diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3e33cf93c..b8a212077 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -16,6 +16,10 @@ The release run heads these entries with the version and opens a fresh
 
 ## Unreleased
 
+- An ODF drawing shape is drawn where its `draw:transform` puts it. New
+  `transform()` on `Frame`, `Rect`, `Line`, `Circle` and `CustomShape`,
+  mirrored in the JNI, Apple and Python bindings.
+
 - A StarView metafile's text is decoded by the charset it names. Every
   encoding but `UCS2` used to emit the file's own bytes, and the invalid utf-8
   a non-ascii label made of that cost the whole image.
diff --git a/CMakeLists.txt b/CMakeLists.txt
index d635ded0b..0d8e0b7b9 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -182,6 +182,7 @@ set(ODR_SOURCE_FILES
         "src/odr/internal/odf/odf_element_registry.cpp"
         "src/odr/internal/odf/odf_file.cpp"
         "src/odr/internal/odf/odf_flat_file.cpp"
+        "src/odr/internal/odf/odf_geometry.cpp"
         "src/odr/internal/odf/odf_list.cpp"
         "src/odr/internal/odf/odf_manifest.cpp"
         "src/odr/internal/odf/odf_meta.cpp"
diff --git a/apple/include/OdrCoreObjC/ODRDocumentElement.h b/apple/include/OdrCoreObjC/ODRDocumentElement.h
index 97ce71903..280a77de6 100644
--- a/apple/include/OdrCoreObjC/ODRDocumentElement.h
+++ b/apple/include/OdrCoreObjC/ODRDocumentElement.h
@@ -249,6 +249,20 @@ NS_SWIFT_NAME(TableCell)
 @property(nonatomic, readonly) ODRTableCellStyle *style;
 @end
 
+/// `odr::DrawingTransform`.
+NS_SWIFT_NAME(DrawingTransform)
+@interface ODRDrawingTransform : NSObject
+@property(nonatomic, readonly) double a;
+@property(nonatomic, readonly) double b;
+@property(nonatomic, readonly) double c;
+@property(nonatomic, readonly) double d;
+@property(nonatomic, readonly) ODRMeasure *e;
+@property(nonatomic, readonly) ODRMeasure *f;
+
+- (instancetype)init NS_UNAVAILABLE;
++ (instancetype)new NS_UNAVAILABLE;
+@end
+
 /// `odr::Frame`.
 NS_SWIFT_NAME(Frame)
 @interface ODRFrame : ODRElement
@@ -259,6 +273,7 @@ NS_SWIFT_NAME(Frame)
 @property(nonatomic, readonly, nullable) ODRMeasure *height;
 /// `int32_t`, boxed; `nil` when the document did not set one.
 @property(nonatomic, readonly, nullable) NSNumber *zIndex;
+@property(nonatomic, readonly, nullable) ODRDrawingTransform *transform;
 @property(nonatomic, readonly) ODRGraphicStyle *style;
 @end
 
@@ -269,6 +284,7 @@ NS_SWIFT_NAME(Rect)
 @property(nonatomic, readonly) ODRMeasure *y;
 @property(nonatomic, readonly) ODRMeasure *width;
 @property(nonatomic, readonly) ODRMeasure *height;
+@property(nonatomic, readonly, nullable) ODRDrawingTransform *transform;
 @property(nonatomic, readonly) ODRGraphicStyle *style;
 @end
 
@@ -279,6 +295,7 @@ NS_SWIFT_NAME(Line)
 @property(nonatomic, readonly) ODRMeasure *y1;
 @property(nonatomic, readonly) ODRMeasure *x2;
 @property(nonatomic, readonly) ODRMeasure *y2;
+@property(nonatomic, readonly, nullable) ODRDrawingTransform *transform;
 @property(nonatomic, readonly) ODRGraphicStyle *style;
 @end
 
