diff --git a/ROADMAP.md b/ROADMAP.md
index 801ddd8..c74bbda 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -128,6 +128,7 @@ app's JSON control channel (`deckcraft --control PORT`).
 
 | Date | What landed |
 |---|---|
+| 2026-10-12 | WordArt text warps (`prstTxWarp`): all 40 presets drawn, curves fitted to PowerPoint by observation; warp adjusts round-trip |
 | 2026-10-10 | Progress docs restructured to the craftrules standard; full re-measure (breadth 79%, ready ~55%, mainstream ~53%, essentials ~62%, alpha). Landed: Animation Painter (#54), Morph geometry outlines (#27), animated GIF playback (#39), hyperlink colour and following links in the show (#37, #45), date fields in their own format (#36), flipped shapes keep readable text (#35), show transition fix (#46), start screen from the Home button (#49), MCP export lists PDF (#65), OmaStore manifest (#57) |
 | 2026-10-09 | v0.4.0 released. UAX #9 bidi and Arabic shaping (#4), Morph with Words and Characters (#5), tables grow to fit and PDF cell text (#14), rotating log file (#7), DX12 default on Windows (#16), H.264/HEVC overflow hardening (#2), PPTX sniffing anywhere in the zip (#19) |
 | 2026-10-08 | v0.2.0 and v0.3.0 released: Windows arm64, Flatpak aarch64, AppImage zsync updates, branded DMG |
diff --git a/crates/geom/src/lib.rs b/crates/geom/src/lib.rs
index 038a6e5..dd41db3 100644
--- a/crates/geom/src/lib.rs
+++ b/crates/geom/src/lib.rs
@@ -8,6 +8,7 @@
 
 pub mod morph;
 pub mod preset;
+pub mod warp;
 
 pub use kurbo::{Affine, BezPath, PathEl, Point, Rect, Shape as KurboShape, Size, Vec2};
 use serde::{Deserialize, Serialize};
diff --git a/crates/geom/src/warp.rs b/crates/geom/src/warp.rs
new file mode 100644
index 0000000..acdee99
--- /dev/null
+++ b/crates/geom/src/warp.rs
@@ -0,0 +1,773 @@
+//! WordArt text warps (DrawingML `a:bodyPr/a:prstTxWarp`).
+//!
+//! A warp preset is a list of bands laid over the shape's text rectangle (insets are ignored).
+//! Text lines are shared out over the bands in order (the first ⌈n/k⌉ lines to the first band
+//! and so on). A band either
+//! - stretches its lines between a top and a bottom guide ([`Band::Fill`]): the ink box of the
+//!   band's lines fills the band vertically (a band whose ink is shorter than the tallest band's
+//!   keeps the same scale, centred), and horizontally the text is scaled so that the
+//!   widest band is filled along the mean length of its guides (one scale for the whole text), or
+//! - sets its lines at their natural size along one guide ([`Band::Follow`], arches and circles):
+//!   glyphs keep their size, are placed by arc length (aligned as in the paragraph, the whole
+//!   guide being the line's width: insets don't count) and stand on
+//!   the guide's left normal; lines further from the guide stack outwards. Lines that are longer
+//!   than the guide are shrunk to fit.
+//!
+//! Positions along a guide are by arc length; a fill band maps the same fraction of its top and
+//! bottom guide's length and interpolates between them. The guide curves were derived from
+//! observation: synthetic decks of `I` bars were drawn with PowerPoint and every curve fitted to
+//! the measured bar ends (most fit within a point on a 420 × 200 pt box).
+use kurbo::{Arc, BezPath, PathEl, Point, Rect, Vec2};
+
+/// Flattening tolerance for guides, in points.
+const TOL: f64 = 0.02;
+
+/// A guide curve flattened to a polyline with cumulative arc lengths.
+#[derive(Clone, Debug, Default)]
+pub struct Guide {
+    pts: Vec<Point>,
+    cum: Vec<f64>,
+    closed: bool,
+}
+
+impl Guide {
+    fn from_points(raw: impl IntoIterator<Item = Point>, closed: bool) -> Guide {
+        let mut pts: Vec<Point> = Vec::new();
+        let mut cum: Vec<f64> = Vec::new();
+        for p in raw {
+            if !(p.x.is_finite() && p.y.is_finite()) {
+                continue;
+            }
+            match pts.last() {
+                Some(q) => {
+                    let d = (p - *q).hypot();
+                    if d > 1e-9 {
+                        cum.push(cum.last().copied().unwrap_or(0.0) + d);
+                        pts.push(p);
+                    }
+                }
+                None => {
+                    pts.push(p);
+                    cum.push(0.0);
+                }
+            }
+            if pts.len() > 100_000 {
+                break;
+            }
+        }
+        Guide { pts, cum, closed }
+    }
+
+    /// A guide through `path` (any curves), flattened.
+    pub fn from_path(path: &BezPath, closed: bool) -> Guide {
+        let mut pts = Vec::new();
+        kurbo::flatten(path.iter(), TOL, |el| match el {
+            PathEl::MoveTo(p) | PathEl::LineTo(p) => pts.push(p),
+            _ => {}
+        });
+        Guide::from_points(pts, closed)
+    }
+
+    /// Total arc length.
+    pub fn length(&self) -> f64 {
+        self.cum.last().copied().unwrap_or(0.0)
+    }
+
+    /// Whether the guide is a closed loop (positions past its end wrap around).
+    pub fn is_closed(&self) -> bool {
+        self.closed
+    }
+
+    /// Point and unit tangent at arc length `s`. Open guides continue along their end tangents
+    /// past either end; closed guides wrap.
+    pub fn at(&self, s: f64) -> (Point, Vec2) {
+        let len = self.length();
+        let (Some(&first), Some(&last)) = (self.pts.first(), self.pts.last()) else {
+            return (Point::ZERO, Vec2::new(1.0, 0.0));
+        };
+        if self.pts.len() < 2 || len <= 1e-9 {
+            return (first, Vec2::new(1.0, 0.0));
+        }
+        let s = if s.is_finite() { s } else { 0.0 };
+        let s = if self.closed { s.rem_euclid(len) } else { s };
+        let seg = |i: usize| -> (Point, Point, f64) {
+            let a = self.pts.get(i).copied().unwrap_or(first);
+            let b = self.pts.get(i + 1).copied().unwrap_or(last);
+            (a, b, self.cum.get(i).copied().unwrap_or(0.0))
+        };
+        let n = self.pts.len();
+        let i = if s <= 0.0 {
+            0
+        } else if s >= len {
+            n - 2
+        } else {
+            self.cum.partition_point(|c| *c <= s).saturating_sub(1).min(n - 2)
+        };
+        let (a, b, c0) = seg(i);
+        let d = b - a;
+        let l = d.hypot();
+        let t = if l > 1e-12 { d / l } else { Vec2::new(1.0, 0.0) };
+        (a + t * (s - c0), t)
+    }
+
+    /// The parallel curve `d` points away on the left of the direction of travel (above a
+    /// guide running left to right).
+    pub fn offset(&self, d: f64) -> Guide {
+        let n = self.pts.len();
+        if n < 2 || !d.is_finite() || d == 0.0 {
+            return self.clone();
+        }
+        let unit = |i: usize| -> Vec2 {
+            let (a, b) = (self.pts.get(i).copied().unwrap_or(Point::ZERO), self.pts.get(i + 1).copied().unwrap_or(Point::ZERO));
+            let v = b - a;
+            let l = v.hypot();
+            if l > 1e-12 { v / l } else { Vec2::ZERO }
+        };
+        let pts = (0..n).map(|i| {
+            let before = if i > 0 {
+                unit(i - 1)
+            } else if self.closed {
+                unit(n - 2)
+            } else {
+                Vec2::ZERO
+            };
+            let after = if i + 1 < n {
+                unit(i)
+            } else if self.closed {
+                unit(0)
+            } else {
+                Vec2::ZERO
+            };
+            let t = before + after;
+            let l = t.hypot();
+            let t = if l > 1e-12 { t / l } else { Vec2::new(1.0, 0.0) };
+            self.pts.get(i).copied().unwrap_or(Point::ZERO) + Vec2::new(t.y, -t.x) * d
+        });
+        Guide::from_points(pts.collect::<Vec<_>>(), self.closed)
+    }
+
+    /// The point at fraction `t` of the length.
+    pub fn at_frac(&self, t: f64) -> Point {
+        self.at(t * self.length()).0
+    }
+}
+
+/// Which line of a follow band sits on its guide.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum LineAnchor {
+    /// The last line; earlier lines stack outwards (arch up, circle).
+    Last,
+    /// The first line; later lines stack below it (arch down).
+    First,
+    /// The middle of the band's lines.
+    Middle,
+}
+
+#[derive(Clone, Debug)]
+pub enum Band {
+    /// Text stretched between two guides.
+    Fill { top: Guide, bottom: Guide },
+    /// Text at its natural size along a guide.
+    Follow { path: Guide, anchor: LineAnchor },
+}
+
+impl Band {
+    /// The length text is measured against: the mean of a fill band's guides.
+    pub fn length(&self) -> f64 {
+        match self {
+            Band::Fill { top, bottom } => (top.length() + bottom.length()) / 2.0,
+            Band::Follow { path, .. } => path.length(),
+        }
+    }
+}
+
+/// A resolved warp: its bands in shape-local points.
+#[derive(Clone, Debug)]
+pub struct Warp {
+    pub bands: Vec<Band>,
+}
+
+/// Presets whose text follows a guide at its natural size (no wrapping).
+pub fn is_follow(name: &str) -> bool {
+    matches!(name, "textArchUp" | "textArchDown" | "textCircle" | "textButton")
+}
+
+/// Default adjust values of a warp preset (`adj`, or `adj1`, `adj2`); empty for unknown presets.
+pub fn adjust_defaults(name: &str) -> &'static [f64] {
+    match name {
+        "textPlain" => &[50_000.0],
+        "textStop" => &[25_000.0],
+        "textTriangle" | "textTriangleInverted" => &[50_000.0],
+        "textChevron" => &[25_000.0],
+        "textChevronInverted" => &[75_000.0],
+        "textRingInside" | "textRingOutside" => &[60_000.0],
+        "textArchUp" | "textCircle" | "textButton" => &[10_800_000.0],
+        "textArchDown" => &[0.0],
+        "textArchUpPour" | "textCirclePour" | "textButtonPour" => &[10_800_000.0, 50_000.0],
+        "textArchDownPour" => &[0.0, 25_000.0],
+        "textCurveUp" | "textCurveDown" => &[45_977.0],
+        "textCanUp" => &[85_000.0],
+        "textCanDown" => &[14_286.0],
+        "textWave1" | "textWave2" => &[12_500.0, 0.0],
+        "textDoubleWave1" | "textWave4" => &[6_250.0, 0.0],
+        "textInflate" | "textDeflate" => &[18_750.0],
+        "textInflateBottom" => &[60_000.0],
+        "textDeflateBottom" | "textDeflateTop" => &[50_000.0],
+        "textInflateTop" => &[40_000.0],
+        "textDeflateInflate" => &[35_000.0],
+        "textDeflateInflateDeflate" => &[25_000.0],
+        "textFadeRight" | "textFadeLeft" | "textFadeUp" | "textFadeDown" => &[33_333.0],
+        "textSlantUp" => &[55_556.0],
+        "textSlantDown" => &[44_444.0],
+        "textCascadeUp" | "textCascadeDown" => &[44_444.0],
+        _ => &[],
+    }
+}
+
+/// Number of adjust values a warp preset takes.
+pub fn adjust_count(name: &str) -> usize {
+    adjust_defaults(name).len()
+}
+
+/// Whether `name` is a warp preset DeckCraft draws.
