diff --git a/crates/drawingml/src/custgeom.rs b/crates/drawingml/src/custgeom.rs
index c4ac5d331..d886d30b9 100644
--- a/crates/drawingml/src/custgeom.rs
+++ b/crates/drawingml/src/custgeom.rs
@@ -28,6 +28,48 @@ pub struct CustomPath {
     pub stroke: bool,
 }
 
+impl CustomPath {
+    /// A path from a `kurbo` path given in a `w` × `h` box (points), its coordinates kept as
+    /// they are. Quadratic segments become cubics: not every reader handles `a:quadBezTo`.
+    pub fn from_bez(bp: &kurbo::BezPath, w: f64, h: f64, filled: bool) -> CustomPath {
+        let mut d = String::new();
+        let mut last = kurbo::Point::ZERO;
+        let mut put = |c: char, pts: &[kurbo::Point]| {
+            if !d.is_empty() {
+                d.push(' ');
+            }
+            d.push(c);
+            for p in pts {
+                let _ = write!(d, " {} {}", finite(p.x), finite(p.y));
+            }
+        };
+        for el in bp.elements() {
+            match *el {
+                kurbo::PathEl::MoveTo(a) => {
+                    put('M', &[a]);
+                    last = a;
+                }
+                kurbo::PathEl::LineTo(a) => {
+                    put('L', &[a]);
+                    last = a;
+                }
+                kurbo::PathEl::QuadTo(a, b) => {
+                    let c1 = last + (a - last) * (2.0 / 3.0);
+                    let c2 = b + (a - b) * (2.0 / 3.0);
+                    put('C', &[c1, c2, b]);
+                    last = b;
+                }
+                kurbo::PathEl::CurveTo(a, b, c) => {
+                    put('C', &[a, b, c]);
+                    last = c;
+                }
+                kurbo::PathEl::ClosePath => put('Z', &[]),
+            }
+        }
+        CustomPath { w, h, d, fill: if filled { FillMode::Norm } else { FillMode::None }, stroke: true }
+    }
+}
+
 impl Default for CustomPath {
     fn default() -> Self {
         CustomPath { w: 0.0, h: 0.0, d: String::new(), fill: FillMode::Norm, stroke: true }
@@ -651,4 +693,20 @@ mod tests {
         let d = format!("M{}", " 1 2".repeat(1_000_001));
         assert_eq!(parse_path(&d).len(), 1_000_000);
     }
+
+    #[test]
+    fn a_kurbo_path_becomes_a_custom_path_with_quads_as_cubics() {
+        let mut bp = kurbo::BezPath::new();
+        bp.move_to((0.0, 0.0));
+        bp.line_to((30.0, 0.0));
+        bp.quad_to((30.0, 30.0), (0.0, 30.0));
+        bp.close_path();
+        let p = CustomPath::from_bez(&bp, 30.0, 30.0, false);
+        assert_eq!(p.d, "M 0 0 L 30 0 C 30 20 20 30 0 30 Z");
+        assert_eq!(p.fill, FillMode::None);
+        let mut w = Writer::new();
+        write_cust_geom(&mut w, std::slice::from_ref(&p));
+        let back = read_cust_geom(&parse(w.finish().as_bytes()).unwrap(), 1.0, 1.0);
+        assert_eq!(parse_path(&back[0].d).len(), 4);
+    }
 }
diff --git a/crates/drawingml/src/lib.rs b/crates/drawingml/src/lib.rs
index 70e57b2c5..87254bcc1 100644
--- a/crates/drawingml/src/lib.rs
+++ b/crates/drawingml/src/lib.rs
@@ -163,6 +163,42 @@ impl Xfrm {
         let r = self.rot.rem_euclid(360.0);
         if r >= 360.0 { 0.0 } else { r }
     }
+    /// The box `inner` occupies under `m` (inner space → parent), as an `a:xfrm`: rotated about
+    /// its centre, flipped vertically for a negative determinant. `None` when `m` shears (an
+    /// `a:xfrm` cannot), or is not finite. A shape drawn in `inner`'s space then maps onto the
+    /// box by the per-axis scales of [`decompose`]`(m)`.