@@ -289,6 +306,7 @@ NS_SWIFT_NAME(Circle)
 @property(nonatomic, readonly) ODRMeasure *y;
 @property(nonatomic, readonly) ODRMeasure *width;
 @property(nonatomic, readonly) ODRMeasure *height;
+@property(nonatomic, readonly, nullable) ODRDrawingTransform *transform;
 @property(nonatomic, readonly) ODRGraphicStyle *style;
 @end
 
@@ -299,6 +317,7 @@ NS_SWIFT_NAME(CustomShape)
 @property(nonatomic, readonly, nullable) ODRMeasure *y;
 @property(nonatomic, readonly) ODRMeasure *width;
 @property(nonatomic, readonly) ODRMeasure *height;
+@property(nonatomic, readonly, nullable) ODRDrawingTransform *transform;
 @property(nonatomic, readonly) ODRGraphicStyle *style;
 @end
 
diff --git a/apple/src/ODRDocumentElement.mm b/apple/src/ODRDocumentElement.mm
index fe0921f0f..22297465c 100644
--- a/apple/src/ODRDocumentElement.mm
+++ b/apple/src/ODRDocumentElement.mm
@@ -733,6 +733,15 @@ - (nullable NSNumber *)zIndex {
       nil);
 }
 
+- (nullable ODRDrawingTransform *)transform {
+  return guarded_value(
+      [&]() -> ODRDrawingTransform * {
+        return [ODRDrawingTransform
+            transformWithHandle:self.handle.as_frame().transform()];
+      },
+      nil);
+}
+
 - (ODRGraphicStyle *)style {
   return guarded_value(
       [&]() -> ODRGraphicStyle * {
@@ -743,6 +752,25 @@ - (ODRGraphicStyle *)style {
 
 @end
 
+@implementation ODRDrawingTransform
+
++ (nullable instancetype)transformWithHandle:
+    (const std::optional<odr::DrawingTransform> &)handle {
+  if (!handle.has_value()) {
+    return nil;
+  }
+  ODRDrawingTransform *const result = [[ODRDrawingTransform alloc] init];
+  result->_a = handle->a;
+  result->_b = handle->b;
+  result->_c = handle->c;
+  result->_d = handle->d;
+  result->_e = [ODRMeasure measureWithHandle:handle->e];
+  result->_f = [ODRMeasure measureWithHandle:handle->f];
+  return result;
+}
+
+@end
+
 @implementation ODRRect
 
 - (ODRMeasure *)x {
@@ -773,6 +801,15 @@ - (ODRMeasure *)height {
       nil);
 }
 
+- (nullable ODRDrawingTransform *)transform {
+  return guarded_value(
+      [&]() -> ODRDrawingTransform * {
+        return [ODRDrawingTransform
+            transformWithHandle:self.handle.as_rect().transform()];
+      },
+      nil);
+}
+
 - (ODRGraphicStyle *)style {
   return guarded_value(
       [&]() -> ODRGraphicStyle * {
@@ -809,6 +846,15 @@ - (ODRMeasure *)y2 {
       nil);
 }
 
+- (nullable ODRDrawingTransform *)transform {
+  return guarded_value(
+      [&]() -> ODRDrawingTransform * {
+        return [ODRDrawingTransform
+            transformWithHandle:self.handle.as_line().transform()];
+      },
+      nil);
+}
+
 - (ODRGraphicStyle *)style {
   return guarded_value(
       [&]() -> ODRGraphicStyle * {
@@ -853,6 +899,15 @@ - (ODRMeasure *)height {
       nil);
 }
 
+- (nullable ODRDrawingTransform *)transform {
+  return guarded_value(
+      [&]() -> ODRDrawingTransform * {
+        return [ODRDrawingTransform
+            transformWithHandle:self.handle.as_circle().transform()];
+      },
+      nil);
+}
+
 - (ODRGraphicStyle *)style {
   return guarded_value(
       [&]() -> ODRGraphicStyle * {
@@ -894,6 +949,15 @@ - (ODRMeasure *)height {
       nil);
 }
 