+pub fn is_supported(name: &str) -> bool {
+    !adjust_defaults(name).is_empty()
+}
+
+/// Segments of a guide in unit coordinates (x, y in 0..1 over the text rectangle).
+#[derive(Clone, Copy, Debug)]
+enum Seg {
+    M(f64, f64),
+    L(f64, f64),
+    Q(f64, f64, f64, f64),
+    C(f64, f64, f64, f64, f64, f64),
+    /// Elliptical arc: centre, radii, start and sweep in degrees (y down: positive = clockwise).
+    A(f64, f64, f64, f64, f64, f64),
+}
+
+enum Spec {
+    Fill(Vec<Seg>, Vec<Seg>),
+    Follow(Vec<Seg>, LineAnchor),
+}
+
+struct Adj<'a> {
+    raw: &'a [f64],
+    defaults: &'static [f64],
+}
+
+impl Adj<'_> {
+    fn raw(&self, i: usize) -> f64 {
+        self.raw.get(i).copied().filter(|v| v.is_finite()).or_else(|| self.defaults.get(i).copied()).unwrap_or(0.0)
+    }
+    /// Adjust `i` as a fraction (1/100 000), pinned to `lo..=hi` (fractions).
+    fn frac(&self, i: usize, lo: f64, hi: f64) -> f64 {
+        (self.raw(i) / 100_000.0).clamp(lo, hi)
+    }
+    /// Adjust `i` as an angle in degrees (1/60 000), in 0..360.
+    fn angle(&self, i: usize) -> f64 {
+        (self.raw(i) / 60_000.0).rem_euclid(360.0)
+    }
+}
+
+fn line(pts: &[(f64, f64)]) -> Vec<Seg> {
+    pts.iter().enumerate().map(|(i, &(x, y))| if i == 0 { Seg::M(x, y) } else { Seg::L(x, y) }).collect()
+}
+
+/// Quadratic from (0, y0) through control (0.5, c) to (1, y0).
+fn quad(y0: f64, c: f64) -> Vec<Seg> {
+    vec![Seg::M(0.0, y0), Seg::Q(0.5, c, 1.0, y0)]
+}
+
+/// A sweep in (0, 360]: zero means a full turn.
+fn turn(deg: f64) -> f64 {
+    let d = deg.rem_euclid(360.0);
+    if d < 1e-9 { 360.0 } else { d }
+}
+
+/// Arc of the ellipse inscribed in the rectangle, scaled by `s` about its centre.
+fn ellipse(s: f64, start: f64, sweep: f64) -> Vec<Seg> {
+    vec![Seg::A(0.5, 0.5, 0.5 * s, 0.5 * s, start, sweep)]
+}
+
+/// The arch-up arc for adjust angle `a`: symmetric about the top (270°), clockwise.
+fn arch_up(a: f64) -> (f64, f64) {
+    (a, turn(2.0 * (270.0 - a)))
+}
+
+/// The arch-down arc for adjust angle `a`: symmetric about the bottom (90°), counter-clockwise.
+fn arch_down(a: f64) -> (f64, f64) {
+    (180.0 - a, -turn(180.0 - 2.0 * a))
+}
+
+/// The circle arc for adjust angle `a`: from `a` clockwise, symmetric about 0°.
+fn circle(a: f64) -> (f64, f64) {
+    (a, turn(2.0 * (360.0 - a)))
+}
+
+/// One cubic wave period from x0 to x1 at height y: up first when `k` > 0 (y decreases).
+fn wave(out: &mut Vec<Seg>, x0: f64, x1: f64, y: f64, k: f64) {
+    let l = x1 - x0;
+    out.push(Seg::C(x0 + l / 3.0, y - k, x0 + 2.0 * l / 3.0, y + k, x1, y));
+}
+
+/// Wave guides: `periods` cubic waves over the width, shifted apart by `shift` (fraction).
+fn waves(a: f64, shift: f64, periods: usize, up_first: bool) -> Spec {
+    let d = 2.0 * shift;
+    let (top_x, bot_x) = if d >= 0.0 { ((0.0, 1.0 - d), (d, 1.0)) } else { ((-d, 1.0), (0.0, 1.0 + d)) };
+    let k = if up_first { a * 10.0 / 3.0 } else { -a * 10.0 / 3.0 };
+    let guide = |(x0, x1): (f64, f64), y: f64| {
+        let mut v = vec![Seg::M(x0, y)];
+        let n = periods.max(1) as f64;
+        for i in 0..periods.max(1) {
+            let f = i as f64;
+            wave(&mut v, x0 + (x1 - x0) * f / n, x0 + (x1 - x0) * (f + 1.0) / n, y, k);
+        }
+        v
+    };
+    Spec::Fill(guide(top_x, a), guide(bot_x, 1.0 - a))
+}
+
+fn spec(name: &str, a: &Adj) -> Option<Vec<Spec>> {
+    use Seg::*;
+    let fill = |t: Vec<Seg>, b: Vec<Seg>| vec![Spec::Fill(t, b)];
+    let top = || line(&[(0.0, 0.0), (1.0, 0.0)]);
+    let bottom = || line(&[(0.0, 1.0), (1.0, 1.0)]);
+    Some(match name {
+        "textPlain" => {
+            let d = 2.0 * (a.frac(0, 0.3, 0.7) - 0.5);
+            if d < 0.0 {
+                fill(line(&[(-d, 0.0), (1.0, 0.0)]), line(&[(0.0, 1.0), (1.0 + d, 1.0)]))
+            } else {
+                fill(line(&[(0.0, 0.0), (1.0 - d, 0.0)]), line(&[(d, 1.0), (1.0, 1.0)]))
+            }
+        }
+        "textStop" => {
+            let y = a.frac(0, 0.14286, 0.5);
+            let t = 1.0 / 3.0;
+            fill(line(&[(0.0, y), (t, 0.0), (1.0 - t, 0.0), (1.0, y)]), line(&[(0.0, 1.0 - y), (t, 1.0), (1.0 - t, 1.0), (1.0, 1.0 - y)]))
+        }
+        "textTriangle" => {
+            let y = a.frac(0, 0.0, 1.0);
+            fill(line(&[(0.0, y), (0.5, 0.0), (1.0, y)]), bottom())
+        }
+        "textTriangleInverted" => {
+            let y = a.frac(0, 0.0, 1.0);
+            fill(top(), line(&[(0.0, y), (0.5, 1.0), (1.0, y)]))
+        }
+        "textChevron" => {
+            let y = a.frac(0, 0.0, 0.5);
+            fill(line(&[(0.0, y), (0.5, 0.0), (1.0, y)]), line(&[(0.0, 1.0), (0.5, 1.0 - y), (1.0, 1.0)]))
+        }
+        "textChevronInverted" => {
+            let y = a.frac(0, 0.5, 1.0);
+            fill(line(&[(0.0, 0.0), (0.5, 1.0 - y), (1.0, 0.0)]), line(&[(0.0, y), (0.5, 1.0), (1.0, y)]))
+        }
+        "textFadeRight" => {
+            let y = a.frac(0, 0.0, 0.49999);
+            fill(line(&[(0.0, 0.0), (1.0, y)]), line(&[(0.0, 1.0), (1.0, 1.0 - y)]))
+        }
+        "textFadeLeft" => {
+            let y = a.frac(0, 0.0, 0.49999);
+            fill(line(&[(0.0, y), (1.0, 0.0)]), line(&[(0.0, 1.0 - y), (1.0, 1.0)]))
+        }
+        "textFadeUp" => {
+            let x = a.frac(0, 0.0, 0.49999);
+            fill(line(&[(x, 0.0), (1.0 - x, 0.0)]), bottom())
+        }
+        "textFadeDown" => {
+            let x = a.frac(0, 0.0, 0.49999);
+            fill(top(), line(&[(x, 1.0), (1.0 - x, 1.0)]))
+        }
+        "textSlantUp" => {
+            let y = a.frac(0, 0.44444, 1.0);
+            fill(line(&[(0.0, y), (1.0, 0.0)]), line(&[(0.0, 1.0), (1.0, 1.0 - y)]))
+        }
+        "textSlantDown" => {
+            let y = a.frac(0, 0.0, 0.55556);
+            fill(line(&[(0.0, 0.0), (1.0, 1.0 - y)]), line(&[(0.0, y), (1.0, 1.0)]))
+        }
+        "textCascadeUp" => {
+            let y = a.frac(0, 0.0, 1.0);
+            fill(line(&[(0.0, (1.0 - y) / 4.0), (1.0, 0.0)]), line(&[(0.0, 1.0), (1.0, y)]))
+        }
+        "textCascadeDown" => {
+            let y = a.frac(0, 0.0, 1.0);
+            fill(line(&[(0.0, 0.0), (1.0, (1.0 - y) / 4.0)]), line(&[(0.0, y), (1.0, 1.0)]))
+        }
+        "textInflate" => {
+            let y = a.frac(0, 0.0, 0.2);
+            fill(quad(y, -y), quad(1.0 - y, 1.0 + y))
+        }
+        "textDeflate" => {
+            let y = a.frac(0, 0.0, 0.375);
+            fill(quad(0.0, 2.0 * y), quad(1.0, 1.0 - 2.0 * y))
+        }
+        "textInflateBottom" => {
+            let y = a.frac(0, 0.6, 1.0);
+            fill(top(), quad(y, 1.0))
+        }
+        "textDeflateBottom" => {
+            let y = a.frac(0, 0.0625, 1.0);
+            fill(top(), quad(1.0, 2.0 * y - 1.0))
+        }
+        "textInflateTop" => {
+            let y = a.frac(0, 0.0, 0.5);
+            fill(quad(y, 0.0), bottom())
+        }
+        "textDeflateTop" => {
+            let y = a.frac(0, 0.0, 0.9375);
+            fill(quad(0.0, 2.0 * y), bottom())
+        }
+        "textDeflateInflate" => {
+            // The bands are split by a curve from mid-height up to `y`, with a gap of a tenth of
+            // a band's height.
