps its size, or scales by the mean scale with Scale Corners on); only a shear distorts them. On a rectangle that isn't square every corner is the same circle: a radius past half the shorter side stops there for all of them, the widgets sit on the corners as drawn and turn the edited corners red at that limit, CSS export writes the drawn radii, and rectangles saved stretched by older versions get circular corners when their corners are next set (#442). Live Corners work on any path's corners too, as on a rectangle's (#511): a star's, a live polygon's (which also shows them to the Selection tool, has a Corner Radius field in the Properties and Transform panels and keeps its radius as its sides change) and a pen path's, wherever two sides meet at an angle at an anchor that isn't smooth: curved sides too, trimmed to what the cut leaves of them (#1144). Direct Selection shows the widgets of every corner, or of the corners holding selected anchors; each corner is a circle tangent to both sides, drawn no larger than takes its cut halfway along its shorter side; a path keeps its uncut outline so its corners stay editable, and the same command, dialog, angle preference and View › Hide Corner Widget apply. With Direct Selection a click on a widget (no drag) selects its corner, as a click on the corner's anchor does, so the next drag on it rounds that corner alone; Shift-click toggles it (#1239). While a corner widget is dragged with the Selection tool the bounding box hides, so the rounding shows against the path alone (#1229). A round corner next to a curved side curves smoothly instead of sticking out of the shape (#1547, fixes #1512).
     View › Hide Edges hides the Live Corners widgets, the bounding box and the type widget, and the selection tools then do not answer a press on them or change the cursor over them.
   - **Blend spine Anchor Point tool (#2544):** on a selected blend, dragging a spine corner makes symmetric Smooth handles; the tool displays and picks existing spine handles when switched to, drags one independently or retracts it on click, and clicking a point with handles retracts both. The spine is edited live without moving its key objects. Windows native canvas checks and screenshots reviewed: symmetric and independent handles, corner/retraction, Shift constraints and perpendicular reshaping, tool switching, key preservation, Undo/Redo, save/reopen, hidden handles and overlapping Path/Blend priority (PR #2643). Behaviour reference: [public path-editing documentation](https://helpx.adobe.com/illustrator/using/adjust-path-segments.html).
-  - **Blend steps of brushed strokes:** the steps interpolate the pen pressure, tilt, bearing and rotation recorded with the Paintbrush, so a Calligraphic, Scatter or Art brush that varies with the pen changes gradually from one key to the next. A key without a recording counts as half pressure, half tilt and 0°, as brushes read it, and angles turn the shorter way round. Different brushes still switch halfway (VectorCraft's own rule; strokes blend their options, as [Blended objects overview](https://helpx.adobe.com/illustrator/desktop/manage-colors/apply-transparency-and-blending/blended-objects-overview.html) describes; `crates/doc/src/blend.rs`, `pen_pressure_tilt_and_angles_interpolate_for_brushes`).
+  - **Blend steps of brushed strokes:** the steps interpolate the pen pressure, tilt, bearing and rotation recorded with the Paintbrush, so a Calligraphic, Scatter or Art brush that varies with the pen changes gradually from one key to the next. A key without a recording counts as half pressure, half tilt and 0°, as brushes read it, and angles turn the shorter way round. When the blend starts a key's path at another anchor (an open path run from its end, a closed one turned to another start), the key's recordings, width profile and arrowheads turn with the path. Different brushes still switch halfway (VectorCraft's own rule; strokes blend their options, as [Blended objects overview](https://helpx.adobe.com/illustrator/desktop/manage-colors/apply-transparency-and-blending/blended-objects-overview.html) describes; `crates/doc/src/blend.rs`, `pen_pressure_tilt_and_angles_interpolate_for_brushes`, `stroke_profiles_turn_with_a_key_path_started_elsewhere`).