+- (nullable ODRDrawingTransform *)transform {
+  return guarded_value(
+      [&]() -> ODRDrawingTransform * {
+        return [ODRDrawingTransform
+            transformWithHandle:self.handle.as_custom_shape().transform()];
+      },
+      nil);
+}
+
 - (ODRGraphicStyle *)style {
   return guarded_value(
       [&]() -> ODRGraphicStyle * {
diff --git a/apple/src/ODRPrivate.h b/apple/src/ODRPrivate.h
index 279d73fd7..4c0944f12 100644
--- a/apple/src/ODRPrivate.h
+++ b/apple/src/ODRPrivate.h
@@ -125,6 +125,11 @@ NS_ASSUME_NONNULL_BEGIN
 + (instancetype)styleWithHandle:(const odr::TableCellStyle &)handle;
 @end
 
+@interface ODRDrawingTransform (Private)
++ (nullable instancetype)transformWithHandle:
+    (const std::optional<odr::DrawingTransform> &)handle;
+@end
+
 @interface ODRGraphicStyle (Private)
 + (instancetype)styleWithHandle:(const odr::GraphicStyle &)handle;
 @end
diff --git a/jni/CMakeLists.txt b/jni/CMakeLists.txt
index 32230c008..4e4b37e5b 100644
--- a/jni/CMakeLists.txt
+++ b/jni/CMakeLists.txt
@@ -79,6 +79,7 @@ add_jar(odr_java
         "java/app/opendocument/core/DocumentFile.java"
         "java/app/opendocument/core/DocumentPath.java"
         "java/app/opendocument/core/DocumentType.java"
+        "java/app/opendocument/core/DrawingTransform.java"
         "java/app/opendocument/core/Element.java"
         "java/app/opendocument/core/ElementType.java"
         "java/app/opendocument/core/EncryptionState.java"
diff --git a/jni/java/app/opendocument/core/Circle.java b/jni/java/app/opendocument/core/Circle.java
index 222073d71..037d451ed 100644
--- a/jni/java/app/opendocument/core/Circle.java
+++ b/jni/java/app/opendocument/core/Circle.java
@@ -22,6 +22,10 @@ public Measure height() {
     return heightNative(handle());
   }
 
+  public DrawingTransform transform() {
+    return transformNative(handle());
+  }
+
   public GraphicStyle style() {
     return styleNative(handle());
   }
@@ -34,5 +38,7 @@ public GraphicStyle style() {
 
   private native Measure heightNative(long handle);
 
+  private native DrawingTransform transformNative(long handle);
+
   private native GraphicStyle styleNative(long handle);
 }
diff --git a/jni/java/app/opendocument/core/CustomShape.java b/jni/java/app/opendocument/core/CustomShape.java
index de48d666e..babac4713 100644
--- a/jni/java/app/opendocument/core/CustomShape.java
+++ b/jni/java/app/opendocument/core/CustomShape.java
@@ -22,6 +22,10 @@ public Measure height() {
     return heightNative(handle());
   }
 
+  public DrawingTransform transform() {
+    return transformNative(handle());
+  }
+
   public GraphicStyle style() {
     return styleNative(handle());
   }
@@ -34,5 +38,7 @@ public GraphicStyle style() {
 
   private native Measure heightNative(long handle);
 