+            let y = a.frac(0, 0.05, 0.95);
+            let g = 0.05;
+            vec![Spec::Fill(top(), quad(0.5 - g, 2.0 * y - 0.5 - g)), Spec::Fill(quad(0.5 + g, 2.0 * y - 0.5 + g), bottom())]
+        }
+        "textDeflateInflateDeflate" => {
+            let y = a.frac(0, 0.01, 1.0 / 3.0);
+            let g = 1.0 / 30.0;
+            let (t1, t2) = (1.0 / 3.0, 2.0 / 3.0);
+            let (c1, c2) = (2.0 * y - t1, 2.0 * (1.0 - y) - t2);
+            vec![
+                Spec::Fill(top(), quad(t1 - g, c1 - g)),
+                Spec::Fill(quad(t1 + g, c1 + g), quad(t2 - g, c2 - g)),
+                Spec::Fill(quad(t2 + g, c2 + g), bottom()),
+            ]
+        }
+        "textCurveUp" | "textCurveDown" => {
+            let y = a.frac(0, 0.0, 0.56818);
+            let b = vec![M(0.0, 1.0 - 3.0 * y / 8.0), C(1.0 / 3.0, 1.0 + y / 8.0, 2.0 / 3.0, 1.0 + y / 8.0, 1.0, 1.0 - 3.0 * y / 8.0)];
+            let t = if name == "textCurveUp" {
+                vec![M(0.0, y), C(1.0 / 3.0, 1.25 * y, 2.0 / 3.0, 0.75 * y, 1.0, 0.0)]
+            } else {
+                vec![M(0.0, 0.0), C(1.0 / 3.0, 0.75 * y, 2.0 / 3.0, 1.25 * y, 1.0, y)]
+            };
+            fill(t, b)
+        }
+        "textCanUp" => {
+            let r = 1.0 - a.frac(0, 0.5, 1.0);
+            fill(vec![A(0.5, r, 0.5, r, 180.0, 180.0)], vec![A(0.5, 1.0, 0.5, r, 180.0, 180.0)])
+        }
+        "textCanDown" => {
+            let r = a.frac(0, 0.0, 0.5);
+            fill(vec![A(0.5, 0.0, 0.5, r, 180.0, -180.0)], vec![A(0.5, 1.0 - r, 0.5, r, 180.0, -180.0)])
+        }
+        "textRingInside" | "textRingOutside" => {
+            let h = a.frac(0, 0.5, 0.99);
+            let sweep = if name == "textRingInside" { 360.0 } else { -360.0 };
+            fill(vec![A(0.5, h / 2.0, 0.5, h / 2.0, 180.0, sweep)], vec![A(0.5, 1.0 - h / 2.0, 0.5, h / 2.0, 180.0, sweep)])
+        }
+        "textWave1" => vec![waves(a.frac(0, 0.0, 0.2), a.frac(1, -0.1, 0.1), 1, true)],
+        "textWave2" => vec![waves(a.frac(0, 0.0, 0.2), a.frac(1, -0.1, 0.1), 1, false)],
+        "textDoubleWave1" => vec![waves(a.frac(0, 0.0, 0.125), a.frac(1, -0.1, 0.1), 2, true)],
+        "textWave4" => vec![waves(a.frac(0, 0.0, 0.125), a.frac(1, -0.1, 0.1), 2, false)],
+        "textArchUp" => {
+            let (s, w) = arch_up(a.angle(0));
+            vec![Spec::Follow(ellipse(1.0, s, w), LineAnchor::Last)]
+        }
+        "textArchDown" => {
+            let (s, w) = arch_down(a.angle(0));
+            vec![Spec::Follow(ellipse(1.0, s, w), LineAnchor::First)]
+        }
+        "textCircle" => {
+            let (s, w) = circle(a.angle(0));
+            vec![Spec::Follow(ellipse(1.0, s, w), LineAnchor::Last)]
+        }
+        "textButton" => {
+            let t = a.angle(0);
+            let (s, w) = arch_up(t);
+            let half = 0.5 * t.to_radians().cos().abs();
+            vec![
+                Spec::Follow(ellipse(1.0, s, w), LineAnchor::Last),
+                Spec::Follow(line(&[(0.5 - half, 0.5), (0.5 + half, 0.5)]), LineAnchor::Middle),
+                Spec::Follow(ellipse(1.0, 360.0 - s, -w), LineAnchor::First),
+            ]
+        }
+        "textArchUpPour" => {
+            let (s, w) = arch_up(a.angle(0));
+            let r = a.frac(1, 0.0, 0.99);
+            fill(ellipse(1.0, s, w), ellipse(r, s, w))
+        }
+        "textArchDownPour" => {
+            let (s, w) = arch_down(a.angle(0));
+            let r = a.frac(1, 0.0, 0.99);
+            fill(ellipse(r, s, w), ellipse(1.0, s, w))
+        }
+        "textCirclePour" => {
+            let (s, w) = circle(a.angle(0));
+            let r = a.frac(1, 0.0, 0.99);
+            fill(ellipse(1.0, s, w), ellipse(r, s, w))
+        }
+        "textButtonPour" => {
+            let (s, w) = arch_up(a.angle(0));
+            let r = a.frac(1, 0.0, 0.99);
+            // The middle band runs between chords of the inner ellipse halfway to its top and
+            // bottom.
+            let (dy, half) = (0.25 * r, 0.25 * r * 3f64.sqrt());
+            vec![
+                Spec::Fill(ellipse(1.0, s, w), ellipse(r, s, w)),
+                Spec::Fill(line(&[(0.5 - half, 0.5 - dy), (0.5 + half, 0.5 - dy)]), line(&[(0.5 - half, 0.5 + dy), (0.5 + half, 0.5 + dy)])),
+                Spec::Fill(ellipse(r, 360.0 - s, -w), ellipse(1.0, 360.0 - s, -w)),
+            ]
+        }
+        _ => return None,
+    })
+}
+
+/// Build a guide from unit-space segments mapped onto `r`.
+fn guide(segs: &[Seg], r: Rect) -> Guide {
+    let mut p = BezPath::new();
+    let mut started = false;
+    let mut closed = false;
+    for s in segs {
+        match *s {
+            Seg::M(x, y) => {
+                p.move_to((x, y));
+                started = true;
+            }
+            Seg::L(x, y) => {
+                if started {
+                    p.line_to((x, y))
+                } else {
+                    p.move_to((x, y))
+                }
+                started = true;
+            }
+            Seg::Q(cx, cy, x, y) => {
+                if started {
+                    p.quad_to((cx, cy), (x, y));
+                }
+            }
+            Seg::C(x1, y1, x2, y2, x, y) => {
+                if started {
+                    p.curve_to((x1, y1), (x2, y2), (x, y));
+                }
+            }
+            Seg::A(cx, cy, rx, ry, start, sweep) => {
+                let arc = Arc::new((cx, cy), (rx.max(0.0), ry.max(0.0)), start.to_radians(), sweep.to_radians(), 0.0);
+                let s0 = Point::new(cx + rx * start.to_radians().cos(), cy + ry * start.to_radians().sin());
+                if started {
+                    p.line_to(s0);
+                } else {
+                    p.move_to(s0);
+                }
+                started = true;
+                for el in arc.append_iter(1e-5) {
+                    p.push(el);
+                }
+                closed = sweep.abs() >= 359.999;
+            }
+        }
+    }
+    let m = kurbo::Affine::new([r.width(), 0.0, 0.0, r.height(), r.x0, r.y0]);
+    p.apply_affine(m);
+    Guide::from_path(&p, closed)
+}
+
+/// The warp `name` with adjust values `adj` (raw guide values; missing ones take the defaults)
+/// over text rectangle `rect`. `None` for unknown presets, `textNoShape` or a non-finite rect.
+pub fn warp(name: &str, adj: &[f64], rect: Rect) -> Option<Warp> {
+    if ![rect.x0, rect.y0, rect.x1, rect.y1].iter().all(|v| v.is_finite()) {
+        return None;
+    }
+    let r = Rect::new(rect.x0.min(rect.x1), rect.y0.min(rect.y1), rect.x0.max(rect.x1), rect.y0.max(rect.y1));
+    let a = Adj { raw: adj, defaults: adjust_defaults(name) };
+    let specs = spec(name, &a)?;
+    let bands = specs
+        .into_iter()
+        .map(|s| match s {
+            Spec::Fill(t, b) => Band::Fill { top: guide(&t, r), bottom: guide(&b, r) },
+            Spec::Follow(p, anchor) => Band::Follow { path: guide(&p, r), anchor },
+        })
+        .collect();
+    Some(Warp { bands })
+}
+
+/// The band line `line` of `lines` goes to when there are `bands` bands: the first ⌈n/k⌉ lines
+/// share the first band, and so on.
+pub fn band_of_line(line: usize, lines: usize, bands: usize) -> usize {
+    if bands <= 1 || lines == 0 {
+        return 0;
+    }
+    // Band b holds lines ceil(b·n/k) .. ceil((b+1)·n/k).
+    (0..bands).rev().find(|&b| (b * lines).div_ceil(bands) <= line).unwrap_or(0)
+}
+
+/// One laid-out line as the warp sees it (layout coordinates, points).
+#[derive(Clone, Copy, Debug)]
+pub struct WarpLine {
+    /// Ink box of the line's glyphs; `None` for a line without ink.
+    pub ink: Option<Rect>,
+    /// Advance extent of the line (left, right).
+    pub extent: (f64, f64),
+    /// Reference height for follow bands: the y that sits on the guide.
+    pub ref_y: f64,
+}
+
+#[derive(Clone, Copy, Debug)]
+enum LineMap {
+    Fill {
+        band: usize,
+        cx: f64,
+        k: f64,
+        len: f64,
+        y0: f64,
+        y1: f64,
+    },
+    /// `guide`: the line's own parallel guide in [`Mapper::offsets`], if it is off the band's.
+    Follow {
+        band: usize,
+        guide: Option<usize>,
+        e0: f64,
+        s0: f64,
+        k: f64,
+        ref_y: f64,
+    },
+}
+
+/// Maps points of laid-out lines onto a warp.
+#[derive(Clone, Debug)]
+pub struct Mapper<'a> {
+    warp: &'a Warp,
+    lines: Vec<LineMap>,
+    offsets: Vec<Guide>,
+    zoom: f64,
+}
+
+impl Warp {
+    /// Plan the mapping of `lines`, laid out in the inner text box `inner` (the line's place in
+    /// it gives its alignment along follow guides; the insets themselves don't shorten a guide).
+    pub fn mapper(&self, lines: &[WarpLine], inner: Rect) -> Mapper<'_> {
+        let nb = self.bands.len().max(1);
+        let n = lines.len();
+        let band_of: Vec<usize> = (0..n).map(|i| band_of_line(i, n, nb).min(nb - 1)).collect();
+        // Ink of the whole text, for the shared horizontal centre and scale of fill bands.
+        let ink_all = lines.iter().filter_map(|l| l.ink).reduce(|a, b| a.union(b));
+        let cx = ink_all.map(|r| r.center().x).unwrap_or(0.0);
+        let mut k_fill = f64::INFINITY;
+        let mut zoom: f64 = 1.0;
+        let mut band_y: Vec<Option<(f64, f64)>> = vec![None; nb];
+        for (i, l) in lines.iter().enumerate() {
+            let Some(r) = l.ink else { continue };
+            let b = band_of.get(i).copied().unwrap_or(0);
+            if let Some(slot) = band_y.get_mut(b) {
+                *slot = Some(match *slot {
+                    Some((y0, y1)) => (y0.min(r.y0), y1.max(r.y1)),
+                    None => (r.y0, r.y1),
+                });
+            }
+        }
+        // Every fill band maps a box as tall as the tallest band's ink, centred on its own ink, so
+        // a band with fewer lines keeps them at the same size, centred between its guides.
+        let tallest = band_y.iter().flatten().map(|(y0, y1)| y1 - y0).fold(0.0, f64::max);
+        let band_y: Vec<Option<(f64, f64)>> =
+            band_y.iter().map(|r| r.map(|(y0, y1)| ((y0 + y1 - tallest) / 2.0, (y0 + y1 + tallest) / 2.0))).collect();
+        for (b, band) in self.bands.iter().enumerate() {
+            if let Band::Fill { top, bottom } = band {
+                let half = lines
+                    .iter()
+                    .enumerate()
+                    .filter(|(i, _)| band_of.get(*i) == Some(&b))
+                    .filter_map(|(_, l)| l.ink)
+                    .map(|r| (r.x0 - cx).abs().max((r.x1 - cx).abs()))
+                    .fold(0.0, f64::max);
+                if half > 1e-9 {
+                    k_fill = k_fill.min(band.length() / (2.0 * half));
+                }
+                if let Some(Some((y0, y1))) = band_y.get(b) {
+                    let thick = [0.0, 0.25, 0.5, 0.75, 1.0].iter().map(|&u| (top.at_frac(u) - bottom.at_frac(u)).hypot()).fold(0.0, f64::max);
+                    if y1 - y0 > 1e-9 {
+                        zoom = zoom.max(thick / (y1 - y0));
+                    }
+                }
+            }
+        }
+        if !k_fill.is_finite() {
+            k_fill = 1.0;
+        }
+        zoom = zoom.max(k_fill);
+        let mut maps = Vec::with_capacity(n);
+        let mut offsets = Vec::new();
+        for (i, l) in lines.iter().enumerate() {
+            let b = band_of.get(i).copied().unwrap_or(0);
+            let in_band = |j: &usize| band_of.get(*j) == Some(&b);
+            match self.bands.get(b) {
+                Some(Band::Fill { .. }) | None => {
+                    let (y0, y1) = band_y.get(b).copied().flatten().unwrap_or((0.0, 1.0));
+                    let len = self.bands.get(b).map(Band::length).unwrap_or(0.0);
+                    maps.push(LineMap::Fill { band: b, cx, k: k_fill, len, y0, y1 });
+                }
+                Some(Band::Follow { path, anchor }) => {
+                    let len = path.length();
+                    let widest = (0..n).filter(in_band).filter_map(|j| lines.get(j)).map(|l| l.extent.1 - l.extent.0).fold(0.0, f64::max);
+                    let k = if widest > len && widest > 1e-9 { len / widest } else { 1.0 };
+                    let members: Vec<&WarpLine> = (0..n).filter(in_band).filter_map(|j| lines.get(j)).collect();
+                    let ref_y = match anchor {
+                        LineAnchor::Last => members.last().map(|l| l.ref_y),
+                        LineAnchor::First => members.first().map(|l| l.ref_y),
+                        LineAnchor::Middle => match (members.first(), members.last()) {
+                            (Some(a), Some(z)) => Some((a.ref_y + z.ref_y) / 2.0),
+                            _ => None,
+                        },
+                    }
+                    .unwrap_or(l.ref_y);
+                    // Lines off the guide run on a parallel curve at their natural length.