+    pub fn from_affine(inner: Rect, m: Affine) -> Option<Xfrm> {
+        let dm = decompose(m);
+        if dm.shear.abs() > 1e-6 || ![dm.sx, dm.sy, dm.rot].iter().all(|v| v.is_finite()) {
+            return None;
+        }
+        let c = m * inner.center();
+        let (w, h) = (inner.width() * dm.sx.abs(), inner.height() * dm.sy.abs());
+        let x = Xfrm { x: c.x - w / 2.0, y: c.y - h / 2.0, w, h, rot: dm.rot, flip_h: false, flip_v: dm.sy < 0.0 };
+        x.is_finite().then_some(x)
+    }
+}
+
+/// An affine split into rotation, axis scales and shear: `m = translate · rotate(rot) ·
+/// [sx, shear·sy; 0, sy]`. `rot` is in degrees; `sy` is negative for a mirroring transform.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct Decomposed {
+    pub rot: f64,
+    pub sx: f64,
+    pub sy: f64,
+    pub shear: f64,
+}
+
+/// See [`Decomposed`].
+pub fn decompose(m: Affine) -> Decomposed {
+    let [a, b, c, d, _, _] = m.as_coeffs();
+    let sx = a.hypot(b);
+    let rot = b.atan2(a);
+    let (cos, sin) = (rot.cos(), rot.sin());
+    let c2 = cos * c + sin * d;
+    let d2 = -sin * c + cos * d;
+    let shear = if d2.abs() > 1e-12 { c2 / d2 } else { 0.0 };
+    Decomposed { rot: rot.to_degrees(), sx, sy: d2, shear }
 }
 
 /// Maps a group's child coordinate space (`ch_off`, `ch_ext`) onto the group's own box.
@@ -218,4 +254,24 @@ mod tests {
             assert!((0.0..360.0).contains(&n), "rot {rot} -> {n}");
         }
     }
+
+    #[test]
+    fn an_affine_without_shear_becomes_an_xfrm_that_places_the_box_the_same_way() {
+        let inner = Rect::new(10.0, 20.0, 110.0, 70.0);
+        for (rot, sx, sy) in [(0.0, 1.0, 1.0), (30.0, 2.0, 0.5), (-120.0, 1.5, -2.0), (90.0, 1.0, -1.0)] {
+            let m = Affine::translate((300.0, 200.0)) * Affine::rotate(f64::to_radians(rot)) * Affine::scale_non_uniform(sx, sy);
+            let x = Xfrm::from_affine(inner, m).unwrap();
+            let dm = decompose(m);
+            assert!((dm.rot - rot).abs() < 1e-9 && (dm.sx - sx).abs() < 1e-9 && (dm.sy - sy).abs() < 1e-9, "{dm:?}");
+            assert_eq!(x.flip_v, sy < 0.0);
+            // The xfrm's local box, scaled from inner space, lands where `m` puts each corner.
+            let local = |p: Point| Point::new((p.x - inner.x0) * sx.abs(), (p.y - inner.y0) * sy.abs());
+            for p in [Point::new(inner.x0, inner.y0), Point::new(inner.x1, inner.y0), Point::new(inner.x1, inner.y1)] {
+                let (a, b) = (x.affine() * local(p), m * p);
+                assert!((a - b).hypot() < 1e-9, "rot {rot} sy {sy}: {a:?} vs {b:?}");
+            }
+        }
+        assert!(Xfrm::from_affine(inner, Affine::skew(0.3, 0.0)).is_none(), "a shear has no xfrm");
+        assert!(Xfrm::from_affine(inner, Affine::scale(f64::NAN)).is_none());
+    }
 }