+  private native DrawingTransform transformNative(long handle);
+
   private native GraphicStyle styleNative(long handle);
 }
diff --git a/jni/java/app/opendocument/core/DrawingTransform.java b/jni/java/app/opendocument/core/DrawingTransform.java
new file mode 100644
index 000000000..4ea09d7f0
--- /dev/null
+++ b/jni/java/app/opendocument/core/DrawingTransform.java
@@ -0,0 +1,43 @@
+package app.opendocument.core;
+
+import java.util.Objects;
+
+/** The affine transform a drawing shape carries. Mirrors {@code odr::DrawingTransform}. */
+public final class DrawingTransform {
+  public final double a;
+  public final double b;
+  public final double c;
+  public final double d;
+  public final Measure e;
+  public final Measure f;
+
+  public DrawingTransform(double a, double b, double c, double d, Measure e, Measure f) {
+    this.a = a;
+    this.b = b;
+    this.c = c;
+    this.d = d;
+    this.e = Objects.requireNonNull(e);
+    this.f = Objects.requireNonNull(f);
+  }
+
+  @Override
+  public boolean equals(Object other) {
+    return other instanceof DrawingTransform transform
+        && a == transform.a
+        && b == transform.b
+        && c == transform.c
+        && d == transform.d
+        && e.equals(transform.e)
+        && f.equals(transform.f);
+  }
+
+  @Override
+  public int hashCode() {
+    return Objects.hash(a, b, c, d, e, f);
+  }
+
+  @Override
+  public String toString() {
+    return "matrix(" + a + " " + b + " " + c + " " + d + " " + e + " " + f + ")";
+  }
+}
diff --git a/jni/java/app/opendocument/core/Frame.java b/jni/java/app/opendocument/core/Frame.java
index d7153f1fb..dabcaefac 100644
--- a/jni/java/app/opendocument/core/Frame.java
+++ b/jni/java/app/opendocument/core/Frame.java
@@ -30,6 +30,10 @@ public Integer zIndex() {
     return zIndexNative(handle());
   }
 
+  public DrawingTransform transform() {
+    return transformNative(handle());
+  }
+
   public GraphicStyle style() {
     return styleNative(handle());
   }
@@ -46,5 +50,7 @@ public GraphicStyle style() {
 
   private native Integer zIndexNative(long handle);
 
+  private native DrawingTransform transformNative(long handle);
+
   private native GraphicStyle styleNative(long handle);
 }
diff --git a/jni/java/app/opendocument/core/Line.java b/jni/java/app/opendocument/core/Line.java
index 113653563..ff20ab3c8 100644
--- a/jni/java/app/opendocument/core/Line.java
+++ b/jni/java/app/opendocument/core/Line.java
@@ -22,6 +22,10 @@ public Measure y2() {
     return y2Native(handle());
   }
 
+  public DrawingTransform transform() {
+    return transformNative(handle());
+  }
+
   public GraphicStyle style() {
     return styleNative(handle());
   }
@@ -34,5 +38,7 @@ public GraphicStyle style() {
 
   private native Measure y2Native(long handle);
 
+  private native DrawingTransform transformNative(long handle);
+
   private native GraphicStyle styleNative(long handle);
 }
diff --git a/jni/java/app/opendocument/core/Rect.java b/jni/java/app/opendocument/core/Rect.java
index ae3b41238..71dd4aa11 100644
--- a/jni/java/app/opendocument/core/Rect.java
+++ b/jni/java/app/opendocument/core/Rect.java
@@ -22,6 +22,10 @@ public Measure height() {
     return heightNative(handle());
   }
 
+  public DrawingTransform transform() {
+    return transformNative(handle());
+  }
+
   public GraphicStyle style() {
     return styleNative(handle());
   }
@@ -34,5 +38,7 @@ public GraphicStyle style() {
 
   private native Measure heightNative(long handle);
 
+  private native DrawingTransform transformNative(long handle);
+
   private native GraphicStyle styleNative(long handle);
 }
diff --git a/jni/src/jni_convert.hpp b/jni/src/jni_convert.hpp
index 91af3f0f0..7c4435b44 100644
--- a/jni/src/jni_convert.hpp
+++ b/jni/src/jni_convert.hpp
@@ -1,5 +1,6 @@
 #pragma once
 
+#include <odr/document_element.hpp>
 #include <odr/file.hpp>
 #include <odr/html.hpp>
 #include <odr/style.hpp>
@@ -34,6 +35,9 @@ jobject make_table_column_style(JNIEnv *env,
 jobject make_table_row_style(JNIEnv *env, const odr::TableRowStyle &style);
 jobject make_table_cell_style(JNIEnv *env, const odr::TableCellStyle &style);
 jobject make_graphic_style(JNIEnv *env, const odr::GraphicStyle &style);
+jobject
+make_drawing_transform(JNIEnv *env,
+                       const std::optional<odr::DrawingTransform> &transform);
 jobject make_page_layout(JNIEnv *env, const odr::PageLayout &layout);
 jobject make_table_dimensions(JNIEnv *env,
                               const odr::TableDimensions &dimensions);
diff --git a/jni/src/jni_document.cpp b/jni/src/jni_document.cpp
index 47533f536..ae2e5f975 100644
--- a/jni/src/jni_document.cpp
+++ b/jni/src/jni_document.cpp
@@ -830,6 +830,15 @@ Java_app_opendocument_core_Frame_zIndexNative(JNIEnv *env, jobject,
   });
 }
 