+                    let d = (ref_y - l.ref_y) * k;
+                    let (guide, len) = if d.abs() > 1e-6 && d.is_finite() && offsets.len() < 4096 {
+                        let g = path.offset(d);
+                        let len = g.length();
+                        offsets.push(g);
+                        (Some(offsets.len() - 1), len)
+                    } else {
+                        (None, len)
+                    };
+                    let (e0, e1) = l.extent;
+                    let w = (e1 - e0).max(0.0) * k;
+                    let (gl, gr) = ((e0 - inner.x0).max(0.0), (inner.x1 - e1).max(0.0));
+                    let f = if gl + gr > 1e-9 { gl / (gl + gr) } else { 0.5 };
+                    let s0 = f * (len - w);
+                    maps.push(LineMap::Follow { band: b, guide, e0, s0, k, ref_y: l.ref_y });
+                }
+            }
+        }
+        Mapper { warp: self, lines: maps, offsets, zoom: if zoom.is_finite() { zoom.clamp(1.0, 1.0e4) } else { 1.0 } }
+    }
+}
+
+impl Mapper<'_> {
+    /// How much the warp magnifies text at most (for flattening tolerances), ≥ 1.
+    pub fn zoom(&self) -> f64 {
+        self.zoom
+    }
+
+    /// Map point `p` of line `line` (layout coordinates) onto the warp.
+    pub fn map(&self, line: usize, p: Point) -> Point {
+        let out = match self.lines.get(line) {
+            Some(&LineMap::Fill { band, cx, k, len, y0, y1 }) => {
+                let Some(Band::Fill { top, bottom }) = self.warp.bands.get(band) else { return p };
+                let u = if len > 1e-9 { 0.5 + (p.x - cx) * k / len } else { 0.5 };
+                let v = if y1 - y0 > 1e-9 { (p.y - y0) / (y1 - y0) } else { 0.5 };
+                let (t, b) = (top.at_frac(u), bottom.at_frac(u));
+                t.lerp(b, v)
+            }
+            Some(&LineMap::Follow { band, guide, e0, s0, k, ref_y }) => {
+                let path = match (guide.and_then(|g| self.offsets.get(g)), self.warp.bands.get(band)) {
+                    (Some(g), _) => g,
+                    (None, Some(Band::Follow { path, .. })) => path,
+                    _ => return p,
+                };
+                let s = s0 + (p.x - e0) * k;
+                let d = (ref_y - p.y) * k;
+                let (q, t) = path.at(s);
+                q + Vec2::new(t.y, -t.x) * d
+            }
+            None => p,
+        };
+        if out.x.is_finite() && out.y.is_finite() { out } else { p }
+    }
+}
+
+#[cfg(test)]
+mod tests;
diff --git a/crates/geom/src/warp/tests.rs b/crates/geom/src/warp/tests.rs
new file mode 100644
index 0000000..2d18b13
--- /dev/null
+++ b/crates/geom/src/warp/tests.rs
@@ -0,0 +1,309 @@
+use super::*;
+
+const ALL: &[&str] = &[
+    "textPlain",
+    "textStop",
+    "textTriangle",
+    "textTriangleInverted",
+    "textChevron",
+    "textChevronInverted",
+    "textRingInside",
+    "textRingOutside",
+    "textArchUp",
+    "textArchDown",
+    "textCircle",
+    "textButton",
+    "textArchUpPour",
+    "textArchDownPour",
+    "textCirclePour",
+    "textButtonPour",
+    "textCurveUp",
+    "textCurveDown",
+    "textCanUp",
+    "textCanDown",
+    "textWave1",
+    "textWave2",
+    "textDoubleWave1",
+    "textWave4",
+    "textInflate",
+    "textDeflate",
+    "textInflateBottom",
+    "textDeflateBottom",
+    "textInflateTop",
+    "textDeflateTop",
+    "textDeflateInflate",
+    "textDeflateInflateDeflate",
+    "textFadeRight",
+    "textFadeLeft",
+    "textFadeUp",
+    "textFadeDown",
+    "textSlantUp",
+    "textSlantDown",
+    "textCascadeUp",
+    "textCascadeDown",
+];
+
+const W: f64 = 420.0;
+const H: f64 = 200.0;
+
+fn rect() -> Rect {
+    Rect::new(0.0, 0.0, W, H)
+}
+
+/// One line whose ink box is `ink`.
+fn one_line(ink: Rect) -> Vec<WarpLine> {
+    vec![WarpLine { ink: Some(ink), extent: (ink.x0, ink.x1), ref_y: ink.y1 }]
+}
+
+/// Where the unit-square point (u, v) of a single line's ink box lands, in unit coordinates.
+fn land(name: &str, adj: &[f64], u: f64, v: f64) -> (f64, f64) {
+    let w = warp(name, adj, rect()).unwrap();
+    let ink = Rect::new(100.0, 50.0, 300.0, 90.0);
+    let lines = one_line(ink);
+    let m = w.mapper(&lines, rect().inset(-5.0));
+    let p = m.map(0, Point::new(ink.x0 + u * ink.width(), ink.y0 + v * ink.height()));
+    (p.x / W, p.y / H)
+}
+
+fn close(a: (f64, f64), b: (f64, f64), tol: f64) -> bool {
+    (a.0 - b.0).abs() <= tol && (a.1 - b.1).abs() <= tol
+}
+
+#[track_caller]
+fn corners(name: &str, adj: &[f64], tl: (f64, f64), tr: (f64, f64), bl: (f64, f64), br: (f64, f64)) {
+    for ((u, v), want) in [((0.0, 0.0), tl), ((1.0, 0.0), tr), ((0.0, 1.0), bl), ((1.0, 1.0), br)] {
+        let got = land(name, adj, u, v);
+        assert!(close(got, want, 0.004), "{name} corner ({u},{v}): got {got:?}, want {want:?}");
+    }
+}
+
+#[test]
+fn every_preset_builds_finite_guides() {
+    for name in ALL {
+        assert!(is_supported(name), "{name}");
+        let w = warp(name, &[], rect()).unwrap_or_else(|| panic!("{name}"));
+        assert!(!w.bands.is_empty(), "{name}");
+        for b in &w.bands {
+            let l = b.length();
+            assert!(l.is_finite() && l > 10.0, "{name}: band length {l}");
+        }
+        assert_eq!(adjust_count(name), adjust_defaults(name).len());
+    }
+    assert!(warp("textNoShape", &[], rect()).is_none());
+    assert!(warp("bogus", &[], rect()).is_none());
+    assert!(!is_supported("textNoShape"));
+}
+
+#[test]
+fn straight_presets_put_the_ink_corners_on_their_guides() {
+    corners("textPlain", &[], (0.0, 0.0), (1.0, 0.0), (0.0, 1.0), (1.0, 1.0));
+    // A smaller adjust shears the text: the top edge starts 40 % in, the bottom edge ends 60 % in.
+    corners("textPlain", &[30_000.0], (0.4, 0.0), (1.0, 0.0), (0.0, 1.0), (0.6, 1.0));
+    corners("textStop", &[], (0.0, 0.25), (1.0, 0.25), (0.0, 0.75), (1.0, 0.75));
+    corners("textTriangle", &[], (0.0, 0.5), (1.0, 0.5), (0.0, 1.0), (1.0, 1.0));
+    corners("textTriangleInverted", &[25_000.0], (0.0, 0.0), (1.0, 0.0), (0.0, 0.25), (1.0, 0.25));
+    corners("textChevron", &[], (0.0, 0.25), (1.0, 0.25), (0.0, 1.0), (1.0, 1.0));
+    corners("textChevronInverted", &[], (0.0, 0.0), (1.0, 0.0), (0.0, 0.75), (1.0, 0.75));
+    corners("textFadeRight", &[], (0.0, 0.0), (1.0, 0.33333), (0.0, 1.0), (1.0, 0.66667));
+    corners("textFadeLeft", &[], (0.0, 0.33333), (1.0, 0.0), (0.0, 0.66667), (1.0, 1.0));
+    corners("textFadeUp", &[], (0.33333, 0.0), (0.66667, 0.0), (0.0, 1.0), (1.0, 1.0));
+    corners("textFadeDown", &[], (0.0, 0.0), (1.0, 0.0), (0.33333, 1.0), (0.66667, 1.0));
+    corners("textSlantUp", &[], (0.0, 0.55556), (1.0, 0.0), (0.0, 1.0), (1.0, 0.44444));
+    corners("textSlantDown", &[], (0.0, 0.0), (1.0, 0.55556), (0.0, 0.44444), (1.0, 1.0));
+    corners("textCascadeUp", &[], (0.0, 0.13889), (1.0, 0.0), (0.0, 1.0), (1.0, 0.44444));
+    corners("textCascadeDown", &[], (0.0, 0.0), (1.0, 0.13889), (0.0, 0.44444), (1.0, 1.0));
+}
+
+#[test]
+fn curved_presets_bend_where_powerpoint_bends_them() {
+    corners("textInflate", &[], (0.0, 0.1875), (1.0, 0.1875), (0.0, 0.8125), (1.0, 0.8125));
+    assert!(close(land("textInflate", &[], 0.5, 0.0), (0.5, 0.0), 0.004));
+    assert!(close(land("textInflate", &[], 0.5, 1.0), (0.5, 1.0), 0.004));
+    corners("textDeflate", &[], (0.0, 0.0), (1.0, 0.0), (0.0, 1.0), (1.0, 1.0));
+    assert!(close(land("textDeflate", &[], 0.5, 0.0), (0.5, 0.1875), 0.004));
+    corners("textInflateBottom", &[], (0.0, 0.0), (1.0, 0.0), (0.0, 0.6), (1.0, 0.6));
+    assert!(close(land("textInflateBottom", &[], 0.5, 1.0), (0.5, 0.8), 0.004));
+    assert!(close(land("textDeflateBottom", &[], 0.5, 1.0), (0.5, 0.5), 0.004));
+    assert!(close(land("textInflateTop", &[], 0.5, 0.0), (0.5, 0.2), 0.004));
+    assert!(close(land("textDeflateTop", &[], 0.5, 0.0), (0.5, 0.5), 0.004));
+    // Cans: half ellipses.
+    corners("textCanUp", &[], (0.0, 0.15), (1.0, 0.15), (0.0, 1.0), (1.0, 1.0));
+    assert!(close(land("textCanUp", &[], 0.5, 0.0), (0.5, 0.0), 0.004));
+    assert!(close(land("textCanUp", &[], 0.5, 1.0), (0.5, 0.85), 0.004));
+    assert!(close(land("textCanDown", &[], 0.5, 0.0), (0.5, 0.14286), 0.004));
+    // Curves and waves.
