diff --git a/moli-svg/src/geometry.rs b/moli-svg/src/geometry.rs
index 8aa1c949ea..83fe8c23d4 100644
--- a/moli-svg/src/geometry.rs
+++ b/moli-svg/src/geometry.rs
@@ -98,7 +98,7 @@ pub enum SvgGeometryElement {
 }
 
 pub fn segments_for_element(element: SvgGeometryElement) -> Vec<SvgGeometrySegment> {
-    let path = geometry_path(&element).unwrap_or_default();
+    let path = distance_query_path(&element).unwrap_or_default();
     let segments = path
         .segments()
         .map(SvgGeometrySegment::new)
@@ -229,6 +229,36 @@ pub fn point_at_length(segments: &[SvgGeometrySegment], distance: f64) -> SvgGeo
         .unwrap_or(SvgGeometryPoint::new(0.0, 0.0))
 }
 
+fn distance_query_path(element: &SvgGeometryElement) -> Option<BezPath> {
+    // A zero axis disables rendering, but distance queries can still compute
+    // the equivalent path along the other axis.
+    match element {
+        SvgGeometryElement::Rect {
+            x,
+            y,
+            width,
+            height,
+            ..
+        } if (*width == 0.0 && *height > 0.0) || (*height == 0.0 && *width > 0.0) => {
+            Some(Rect::new(*x, *y, *x + *width, *y + *height).to_path(SHAPE_PATH_TOLERANCE))
+        }
+        SvgGeometryElement::Ellipse { cx, cy, rx, ry }
+            if (*rx == 0.0 && *ry > 0.0) || (*ry == 0.0 && *rx > 0.0) =>
+        {
+            // Collapsed quarter arcs are lines. Preserve SVG's starting point
+            // and sweep instead of normalizing the ellipse's axes.
+            let mut path = BezPath::new();
+            path.move_to((*cx + *rx, *cy));
+            path.line_to((*cx, *cy + *ry));
+            path.line_to((*cx - *rx, *cy));
+            path.line_to((*cx, *cy - *ry));
+            path.close_path();
+            Some(path)
+        }
+        _ => geometry_path(element),
+    }
+}
+
 fn geometry_path(element: &SvgGeometryElement) -> Option<BezPath> {
     match element {
         SvgGeometryElement::Circle { cx, cy, r } => Some(if *r > 0.0 {
diff --git a/moli-svg/src/lib.rs b/moli-svg/src/lib.rs
index bf6853b8f2..6ab8b2f2d7 100644
--- a/moli-svg/src/lib.rs
+++ b/moli-svg/src/lib.rs
@@ -74,6 +74,121 @@ mod tests {
         })
     }
 
+    #[test]
+    fn degenerate_shapes_keep_distance_paths_without_rendered_bounds() {
+        for (element, length, endpoint) in [
+            (
+                SvgGeometryElement::Rect {
+                    x: 7.0,
+                    y: 9.0,
+                    width: 0.0,
+                    height: 10.0,
+                    rx: 0.0,
+                    ry: 0.0,
+                },
+                20.0,
+                SvgGeometryPoint::new(7.0, 9.0),
+            ),
+            (
+                SvgGeometryElement::Rect {
+                    x: 7.0,
+                    y: 9.0,
+                    width: 10.0,
+                    height: 0.0,
+                    rx: 0.0,
+                    ry: 0.0,
+                },
+                20.0,
+                SvgGeometryPoint::new(7.0, 9.0),
+            ),
+            (
+                SvgGeometryElement::Ellipse {
+                    cx: 7.0,
+                    cy: 9.0,
+                    rx: 0.0,
+                    ry: 10.0,
+                },
+                40.0,
+                SvgGeometryPoint::new(7.0, 9.0),
+            ),
+            (
+                SvgGeometryElement::Ellipse {
+                    cx: 7.0,
+                    cy: 9.0,
+                    rx: 10.0,
+                    ry: 0.0,
+                },
+                40.0,
+                SvgGeometryPoint::new(17.0, 9.0),
+            ),
+        ] {
+            assert!(bounding_box_for_element(&element).is_none());
+            let segments = segments_for_element(element);
+            assert_near(
+                segments.iter().map(SvgGeometrySegment::length).sum(),
+                length,
+                1e-6,
+            );
+            let point = point_at_length(&segments, 300.0);
+            assert_close(point.x, endpoint.x);
+            assert_close(point.y, endpoint.y);
+        }
+        for element in [
+            SvgGeometryElement::Rect {
+                x: 7.0,
+                y: 9.0,
+                width: 0.0,
+                height: 0.0,
+                rx: 0.0,
+                ry: 0.0,
+            },
+            SvgGeometryElement::Ellipse {
+                cx: 7.0,
+                cy: 9.0,
+                rx: 0.0,
+                ry: 0.0,
+            },
+            SvgGeometryElement::Circle {
+                cx: 7.0,
+                cy: 9.0,
+                r: 0.0,
+            },
+            SvgGeometryElement::Path { d: String::new() },
+        ] {
+            assert!(segments_for_element(element).is_empty());
+        }
+        for (rx, ry, points) in [
+            (
+                0.0,
+                10.0,
+                [(7.0, 9.0), (7.0, 19.0), (7.0, 9.0), (7.0, -1.0), (7.0, 9.0)],
+            ),
+            (
+                10.0,
+                0.0,
+                [
+                    (17.0, 9.0),
+                    (7.0, 9.0),
+                    (-3.0, 9.0),
+                    (7.0, 9.0),
+                    (17.0, 9.0),
+                ],
+            ),
+        ] {
+            let segments = segments_for_element(SvgGeometryElement::Ellipse {
+                cx: 7.0,
+                cy: 9.0,
+                rx,
+                ry,
+            });
+            for (distance, (x, y)) in [0.0, 10.0, 20.0, 30.0, 40.0].into_iter().zip(points) {
+                let point = point_at_length(&segments, distance);
+                assert_close(point.x, x);
+                assert_close(point.y, y);
+            }
+        }
+    }
+
     fn assert_close(actual: f64, expected: f64) {
         assert!(
             (actual - expected).abs() < 1e-9,