+extern "C" JNIEXPORT jobject JNICALL
+Java_app_opendocument_core_Frame_transformNative(JNIEnv *env, jobject,
+                                                 jlong handle) {
+  return guarded(env, [&] {
+    return odr_jni::make_drawing_transform(
+        env, element(handle).as_frame().transform());
+  });
+}
+
 extern "C" JNIEXPORT jobject JNICALL
 Java_app_opendocument_core_Frame_styleNative(JNIEnv *env, jobject,
                                              jlong handle) {
@@ -870,6 +879,15 @@ Java_app_opendocument_core_Rect_heightNative(JNIEnv *env, jobject,
   });
 }
 
+extern "C" JNIEXPORT jobject JNICALL
+Java_app_opendocument_core_Rect_transformNative(JNIEnv *env, jobject,
+                                                jlong handle) {
+  return guarded(env, [&] {
+    return odr_jni::make_drawing_transform(
+        env, element(handle).as_rect().transform());
+  });
+}
+
 extern "C" JNIEXPORT jobject JNICALL
 Java_app_opendocument_core_Rect_styleNative(JNIEnv *env, jobject,
                                             jlong handle) {
@@ -908,6 +926,15 @@ Java_app_opendocument_core_Line_y2Native(JNIEnv *env, jobject, jlong handle) {
   });
 }
 
+extern "C" JNIEXPORT jobject JNICALL
+Java_app_opendocument_core_Line_transformNative(JNIEnv *env, jobject,
+                                                jlong handle) {
+  return guarded(env, [&] {
+    return odr_jni::make_drawing_transform(
+        env, element(handle).as_line().transform());
+  });
+}
+
 extern "C" JNIEXPORT jobject JNICALL
 Java_app_opendocument_core_Line_styleNative(JNIEnv *env, jobject,
                                             jlong handle) {
@@ -948,6 +975,15 @@ Java_app_opendocument_core_Circle_heightNative(JNIEnv *env, jobject,
   });
 }
 
+extern "C" JNIEXPORT jobject JNICALL
+Java_app_opendocument_core_Circle_transformNative(JNIEnv *env, jobject,
+                                                  jlong handle) {
+  return guarded(env, [&] {
+    return odr_jni::make_drawing_transform(
+        env, element(handle).as_circle().transform());
+  });
+}
+
 extern "C" JNIEXPORT jobject JNICALL
 Java_app_opendocument_core_Circle_styleNative(JNIEnv *env, jobject,
                                               jlong handle) {
@@ -993,6 +1029,15 @@ Java_app_opendocument_core_CustomShape_heightNative(JNIEnv *env, jobject,
   });
 }
 
+extern "C" JNIEXPORT jobject JNICALL
+Java_app_opendocument_core_CustomShape_transformNative(JNIEnv *env, jobject,
+                                                       jlong handle) {
+  return guarded(env, [&] {
+    return odr_jni::make_drawing_transform(
+        env, element(handle).as_custom_shape().transform());
+  });
+}
+
 extern "C" JNIEXPORT jobject JNICALL
 Java_app_opendocument_core_CustomShape_styleNative(JNIEnv *env, jobject,
                                                    jlong handle) {
diff --git a/jni/src/jni_style.cpp b/jni/src/jni_style.cpp
index 2bc76103b..1d3d1c10a 100644
--- a/jni/src/jni_style.cpp
+++ b/jni/src/jni_style.cpp
@@ -160,6 +160,20 @@ jobject make_measure(JNIEnv *env, const std::optional<odr::Measure> &value) {
   return value.has_value() ? make_measure(env, *value) : nullptr;
 }
 