+    let a = 0.45977;
+    corners("textCurveUp", &[], (0.0, a), (1.0, 0.0), (0.0, 1.0 - 3.0 * a / 8.0), (1.0, 1.0 - 3.0 * a / 8.0));
+    assert!(close(land("textCurveUp", &[], 0.5, 1.0), (0.5, 1.0), 0.004));
+    corners("textCurveDown", &[], (0.0, 0.0), (1.0, a), (0.0, 1.0 - 3.0 * a / 8.0), (1.0, 1.0 - 3.0 * a / 8.0));
+    corners("textWave1", &[], (0.0, 0.125), (1.0, 0.125), (0.0, 0.875), (1.0, 0.875));
+    // Wave 1 rises first: its top is near the box top a quarter of the way along.
+    assert!(land("textWave1", &[], 0.25, 0.0).1 < 0.02);
+    assert!(land("textWave2", &[], 0.25, 0.0).1 > 0.23);
+    // A horizontal shift moves the bottom guide right.
+    corners("textWave1", &[12_500.0, 5_000.0], (0.0, 0.125), (0.9, 0.125), (0.1, 0.875), (1.0, 0.875));
+    assert!(land("textDoubleWave1", &[], 0.125, 0.0).1 < 0.02);
+    assert!(land("textWave4", &[], 0.125, 0.0).1 > 0.1);
+}
+
+#[test]
+fn arc_presets_follow_ellipses() {
+    // Pour arches: the outer arc from the left end over the top; the inner one is scaled by adj2.
+    corners("textArchUpPour", &[], (0.0, 0.5), (1.0, 0.5), (0.25, 0.5), (0.75, 0.5));
+    assert!(close(land("textArchUpPour", &[], 0.5, 0.0), (0.5, 0.0), 0.004));
+    assert!(close(land("textArchUpPour", &[], 0.5, 1.0), (0.5, 0.25), 0.004));
+    assert!(close(land("textArchUpPour", &[10_800_000.0, 30_000.0], 0.5, 1.0), (0.5, 0.35), 0.004));
+    assert!(close(land("textArchDownPour", &[], 0.5, 0.0), (0.5, 0.625), 0.004));
+    assert!(close(land("textArchDownPour", &[], 0.5, 1.0), (0.5, 1.0), 0.004));
+    // Circle pour: once round from the left; the middle of the text is at the right.
+    assert!(close(land("textCirclePour", &[], 0.5, 0.0), (1.0, 0.5), 0.004));
+    // Rings: the text goes round two stacked ellipses.
+    assert!(close(land("textRingInside", &[], 0.0, 0.0), (0.0, 0.3), 0.004));
+    assert!(close(land("textRingInside", &[], 0.0, 1.0), (0.0, 0.7), 0.004));
+    assert!(close(land("textRingInside", &[], 0.25, 0.0), (0.5, 0.0), 0.01));
+    assert!(close(land("textRingOutside", &[], 0.25, 1.0), (0.5, 1.0), 0.01));
+}
+
+#[test]
+fn follow_presets_keep_text_size_and_stack_lines_outwards() {
+    let w = warp("textArchUp", &[], rect()).unwrap();
+    // A 40-wide centred line whose reference height is 80.
+    let line = WarpLine { ink: Some(Rect::new(190.0, 50.0, 230.0, 88.0)), extent: (190.0, 230.0), ref_y: 80.0 };
+    let inner = Rect::new(7.2, 3.6, W - 7.2, H - 3.6);
+    let m = w.mapper(&[line], inner);
+    // The middle of the reference line lands on the top of the ellipse; 10 pt above it lands
+    // 10 pt above the top.
+    let p = m.map(0, Point::new(210.0, 80.0));
+    assert!((p.x - 210.0).abs() < 0.05 && p.y.abs() < 0.05, "{p:?}");
+    let q = m.map(0, Point::new(210.0, 70.0));
+    assert!((q.x - 210.0).abs() < 0.15 && (q.y + 10.0).abs() < 0.05, "{q:?}");
+    // Natural size: 40 pt of text spans about 40 pt of arc.
+    let (a, b) = (m.map(0, Point::new(190.0, 80.0)), m.map(0, Point::new(230.0, 80.0)));
+    assert!(((b - a).hypot() - 40.0).abs() < 0.5);
+    // Left-aligned text starts at the very start of the arc: insets don't shorten it.
+    let left = WarpLine { ink: Some(Rect::new(7.2, 50.0, 47.2, 88.0)), extent: (7.2, 47.2), ref_y: 80.0 };
+    let m = w.mapper(&[left], inner);
+    let p = m.map(0, Point::new(7.2, 80.0));
+    assert!(p.x.abs() < 0.01 && (p.y - 100.0).abs() < 0.01, "{p:?}");
+    // Two lines on an arch up: the last sits on the arc, the first stacks outside it.
+    let l1 = WarpLine { ink: Some(Rect::new(190.0, 10.0, 230.0, 40.0)), extent: (190.0, 230.0), ref_y: 34.0 };
+    let l2 = WarpLine { ink: Some(Rect::new(190.0, 50.0, 230.0, 80.0)), extent: (190.0, 230.0), ref_y: 74.0 };
+    let m = w.mapper(&[l1, l2], inner);
+    assert!(m.map(1, Point::new(210.0, 74.0)).y.abs() < 0.05);
+    assert!((m.map(0, Point::new(210.0, 34.0)).y + 40.0).abs() < 0.05);
+    // Arch down: the first line sits on the bottom of the ellipse.
+    let w = warp("textArchDown", &[], rect()).unwrap();
+    let m = w.mapper(&[l1, l2], inner);
+    assert!((m.map(0, Point::new(210.0, 34.0)).y - H).abs() < 0.05);
+    assert!((m.map(1, Point::new(210.0, 74.0)).y - H - 40.0).abs() < 0.05);
+    // Text longer than the arc is shrunk to fit it.
+    let w = warp("textArchUp", &[], rect()).unwrap();
+    let long = WarpLine { ink: Some(Rect::new(-500.0, 50.0, 900.0, 88.0)), extent: (-500.0, 900.0), ref_y: 80.0 };
+    let m = w.mapper(&[long], inner);
+    let (a, b) = (m.map(0, Point::new(-500.0, 80.0)), m.map(0, Point::new(900.0, 80.0)));
+    assert!(a.x < 5.0 && b.x > W - 5.0 && (a.y - 100.0).abs() < 10.0 && (b.y - 100.0).abs() < 10.0, "{a:?} {b:?}");
+}
+
+#[test]
+fn lines_share_bands_in_order() {
+    assert_eq!((0..2).map(|i| band_of_line(i, 2, 2)).collect::<Vec<_>>(), [0, 1]);
+    assert_eq!((0..3).map(|i| band_of_line(i, 3, 2)).collect::<Vec<_>>(), [0, 0, 1]);
+    assert_eq!((0..5).map(|i| band_of_line(i, 5, 2)).collect::<Vec<_>>(), [0, 0, 0, 1, 1]);
+    assert_eq!((0..5).map(|i| band_of_line(i, 5, 3)).collect::<Vec<_>>(), [0, 0, 1, 1, 2]);
+    assert_eq!((0..4).map(|i| band_of_line(i, 4, 3)).collect::<Vec<_>>(), [0, 0, 1, 2]);
+    assert_eq!((0..2).map(|i| band_of_line(i, 2, 3)).collect::<Vec<_>>(), [0, 1]);
+    assert_eq!(band_of_line(0, 1, 3), 0);
+    assert_eq!(band_of_line(7, 9, 1), 0);
+    assert_eq!(band_of_line(0, 0, 3), 0);
+}
+
+#[test]
+fn deflate_inflate_maps_each_band_separately() {
+    let w = warp("textDeflateInflate", &[], rect()).unwrap();
+    assert_eq!(w.bands.len(), 2);
+    let l1 = WarpLine { ink: Some(Rect::new(100.0, 10.0, 300.0, 40.0)), extent: (100.0, 300.0), ref_y: 34.0 };
+    let l2 = WarpLine { ink: Some(Rect::new(100.0, 50.0, 300.0, 80.0)), extent: (100.0, 300.0), ref_y: 74.0 };
+    let m = w.mapper(&[l1, l2], rect());
+    // Band 1 ends at 45 % height on the sides, band 2 starts at 55 %.
+    assert!((m.map(0, Point::new(100.0, 40.0)).y / H - 0.45).abs() < 0.004);
+    assert!((m.map(1, Point::new(100.0, 50.0)).y / H - 0.55).abs() < 0.004);
+    assert!((m.map(1, Point::new(300.0, 80.0)).y / H - 1.0).abs() < 0.004);
+    // A band with fewer lines keeps them at the size of the fuller band, centred in its band:
+    // two lines (ink 10..60) in band 1, one line (ink 70..80) in band 2 of three.
+    let a = WarpLine { ink: Some(Rect::new(100.0, 10.0, 300.0, 30.0)), extent: (100.0, 300.0), ref_y: 28.0 };
+    let b = WarpLine { ink: Some(Rect::new(100.0, 40.0, 300.0, 60.0)), extent: (100.0, 300.0), ref_y: 58.0 };
+    let c = WarpLine { ink: Some(Rect::new(100.0, 70.0, 300.0, 80.0)), extent: (100.0, 300.0), ref_y: 78.0 };
+    let m = w.mapper(&[a, b, c], rect());
+    let (top, bot) = (m.map(2, Point::new(200.0, 70.0)).y / H, m.map(2, Point::new(200.0, 80.0)).y / H);
+    // Band 2 runs from 0.4 to 1 at the centre; the line takes the middle fifth of it.
+    assert!((top - 0.64).abs() < 0.005 && (bot - 0.76).abs() < 0.005, "{top} {bot}");
+    // A shorter first line keeps its share of the width.