   - **Path editing (#494):** the handles shown are the handles that drag: Direct Selection drags those of a path selected as a whole (as the Pen leaves it), the Anchor Point tool and Pen+Alt no longer grab handles that Show handles when multiple anchors are selected hides, a handle shorter than the tolerance leaves its anchor to be picked, and the anchor tools pick within Selection & Anchor Display › Tolerance. A dragged segment keeps a smooth anchor at either end smooth. With Direct Selection, the Pen, the Curvature and the anchor tools, a path selected as a whole shows all its anchors selected, and the Control bar and the Properties panel offer Convert (corner, smooth) for them too; Remove and Cut wait for anchors direct-selected (#504). A handle drag gathers its snap targets once per drag (it took 21 ms per pointer move on a 20,000-path document, now 1 ms; `vectorcraft-cli perf` measures handle and segment drags on a 5,000-anchor path). Join merges the selected anchor points that lie on one another, as after Average, into one anchor (#1582, fixes #1533); Object › Path › Average & Join… (`path.averageJoin`, Cmd+Alt+Shift+J, the "Create corner or smooth join" shortcut of [Default keyboard shortcuts](https://helpx.adobe.com/illustrator/using/default-keyboard-shortcuts.html)) moves two open path ends to their midpoint and joins them there, a corner or smooth point as its dialog's Points choice asks, in one undo step.
   - **Graphs:** Column, Stacked Column, Bar, Stacked Bar, Line, Area, Scatter, Pie and Radar graph tools with Graph Data and Graph Type. A series starts in greyscale; Group Selection's fill and stroke, the paint, weight, opacity and blend mode of a mark's top visible fill or stroke row after an Appearance command, the Eyedropper, a graphic style, Default Fill and Stroke or Swap Fill and Stroke, and a mark's object opacity and blend mode, are kept separately on the graph and reapplied when its data, type or size changes, and through save, open and undo. Graph Type's Override Calculated Values (both `axisMin` and `axisMax`) uses exactly that value-axis range, split into the tick count (5 when automatic). Line graphs take Edge-to-Edge Lines (off by default: the points sit at the centres of their categories; graphs saved before the option keep their edge-to-edge lines), and radar graphs follow Mark Data Points and Connect Data Points. Blank cells (an empty CSV cell or `null`) are values left out, not zeros: columns, bars and stacked segments skip them, lines and scatter lines break around them and the value axis ignores them, while area, pie and radar draw them as 0; a number in straight quotes is a label, and the data window writes it back quoted. Graph types combine: Graph Type on series picked with Group Selection (or `series` indexes) draws them as their own type, with column, stacked column, line and area mixing on the vertical value axis and bar and stacked bar on the horizontal one; stacked columns take one slot of the cluster, lines draw in front of columns and areas behind. The value axis goes on the left, the right or both sides (column, stacked column, line, area and scatter graphs; bar graphs keep theirs along the bottom), and Separate Scales gives the series assigned to the right axis a scale of their own with its own tick values. Each value axis takes tick marks of no, short or full (across the plot) length and a count per division, and a prefix and suffix for its numbers; the category axis takes tick marks too (none by default), at or between its labels. Graph designs: Object › Graph › Design lists the designs with a preview of the selected one, and New Design (the selected art), Rename, Delete Design, Paste Design (a copy back to edit) and Select Unused, and Marker draws the data points and legend swatches of line, scatter and radar series with a design, scaled so its backmost object fills the default marker's square. Graph Data transposes rows and columns and switches a scatter graph's x and y, and a `|` in a category or series label starts a new line. Pie graphs take Legends in Wedges, Position (Even, Ratio sized by area, Stacked on one centre) and Sort (None, All, First). Graph Type takes column and cluster widths up to 1000% (overlapping past 100%) with First Row and First Column in Front (First Row orders each series' categories; across series the series order decides, so series stay one group each for Group Selection), draws filled lines, adds drop shadows behind columns, bars, lines and wedges, and puts the legend in rows across the top. Text formatted with the Character, Paragraph or Appearance controls, on the whole graph or on labels picked with Group Selection, is kept per kind of label (value axis numbers, category labels, legend labels) through the graph being drawn again. Object › Graph › Data opens a worksheet: cells picked with a click and edited above the sheet (Tab moves right, Enter down, the arrows between cells), Import Data from a tab-separated text file, Transpose, Switch x/y, Cell Style (decimals shown, column width), Revert and Apply. `graph.setData` returns and takes the data as CSV with each value written exactly, not rounded to two decimals, so applying the returned CSV changes nothing (#1485).
   - **Graph column designs:** Object › Graph › Column (`graph.column`) draws the columns, bars or stacked segments and the legend swatch of the series picked with Group Selection with a graph design: Vertically Scaled stretches it to each column's length, Uniformly Scaled scales it both ways and centers it, Repeating stacks a copy for each Each Design Represents value and chops or scales the last one (For Fractions), and Sliding keeps the part above the design's guide line in proportion and stretches the part below. The dialog lists the designs with a preview; the choice is saved with the graph and follows the design's rename and delete.