+jobject
+make_drawing_transform(JNIEnv *env,
+                       const std::optional<odr::DrawingTransform> &transform) {
+  if (!transform.has_value()) {
+    return nullptr;
+  }
+  return new_object(env, "app/opendocument/core/DrawingTransform",
+                    "(DDDDLapp/opendocument/core/Measure;"
+                    "Lapp/opendocument/core/Measure;)V",
+                    transform->a, transform->b, transform->c, transform->d,
+                    make_measure(env, transform->e),
+                    make_measure(env, transform->f));
+}
+
 jobject make_color(JNIEnv *env, const std::optional<odr::Color> &value) {
   if (!value.has_value()) {
     return nullptr;
diff --git a/python/src/bind_document.cpp b/python/src/bind_document.cpp
index 456c19f60..aad0a3072 100644
--- a/python/src/bind_document.cpp
+++ b/python/src/bind_document.cpp
@@ -277,6 +277,15 @@ void odr_python::bind_document(py::module_ &m) {
       .def("value_type", &odr::TableCell::value_type)
       .def("style", &odr::TableCell::style);
 
+  py::class_<odr::DrawingTransform>(m, "DrawingTransform")
+      .def(py::init<>())
+      .def_readwrite("a", &odr::DrawingTransform::a)
+      .def_readwrite("b", &odr::DrawingTransform::b)
+      .def_readwrite("c", &odr::DrawingTransform::c)
+      .def_readwrite("d", &odr::DrawingTransform::d)
+      .def_readwrite("e", &odr::DrawingTransform::e)
+      .def_readwrite("f", &odr::DrawingTransform::f);
+
   bind_element<odr::Frame>(m, "Frame")
       .def("anchor_type", &odr::Frame::anchor_type)
       .def("x", &odr::Frame::x)
@@ -284,6 +293,7 @@ void odr_python::bind_document(py::module_ &m) {
       .def("width", &odr::Frame::width)
       .def("height", &odr::Frame::height)
       .def("z_index", &odr::Frame::z_index)
+      .def("transform", &odr::Frame::transform)
       .def("style", &odr::Frame::style);
 
   bind_element<odr::Rect>(m, "Rect")
@@ -291,6 +301,7 @@ void odr_python::bind_document(py::module_ &m) {
       .def("y", &odr::Rect::y)
       .def("width", &odr::Rect::width)
       .def("height", &odr::Rect::height)
+      .def("transform", &odr::Rect::transform)
       .def("style", &odr::Rect::style);
 
   bind_element<odr::Line>(m, "Line")
@@ -298,6 +309,7 @@ void odr_python::bind_document(py::module_ &m) {
       .def("y1", &odr::Line::y1)
       .def("x2", &odr::Line::x2)
       .def("y2", &odr::Line::y2)
+      .def("transform", &odr::Line::transform)
       .def("style", &odr::Line::style);
 
   bind_element<odr::Circle>(m, "Circle")
@@ -305,6 +317,7 @@ void odr_python::bind_document(py::module_ &m) {
       .def("y", &odr::Circle::y)
       .def("width", &odr::Circle::width)
       .def("height", &odr::Circle::height)
+      .def("transform", &odr::Circle::transform)
       .def("style", &odr::Circle::style);
 
   bind_element<odr::CustomShape>(m, "CustomShape")
@@ -312,6 +325,7 @@ void odr_python::bind_document(py::module_ &m) {
       .def("y", &odr::CustomShape::y)
       .def("width", &odr::CustomShape::width)
       .def("height", &odr::CustomShape::height)
+      .def("transform", &odr::CustomShape::transform)
       .def("style", &odr::CustomShape::style);
 
   bind_element<odr::Image>(m, "Image")
diff --git a/src/odr/document_element.cpp b/src/odr/document_element.cpp
index d9c03e9eb..853c84da2 100644
--- a/src/odr/document_element.cpp
+++ b/src/odr/document_element.cpp
@@ -577,6 +577,11 @@ std::optional<std::int32_t> Frame::z_index() const {
                    : std::optional<std::int32_t>();
 }
 