+    let short = WarpLine { ink: Some(Rect::new(150.0, 10.0, 250.0, 40.0)), extent: (150.0, 250.0), ref_y: 34.0 };
+    let m = w.mapper(&[short, l2], rect());
+    let p = m.map(0, Point::new(150.0, 10.0));
+    assert!((p.x / W - 0.25).abs() < 0.01, "{p:?}");
+}
+
+#[test]
+fn guides_extrapolate_and_wrap() {
+    let mut p = BezPath::new();
+    p.move_to((0.0, 0.0));
+    p.line_to((10.0, 0.0));
+    let g = Guide::from_path(&p, false);
+    assert!((g.length() - 10.0).abs() < 1e-9);
+    assert!((g.at(15.0).0.x - 15.0).abs() < 1e-9);
+    assert!((g.at(-5.0).0.x + 5.0).abs() < 1e-9);
+    assert!(g.at(f64::NAN).0.x.is_finite());
+    let w = warp("textCircle", &[], rect()).unwrap();
+    let Some(Band::Follow { path, .. }) = w.bands.first() else { panic!() };
+    assert!(path.is_closed());
+    let l = path.length();
+    let (a, b) = (path.at(5.0).0, path.at(l + 5.0).0);
+    assert!((a - b).hypot() < 1e-6);
+    let empty = Guide::default();
+    assert_eq!(empty.length(), 0.0);
+    assert!(empty.at(3.0).0.x.is_finite());
+}
+
+#[test]
+fn hostile_adjusts_and_boxes_stay_finite() {
+    let adjs: &[&[f64]] =
+        &[&[], &[f64::NAN, f64::INFINITY], &[f64::NEG_INFINITY, f64::NAN], &[1e300, -1e300], &[-1e9, 1e9], &[0.0, 0.0], &[21_599_999.0, 100_000.0]];
+    let rects = [
+        Rect::new(0.0, 0.0, 0.0, 0.0),
+        Rect::new(10.0, 10.0, 10.0, 200.0),
+        Rect::new(0.0, 0.0, 300.0, 0.0),
+        Rect::new(100.0, 100.0, -50.0, -20.0),
+        Rect::new(0.0, 0.0, 1e7, 1e7),
+    ];
+    let lines = [
+        WarpLine { ink: Some(Rect::new(0.0, 0.0, 0.0, 0.0)), extent: (0.0, 0.0), ref_y: 0.0 },
+        WarpLine { ink: None, extent: (5.0, 5.0), ref_y: 3.0 },
+        WarpLine { ink: Some(Rect::new(-1e6, -5.0, 1e6, 5.0)), extent: (-1e6, 1e6), ref_y: 4.0 },
+    ];
+    for name in ALL {
+        for adj in adjs {
+            for r in rects {
+                let Some(w) = warp(name, adj, r) else { panic!("{name} {adj:?} {r:?}") };
+                for b in &w.bands {
+                    assert!(b.length().is_finite());
+                }
+                let m = w.mapper(&lines, r);
+                assert!(m.zoom().is_finite() && m.zoom() >= 1.0);
+                let probes = [
+                    (0, Point::ZERO),
+                    (1, Point::new(5.0, 3.0)),
+                    (2, Point::new(1e6, -5.0)),
+                    (2, Point::new(f64::NAN, 1.0)),
+                    (9, Point::new(1.0, 1.0)),
+                ];
+                for (i, p) in probes {
+                    let q = m.map(i, p);
+                    assert!(q.x.is_finite() || !p.x.is_finite(), "{name} {adj:?} {r:?}: {q:?}");
+                    assert!(q.y.is_finite(), "{name} {adj:?} {r:?}: {q:?}");
+                }
+            }
+        }
+    }
+    assert!(warp("textPlain", &[], Rect::new(f64::NAN, 0.0, 1.0, 1.0)).is_none());
+}
diff --git a/crates/model/src/resolve.rs b/crates/model/src/resolve.rs
index 3ea7f99..54eb4c8 100644
--- a/crates/model/src/resolve.rs
+++ b/crates/model/src/resolve.rs
@@ -223,6 +223,7 @@ pub fn body(ctx: &Ctx, shape: &Shape) -> BodyProps {
         columns: Some(1),
         col_spacing: Some(0.0),
         warp: None,
+        warp_adj: Vec::new(),
         rtl_col: Some(false),
         upright: Some(false),
     });
diff --git a/crates/model/src/text.rs b/crates/model/src/text.rs
index feaff46..b8138a3 100644
--- a/crates/model/src/text.rs
+++ b/crates/model/src/text.rs
@@ -98,6 +98,10 @@ pub struct BodyProps {
     pub col_spacing: Option<f64>,
     /// WordArt transform (`prstTxWarp`), e.g. `textArchUp`.
     pub warp: Option<String>,
+    /// The warp's adjust values (`prstTxWarp/avLst`: `adj` or `adj1`, `adj2`…, raw guide values);
+    /// empty = the preset's defaults.
+    #[serde(skip_serializing_if = "Vec::is_empty")]
+    pub warp_adj: Vec<f64>,
     pub rtl_col: Option<bool>,
     /// Keep text upright when the shape rotates.
     pub upright: Option<bool>,
@@ -119,6 +123,7 @@ impl BodyProps {
         self.col_spacing = self.col_spacing.or(p.col_spacing);
         if self.warp.is_none() {
             self.warp.clone_from(&p.warp);
+            self.warp_adj.clone_from(&p.warp_adj);
         }
         self.rtl_col = self.rtl_col.or(p.rtl_col);
         self.upright = self.upright.or(p.upright);
diff --git a/crates/pptx/src/read/dml.rs b/crates/pptx/src/read/dml.rs
index 36f2a66..c902776 100644
--- a/crates/pptx/src/read/dml.rs
+++ b/crates/pptx/src/read/dml.rs
@@ -321,13 +321,45 @@ pub fn body_pr(b: &El) -> BodyProps {
             }
             "spAutoFit" => p.autofit = Some(AutoFit::Shape),
             "noAutofit" => p.autofit = Some(AutoFit::None),
-            "prstTxWarp" => p.warp = e.attr("prst").filter(|w| *w != "textNoShape").map(String::from),
+            "prstTxWarp" => {
+                p.warp = e.attr("prst").filter(|w| *w != "textNoShape" && !w.is_empty()).map(String::from);
+                p.warp_adj = p.warp.as_deref().map(|w| warp_adjusts(w, e)).unwrap_or_default();
+            }
             _ => {}
         }
     }
     p
 }
 
+/// `prstTxWarp/avLst` guides `adj` / `adj1`… as raw values by index (empty when none is given);
+/// slots the file leaves out keep the preset's default.
+fn warp_adjusts(preset: &str, e: &El) -> Vec<f64> {
+    let mut adj: Vec<f64> = Vec::new();
+    let Some(av) = e.child("avLst") else { return adj };
+    let defaults = deckcraft_geom::warp::adjust_defaults(preset);
+    for gd in av.children_named("gd").take(16) {
+        let n = gd.attr("name").unwrap_or("");
+        let idx = if n == "adj" {
+            0
+        } else if let Some(k) = n.strip_prefix("adj").and_then(|k| k.parse::<usize>().ok()).filter(|k| (1..=8).contains(k)) {
+            k - 1
+        } else {
+            continue;
+        };
+        let Some(v) = gd.attr("fmla").and_then(|f| f.trim().strip_prefix("val")).and_then(|v| v.trim().parse::<f64>().ok()).filter(|v| v.is_finite())
+        else {
+            continue;
+        };
+        while adj.len() <= idx {
+            adj.push(defaults.get(adj.len()).copied().unwrap_or(0.0));
+        }
+        if let Some(slot) = adj.get_mut(idx) {
+            *slot = v.clamp(-1.0e9, 1.0e9);
+        }
+    }
+    adj
+}
+
 fn spacing(e: &El) -> Option<Spacing> {
     if let Some(p) = e.child("spcPct") {
         return Some(Spacing::Pct(pct(p, "val").unwrap_or(1.0).clamp(0.0, 100.0)));
diff --git a/crates/pptx/src/write/dml.rs b/crates/pptx/src/write/dml.rs
index 23d3340..4c2e5d9 100644
--- a/crates/pptx/src/write/dml.rs
+++ b/crates/pptx/src/write/dml.rs
@@ -392,7 +392,19 @@ pub fn body_pr(w: &mut W, b: &BodyProps) {
     w.open("a:bodyPr", a);
     if let Some(p) = warp {
         w.open("a:prstTxWarp", A::new().a("prst", p));
-        w.empty0("a:avLst");
+        let adj: Vec<(usize, i64)> =
+            b.warp_adj.iter().take(8).enumerate().filter(|(_, v)| v.is_finite()).map(|(i, v)| (i, v.round().clamp(-2.0e9, 2.0e9) as i64)).collect();
+        if adj.is_empty() {
+            w.empty0("a:avLst");
+        } else {
+            let single = deckcraft_geom::warp::adjust_count(p) <= 1 && b.warp_adj.len() == 1;
+            w.open0("a:avLst");
+            for (i, v) in adj {
+                let n = if single { "adj".to_string() } else { format!("adj{}", i + 1) };
+                w.empty("a:gd", A::new().a("name", n).a("fmla", format!("val {v}")));
+            }
+            w.close("a:avLst");
+        }
         w.close("a:prstTxWarp");
     }
     match b.autofit {
diff --git a/crates/pptx/tests/roundtrip.rs b/crates/pptx/tests/roundtrip.rs
index 08fcbdc..c9f33fe 100644
--- a/crates/pptx/tests/roundtrip.rs
+++ b/crates/pptx/tests/roundtrip.rs
@@ -796,3 +796,64 @@ fn a_table_fill_round_trips() {
         matches!(&t.background, Some(Fill::Solid { color }) if matches!(color.base, deckcraft_model::ColorBase::Rgb { rgb } if rgb == Rgba::rgb(0, 112, 192)))
     );
 }
+
+#[test]
+fn wordart_warps_and_their_adjusts_round_trip() {
+    let mut p = Presentation::default();
+    let cases: [(&str, &str, Vec<f64>); 5] = [
+        ("Arch pour", "textArchUpPour", vec![13_500_000.0, 30_000.0]),
+        ("Wave", "textWave1", vec![18_000.0, -5_000.0]),
+        ("Inflate", "textInflate", vec![30_000.0]),
+        ("Arch", "textArchUp", vec![]),
+        ("Ring", "textRingInside", vec![75_000.0]),
+    ];
+    let mut shapes = vec![];
+    for (i, (name, warp, adj)) in cases.iter().enumerate() {
+        let mut s = shape(&mut p, name, 10.0, 10.0 + 50.0 * i as f64, 300.0, 40.0);
+        let mut body = TextBody::from_text("WordArt");
+        body.body.warp = Some((*warp).into());
+        body.body.warp_adj = adj.clone();
+        s.text = Some(body);
+        shapes.push(s);
+    }
+    Arc::make_mut(&mut p.slides[0]).shapes = shapes;
+    let q = round(&p);
+    for (name, warp, adj) in &cases {
+        let b = &by_name(&q.slides[0], name).text.as_ref().expect("text").body;
+        assert_eq!(b.warp.as_deref(), Some(*warp), "{name}");
+        assert_eq!(&b.warp_adj, adj, "{name}");
+    }
+    // The single-adjust preset is written with the guide name `adj`, two-adjust ones with
+    // `adj1`/`adj2`, and a preset with no adjusts given gets an empty list.
+    let bytes = deckcraft_pptx::export(&p).expect("export");
+    let mut zip = zip::ZipArchive::new(std::io::Cursor::new(bytes)).expect("zip");
+    let mut xml = String::new();
+    std::io::Read::read_to_string(&mut zip.by_name("ppt/slides/slide1.xml").expect("slide"), &mut xml).expect("read");
+    assert!(xml.contains(r#"<a:prstTxWarp prst="textInflate"><a:avLst><a:gd name="adj" fmla="val 30000"/></a:avLst></a:prstTxWarp>"#), "{xml}");
+    assert!(xml.contains(r#"<a:gd name="adj1" fmla="val 13500000"/><a:gd name="adj2" fmla="val 30000"/>"#));
+    assert!(xml.contains(r#"<a:prstTxWarp prst="textArchUp"><a:avLst/></a:prstTxWarp>"#));
+    // A file that gives only `adj2` keeps the preset's default for `adj1`; hostile values are
+    // read as numbers or dropped.
+    let edited = xml
+        .replace(r#"<a:gd name="adj1" fmla="val 13500000"/>"#, "")
+        .replace(r#"<a:gd name="adj" fmla="val 30000"/>"#, r#"<a:gd name="adj" fmla="val NaN"/>"#);
+    let mut out = zip::ZipWriter::new(std::io::Cursor::new(Vec::new()));
+    for i in 0..zip.len() {
+        let mut f = zip.by_index(i).expect("entry");
+        let name = f.name().to_string();
+        let mut data = vec![];
+        std::io::Read::read_to_end(&mut f, &mut data).expect("read");
+        if name == "ppt/slides/slide1.xml" {
+            data = edited.clone().into_bytes();
+        }
+        out.start_file(name, zip::write::SimpleFileOptions::default()).expect("start");
+        std::io::Write::write_all(&mut out, &data).expect("write");
+    }
+    let bytes = out.finish().expect("finish").into_inner();
+    let q = deckcraft_pptx::import(&bytes).expect("import");
+    let pour = &by_name(&q.slides[0], "Arch pour").text.as_ref().expect("text").body;
+    assert_eq!(pour.warp_adj, vec![10_800_000.0, 30_000.0]);
+    let inflate = &by_name(&q.slides[0], "Inflate").text.as_ref().expect("text").body;
+    assert_eq!(inflate.warp.as_deref(), Some("textInflate"));
+    assert!(inflate.warp_adj.is_empty());
+}
diff --git a/crates/render/src/lib.rs b/crates/render/src/lib.rs
index b493889..4e8058a 100644
--- a/crates/render/src/lib.rs
+++ b/crates/render/src/lib.rs
@@ -21,6 +21,7 @@ mod pathgrad;
 mod placed;
 mod ramp;
 mod table;
+mod warp;
 
 use std::collections::HashMap;
 use std::sync::Arc;
@@ -816,7 +817,10 @@ impl Renderer {
             let tr = geo.text_rect;
             if !body.is_empty() {
                 let l = deckcraft_text::layout(rctx, s, body, &Opts { rect: tr, fields: &f.fields, prompt_color: None, no_shrink: false });
-                draw_layout_with(ctx, &l, tr, m, &st.paras);
+                match text_warp(rctx, s, tr).filter(|_| l.rotation == 0.0) {
+                    Some(w) => warp::draw(ctx, &l, tr, m, &st.paras, &w),
+                    None => draw_layout_with(ctx, &l, tr, m, &st.paras),
+                }
             } else if f.opts.edit && s.ph.is_some() {
                 let kind = s.ph_type().unwrap_or(PhType::Body);
                 let prompt_body = prompt_body(rctx, s, kind);
@@ -1146,6 +1150,13 @@ pub fn text_transform(m: Affine, tr: Rect, rotation: f64) -> Affine {
     t
 }
 
+/// The WordArt warp of `s`'s text over its text rectangle `tr`, if it has one DeckCraft draws.
+pub fn text_warp(rctx: &Ctx, s: &Shape, tr: Rect) -> Option<deckcraft_geom::warp::Warp> {
+    let bp = resolve::body(rctx, s);
+    let name = bp.warp.as_deref()?;
+    deckcraft_geom::warp::warp(name, &bp.warp_adj, tr)
+}
+
 /// Draw an already laid-out text block.
 pub fn draw_layout(ctx: &mut RenderContext, l: &deckcraft_text::TextLayout, tr: Rect, m: Affine) {
     draw_layout_with(ctx, l, tr, m, &[]);
diff --git a/crates/render/src/tests.rs b/crates/render/src/tests.rs
index 9a0c6fe..adcc449 100644
--- a/crates/render/src/tests.rs
+++ b/crates/render/src/tests.rs
@@ -994,3 +994,84 @@ fn shadows_and_glows_spread_like_powerpoints() {
     assert!((60..170).contains(&red(&img, 15, 120)), "{}", red(&img, 15, 120));
     assert!(red(&img, 10, 120) > 245);
 }
+
+/// A 400 × 200 text box at (100, 100) holding `text` at 40 pt, warped by `warp`.
+fn wordart(warp: Option<&str>, text: &str) -> Presentation {
+    let mut t = TextBody::from_text(text);
+    t.paragraphs[0].runs[0].props.size = Some(40.0);
+    t.paragraphs[0].props.align = Some(deckcraft_model::text::Align::Center);
+    t.body.warp = warp.map(String::from);
+    deck_with(vec![Shape { id: ShapeId(700), xfrm: Some(Xfrm::new(100.0, 100.0, 400.0, 200.0)), text: Some(t), ..Default::default() }])
+}
+
+/// Ink box (x0, y0, x1, y1) of dark pixels, and the top ink row of each column.
+fn ink(img: &Image) -> ((u32, u32, u32, u32), Vec<Option<u32>>) {
+    let mut b = (u32::MAX, u32::MAX, 0, 0);
+    let mut tops = vec![None; img.width as usize];
+    for y in 0..img.height {
+        for x in 0..img.width {
+            if img.pixel(x, y)[0] < 128 {
+                b = (b.0.min(x), b.1.min(y), b.2.max(x), b.3.max(y));
+                if tops[x as usize].is_none() {
+                    tops[x as usize] = Some(y);
+                }
+            }
+        }
+    }
+    (b, tops)
+}
+
+#[test]
+fn wordart_arch_up_lifts_the_middle_of_the_line() {
+    let o = RenderOpts { scale: 1.0, ..Default::default() };
+    let flat = render_slide(&wordart(None, "ARCHED WORDART"), 0, &o);
+    let arched = render_slide(&wordart(Some("textArchUp"), "ARCHED WORDART"), 0, &o);
+    assert!(diff_px(&flat, &arched) > 1000);
+    let ((fx0, _, fx1, _), ftops) = ink(&flat);
+    let ((ax0, ay0, ax1, _), atops) = ink(&arched);
+    let top_near = |tops: &[Option<u32>], x: u32| (x.saturating_sub(15)..x + 15).filter_map(|i| tops.get(i as usize).copied().flatten()).min();
+    // Flat text: the ends and the middle stand on one line.
+    let (fl, fm) = (top_near(&ftops, fx0 + 20).unwrap(), top_near(&ftops, (fx0 + fx1) / 2).unwrap());
+    assert!(fl.abs_diff(fm) < 4, "flat {fl} {fm}");
+    // Arched: the line follows the top of the ellipse inscribed in the box, so the middle is
+    // at the box top and the ends sit clearly lower.
+    let (al, am, ar) = (top_near(&atops, ax0 + 20).unwrap(), top_near(&atops, (ax0 + ax1) / 2).unwrap(), top_near(&atops, ax1 - 20).unwrap());
+    assert!(al > am + 10 && ar > am + 10, "arched {al} {am} {ar}");
+    assert!((80..=110).contains(&ay0), "arch top {ay0}");
+}
+
+#[test]
+fn wordart_plain_stretches_the_ink_over_the_text_rect() {
+    let img = render_slide(&wordart(Some("textPlain"), "PLAIN"), 0, &RenderOpts { scale: 1.0, ..Default::default() });
+    let ((x0, y0, x1, y1), _) = ink(&img);
+    for (got, want) in [(x0, 100), (y0, 100), (x1, 499), (y1, 299)] {
+        assert!(got.abs_diff(want) <= 2, "ink box {:?}", (x0, y0, x1, y1));
+    }
+}
+
+#[test]
+fn unknown_or_absent_warps_draw_flat_text() {
+    let o = RenderOpts { scale: 0.5, ..Default::default() };
+    // Warm the font database first (other tests load fonts concurrently).
+    let _ = render_slide(&wordart(None, "FLAT"), 0, &o);
+    let flat = render_slide(&wordart(None, "FLAT"), 0, &o);
+    for w in ["textNoShape", "bogus", ""] {
+        assert_eq!(diff_px(&flat, &render_slide(&wordart(Some(w), "FLAT"), 0, &o)), 0, "{w}");
+    }
+}
+
+#[test]
+fn every_warp_preset_renders_text_inside_the_slide() {
+    let o = RenderOpts { scale: 0.5, ..Default::default() };
+    for name in
+        ["textArchUp", "textArchDown", "textCircle", "textButton", "textWave1", "textRingInside", "textCirclePour", "textDeflateInflateDeflate"]
+    {
+        let mut p = wordart(Some(name), "One line\nTwo line\nThree");
+        if let Some(b) = std::sync::Arc::make_mut(&mut p.slides[0]).shapes[0].text.as_mut() {
+            b.body.warp_adj = vec![f64::NAN, -1e12];
+        }
+        let img = render_slide(&p, 0, &o);
+        let ((x0, y0, x1, y1), _) = ink(&img);
+        assert!(x0 <= x1 && y0 <= y1, "{name}: no ink");
+    }
+}
diff --git a/crates/render/src/warp.rs b/crates/render/src/warp.rs
new file mode 100644
index 0000000..de0ff12
--- /dev/null
+++ b/crates/render/src/warp.rs
@@ -0,0 +1,209 @@
+//! Drawing laid-out text through a WordArt warp ([`deckcraft_geom::warp`]).
+//!
+//! Glyph outlines are placed in layout space, flattened, cut into short segments and every point
+//! is mapped through the warp, so straight glyph edges bend with the guides. Underlines and
+//! highlights are warped the same way.
+
+use deckcraft_geom::warp::{Warp, WarpLine};
+use deckcraft_text::{GlyphRun, TextLayout};
+use kurbo::{Affine, BezPath, PathEl, Point, Rect, Shape as _};
+use vello_cpu::{RenderContext, peniko};
+
+use crate::{ParaState, color, glyph, scale_of, text_transform};
+
+/// Most points one warped glyph may have (a hostile size or zoom can't explode the work).
+const MAX_POINTS: usize = 40_000;
+
+/// The line of `l` a glyph of paragraph `para` on baseline `y` belongs to.
+fn line_of(l: &TextLayout, para: usize, y: f64) -> Option<usize> {
+    let mut best: Option<(usize, f64)> = None;
+    for (i, li) in l.lines.iter().enumerate().filter(|(_, li)| li.para == para) {
+        let inside = y >= li.top - 0.01 && y <= li.bottom + 0.01;
+        let d = if inside { 0.0 } else { (li.baseline - y).abs() };
+        if best.is_none_or(|(_, bd)| d < bd) {
+            best = Some((i, d));
+        }
+    }
+    best.map(|(i, _)| i)
+}
+
+/// Where a line meets a follow guide, above its baseline: 3/8 of the way up the font's
+/// ascent + descent box (measured on Arial, Times New Roman and Courier New in PowerPoint).
+fn ref_offset(run: &GlyphRun) -> f64 {
+    let f = &run.face;
+    let k = run.size / f.upem.max(1.0);
+    ((0.375 * (f.ascent + f.descent) - f.descent) * k).clamp(-run.size, run.size)
+}
+
+/// `path` flattened with tolerance `tol`, cut into pieces of at most `seg` and mapped by `f`.
+fn warp_path(path: &BezPath, tol: f64, seg: f64, f: &dyn Fn(Point) -> Point) -> BezPath {
+    let mut out = BezPath::new();
+    let mut last: Option<Point> = None;
+    let mut start: Option<Point> = None;
+    let mut budget = MAX_POINTS;
+    let segment = |out: &mut BezPath, a: Point, b: Point, budget: &mut usize| {
+        let n = ((b - a).hypot() / seg).ceil();
+        let n = if n.is_finite() { (n as usize).clamp(1, 512) } else { 1 };
+        for i in 1..=n {
+            if *budget == 0 {
+                return;
+            }
+            *budget -= 1;
+            out.line_to(f(a.lerp(b, i as f64 / n as f64)));
+        }
+    };
+    kurbo::flatten(path.iter(), tol, |el| match el {
+        PathEl::MoveTo(p) => {
+            if let (Some(a), Some(s)) = (last, start)
+                && (a - s).hypot() > 1e-9
+            {
+                segment(&mut out, a, s, &mut budget);
+            }
+            out.move_to(f(p));
+            last = Some(p);
+            start = Some(p);
+        }
+        PathEl::LineTo(p) => {
+            if let Some(a) = last {
+                segment(&mut out, a, p, &mut budget);
+            }
+            last = Some(p);
+        }
+        PathEl::ClosePath => {
+            if let (Some(a), Some(s)) = (last, start) {
+                segment(&mut out, a, s, &mut budget);
+            }
+            out.close_path();
+            last = start;
+        }
+        _ => {}
+    });
+    out
+}
+
+struct Item<'a> {
+    run: &'a GlyphRun,
+    path: BezPath,
+    line: usize,
+    state: ParaState,
+}
+
+/// Draw `l` (laid out in text rect `tr`, shape transform `m`) through `warp`.
+pub(crate) fn draw(ctx: &mut RenderContext, l: &TextLayout, tr: Rect, m: Affine, paras: &[(usize, ParaState)], warp: &Warp) {
+    let para = |i: usize| paras.iter().find(|(p, _)| *p == i).map(|(_, s)| *s).unwrap_or_default();
+    let m = text_transform(m, tr, l.rotation);
+    let n = l.lines.len();
+    let mut ink: Vec<Option<Rect>> = vec![None; n];
+    let mut off: Vec<Option<f64>> = vec![None; n];
+    let mut items: Vec<Item> = Vec::new();
+    for run in &l.runs {
+        let k = run.size / run.face.upem.max(1.0);
+        let skew = if run.fake_italic { Affine::new([1.0, 0.0, -0.2, 1.0, 0.0, 0.0]) } else { Affine::IDENTITY };
+        for (gid, x, y) in &run.glyphs {
+            let Some(li) = line_of(l, run.para, *y) else { continue };
+            if let Some(o) = off.get_mut(li) {
+                *o = Some(o.map_or(ref_offset(run), |v| v.max(ref_offset(run))));
+            }
+            let outline = glyph(&run.face, *gid);
+            if outline.elements().is_empty() {
+                continue;
+            }
+            let mut path = (*outline).clone();
+            path.apply_affine(Affine::translate((*x, *y)) * skew * Affine::scale(k));
+            let b = path.bounding_box();
+            if !(b.x0.is_finite() && b.y0.is_finite() && b.x1.is_finite() && b.y1.is_finite()) {
+                continue;
+            }
+            if let Some(slot) = ink.get_mut(li) {
+                *slot = Some(slot.map_or(b, |r| r.union(b)));
+            }
+            items.push(Item { run, path, line: li, state: para(run.para) });
+        }
+    }
+    let lines: Vec<WarpLine> = l
+        .lines
+        .iter()
+        .enumerate()
+        .map(|(i, li)| {
+            let o = off.get(i).copied().flatten().unwrap_or(0.18 * (li.bottom - li.top));
+            WarpLine { ink: ink.get(i).copied().flatten(), extent: li.extent, ref_y: li.baseline - o }
+        })
+        .collect();
+    let mapper = warp.mapper(&lines, l.inner);
+    let px = scale_of(m).max(1e-6) * mapper.zoom();
+    let tol = (0.1 / px).clamp(1e-4, 2.0);
+    let seg = (2.0 / px).clamp(1e-3, 50.0);
+    let deco = |ctx: &mut RenderContext, d: &deckcraft_text::Deco| {
+        let ps = para(d.para);
+        if !ps.visible || ps.opacity <= 0.001 {
+            return;
+        }
+        let y = (d.rect.y0 + d.rect.y1) / 2.0;
+        let Some(li) = line_of(l, d.para, y) else { return };
+        let path = warp_path(&d.rect.to_path(0.1), tol, seg, &|p| mapper.map(li, p));
+        ctx.set_transform(m * Affine::translate(ps.offset));
+        ctx.set_paint(color(d.color, ps.opacity));
+        ctx.fill_path(&path);
+    };
+    for d in l.decos.iter().filter(|d| d.behind) {
+        deco(ctx, d);
+    }
+    for it in &items {
+        let (run, ps) = (it.run, it.state);
+        if !ps.visible || ps.opacity <= 0.001 {
+            continue;
+        }
+        let alpha = run.alpha * ps.opacity;
+        if (alpha <= 0.0 || run.color.a == 0) && run.outline.is_none() {
+            continue;
+        }
+        let path = warp_path(&it.path, tol, seg, &|p| mapper.map(it.line, p));
+        ctx.set_transform(m * Affine::translate(ps.offset));
+        if alpha > 0.0 && run.color.a > 0 {
+            ctx.set_paint(color(run.color, alpha));
+            ctx.fill_path(&path);
+            if run.fake_bold {
+                ctx.set_stroke(kurbo::Stroke::new(run.size * 0.025).with_join(kurbo::Join::Round));
+                ctx.stroke_path(&path);
+            }
+        }
+        if let Some((oc, ow)) = run.outline {
+            ctx.set_paint(color(oc, ps.opacity));
+            ctx.set_stroke(kurbo::Stroke::new(ow.max(0.0)).with_join(kurbo::Join::Round));
+            ctx.stroke_path(&path);
+        }
+    }
+    for d in l.decos.iter().filter(|d| !d.behind) {
+        deco(ctx, d);
+    }
+    ctx.set_fill_rule(peniko::Fill::NonZero);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn warp_path_subdivides_and_maps_every_point() {
+        let mut p = BezPath::new();
+        p.move_to((0.0, 0.0));
+        p.line_to((10.0, 0.0));
+        p.line_to((10.0, 10.0));
+        p.close_path();
+        let out = warp_path(&p, 0.01, 1.0, &|q| Point::new(q.x, q.y + q.x * q.x * 0.01));
+        // 10 + 10 + ~15 pieces of at most 1 pt.
+        let n = out.elements().len();
+        assert!(n > 30, "{n}");
+        // The first edge is bent onto the parabola.
+        let mid = out.elements().iter().find_map(|e| if let PathEl::LineTo(q) = e { (q.x == 5.0).then_some(*q) } else { None });
+        assert_eq!(mid, Some(Point::new(5.0, 0.25)));
+        // A huge path with a tiny segment length stays bounded.
+        let mut big = BezPath::new();
+        big.move_to((0.0, 0.0));
+        for i in 0..1000 {
+            big.line_to((1e6 * (i % 2) as f64, i as f64));
+        }
+        let out = warp_path(&big, 0.01, 1e-3, &|q| q);
+        assert!(out.elements().len() <= MAX_POINTS + 2);
+    }
+}
diff --git a/crates/text/src/lib.rs b/crates/text/src/lib.rs
index 32ef2f1..7144c55 100644
--- a/crates/text/src/lib.rs
+++ b/crates/text/src/lib.rs
@@ -1074,7 +1074,9 @@ fn layout_scaled(ctx: &Ctx, shape: &Shape, body: &TextBody, bp: &BodyProps, opts
         (r.x1 - bp.inset_r.unwrap_or(7.2)).max(r.x0 + bp.inset_l.unwrap_or(7.2)),
         (r.y1 - bp.inset_b.unwrap_or(3.6)).max(r.y0 + bp.inset_t.unwrap_or(3.6)),
     );
-    let wrap = bp.wrap.unwrap_or(true) && !matches!(bp.autofit, Some(AutoFit::Shape) if shape.text_box && !bp.wrap.unwrap_or(true));
+    // Text that follows a WordArt arch or circle is set on one line per paragraph.
+    let follow = bp.warp.as_deref().is_some_and(deckcraft_geom::warp::is_follow);
+    let wrap = bp.wrap.unwrap_or(true) && !follow && !matches!(bp.autofit, Some(AutoFit::Shape) if shape.text_box && !bp.wrap.unwrap_or(true));
     let ncols = bp.columns.unwrap_or(1).clamp(1, 16) as usize;
     let col_gap = bp.col_spacing.unwrap_or(0.0).max(0.0);
     let col_w = ((inner.width() - col_gap * (ncols as f64 - 1.0)) / ncols as f64).max(1.0);
diff --git a/docs/file-format-parity.md b/docs/file-format-parity.md
index 1d87c9a..6a8c992 100644
--- a/docs/file-format-parity.md
+++ b/docs/file-format-parity.md
@@ -69,7 +69,7 @@ the round trip even though DeckCraft doesn't model it.
 | Effects: shadow, glow, soft edges, reflection | yes | yes | |
 | 3-D: `scene3d`, `sp3d` | kept | kept | Not rendered |
 | Text: runs, paragraphs, bullets, numbering, levels, autofit, columns, vertical, RTL, script fonts, fields, hyperlinks | yes | yes | Round-trip tests incl. `justLow` and date fields |
-| Text warp (`prstTxWarp`) | yes | yes | Not rendered |
+| Text warp (`prstTxWarp`) | yes | yes | All 40 presets rendered (`crates/geom/src/warp.rs`); adjust values (`avLst`) round-trip |
 | Pictures with crop, recolour, duotone, alpha, luminance | yes | yes | |
 | Tables with styles | yes | yes | |
 | Charts (`c:chartSpace`) | yes | yes | Original XML kept in `Chart.raw` |
@@ -99,4 +99,5 @@ the round trip even though DeckCraft doesn't model it.
 
 | Date | Change | Summary |
 |---|---|---|
+| 2026-10-12 | minor | Text warps rendered; their adjust values read and written |
 | 2026-10-10 | major | Created from PowerPoint 16.113.4's `CFBundleDocumentTypes`, `crates/pptx` reader/writer and tests, and the open round-trip issues |
diff --git a/docs/gaps.md b/docs/gaps.md
index 6ea4130..a13383a 100644
--- a/docs/gaps.md
+++ b/docs/gaps.md
@@ -165,9 +165,13 @@ Detail in [animation-parity.md](animation-parity.md). 10–16 h; the pane is a *
 - **Estimate:** 4–6 h.
 
 ### Edit points, text warp, 3-D
-- **Evidence:** checklist rows "Edit points" (P1 missing), "Text warp transforms", "Bevel and 3-D
-  rotation" (missing; `scene3d`/`sp3d` kept as raw XML on round trip).
-- **Estimate:** 4–6 h (edit points), 6–10 h (warp), 8–12 h (3-D render approximation).
+- **Evidence:** checklist rows "Edit points" (P1 missing), "Text warp transforms" (partial: all 40
+  `prstTxWarp` presets render and their adjusts round-trip, but there is no Transform gallery or
+  command to apply one, no adjust handles, and arc/circle placement can differ from PowerPoint by
+  1–3 % of the path length), "Bevel and 3-D rotation" (missing; `scene3d`/`sp3d` kept as raw XML on
+  round trip).
+- **Estimate:** 4–6 h (edit points), 2–4 h (warp gallery, command and handles), 8–12 h (3-D render
+  approximation).
 
 ### Proofing: spelling, thesaurus, AutoCorrect
 - **Evidence:** `review.spelling` checks a small built-in list of frequent misspellings
@@ -247,5 +251,6 @@ Detail in [localization-parity.md](localization-parity.md).
 
 | Date | Change | Summary |
 |---|---|---|
+| 2026-10-12 | minor | Text warps render (all 40 presets, adjusts round-trip); the warp gap is now the gallery, command and handles |
 | 2026-10-10 | minor | Noted that no gap blocks alpha (core-workflow gate passes) |
 | 2026-10-10 | major | Created: every gap from the 2026-10-10 re-measure and the 16 open GitHub issues, ranked, with beta blockers marked |
diff --git a/docs/parity-checklist.md b/docs/parity-checklist.md
index 8c7337f..bfd5c07 100644
--- a/docs/parity-checklist.md
+++ b/docs/parity-checklist.md
@@ -9,7 +9,7 @@ The summary between `<!-- SUMMARY -->
 |---|---|---|---|---|---|
 | P0 | 72 | 60 | 12 | 0 | 92% |
 | P1 | 65 | 38 | 21 | 6 | 75% |
-| P2 | 54 | 13 | 13 | 28 | 36% |
+| P2 | 54 | 13 | 14 | 27 | 37% |
 
 | Area | Parity |
 |---|---|
@@ -18,7 +18,7 @@ The summary between `<!-- SUMMARY -->
 | Slides | 90% |
 | Views | 90% |
 | Masters & themes | 85% |
-| Shapes | 86% |
+| Shapes | 88% |
 | Format | 81% |
 | Arrange | 100% |
 | Text | 80% |
@@ -115,7 +115,7 @@ Open P0 items: Start screen (new, templates/themes, recent), Contextual tabs (Sh
 | Shapes | Change shape | P1 | D |
 | Shapes | Text boxes | P0 | D |
 | Shapes | WordArt | P1 | P |
-| Shapes | Text warp transforms | P2 | M |
+| Shapes | Text warp transforms | P2 | P |
 | Shapes | Shape quick styles | P1 | D |
 | Shapes | Set as default shape | P2 | D |
 | Format | Solid fill and transparency | P0 | D |