+std::optional<DrawingTransform> Frame::transform() const {
+  return exists_() ? m_adapter2->frame_transform(m_identifier)
+                   : std::optional<DrawingTransform>();
+}
+
 GraphicStyle Frame::style() const {
   return exists_() ? m_adapter2->frame_style(m_identifier) : GraphicStyle();
 }
@@ -597,6 +602,11 @@ Measure Rect::height() const {
   return exists_() ? m_adapter2->rect_height(m_identifier) : Measure(0, {});
 }
 
+std::optional<DrawingTransform> Rect::transform() const {
+  return exists_() ? m_adapter2->rect_transform(m_identifier)
+                   : std::optional<DrawingTransform>();
+}
+
 GraphicStyle Rect::style() const {
   return exists_() ? m_adapter2->rect_style(m_identifier) : GraphicStyle();
 }
@@ -617,6 +627,11 @@ Measure Line::y2() const {
   return exists_() ? m_adapter2->line_y2(m_identifier) : Measure(0, {});
 }
 
+std::optional<DrawingTransform> Line::transform() const {
+  return exists_() ? m_adapter2->line_transform(m_identifier)
+                   : std::optional<DrawingTransform>();
+}
+
 GraphicStyle Line::style() const {
   return exists_() ? m_adapter2->line_style(m_identifier) : GraphicStyle();
 }
@@ -637,6 +652,11 @@ Measure Circle::height() const {
   return exists_() ? m_adapter2->circle_height(m_identifier) : Measure(0, {});
 }
 
+std::optional<DrawingTransform> Circle::transform() const {
+  return exists_() ? m_adapter2->circle_transform(m_identifier)
+                   : std::optional<DrawingTransform>();
+}
+
 GraphicStyle Circle::style() const {
   return exists_() ? m_adapter2->circle_style(m_identifier) : GraphicStyle();
 }
@@ -661,6 +681,11 @@ Measure CustomShape::height() const {
                    : Measure(0, {});
 }
 
+std::optional<DrawingTransform> CustomShape::transform() const {
+  return exists_() ? m_adapter2->custom_shape_transform(m_identifier)
+                   : std::optional<DrawingTransform>();
+}
+
 GraphicStyle CustomShape::style() const {
   return exists_() ? m_adapter2->custom_shape_style(m_identifier)
                    : GraphicStyle();
diff --git a/src/odr/document_element.hpp b/src/odr/document_element.hpp
index 5a38d684b..334e5964f 100644
--- a/src/odr/document_element.hpp
+++ b/src/odr/document_element.hpp
@@ -482,6 +482,20 @@ class TableCell final
   [[nodiscard]] TableCellStyle style() const;
 };
 
+/// @brief Represents the affine transform a drawing shape carries.
+///
+/// `(x, y)` maps to `(a*x + c*y + e, b*x + d*y + f)`, the lettering of
+/// `matrix(a b c d e f)`. `e` and `f` are lengths in the unit the document
+/// wrote, and unitless only where they are zero.
+struct DrawingTransform final {
+  double a{1};
+  double b{0};
+  double c{0};
+  double d{1};
+  Measure e{0, DynamicUnit()};
+  Measure f{0, DynamicUnit()};
+};
+
 /// @brief Represents a frame element in a document.
 class Frame final : public ElementBase<internal::abstract::FrameAdapter> {
 public:
@@ -493,6 +507,7 @@ class Frame final : public ElementBase<internal::abstract::FrameAdapter> {
   [[nodiscard]] std::optional<Measure> width() const;
   [[nodiscard]] std::optional<Measure> height() const;
   [[nodiscard]] std::optional<std::int32_t> z_index() const;
+  [[nodiscard]] std::optional<DrawingTransform> transform() const;
 
   [[nodiscard]] GraphicStyle style() const;
 };
@@ -506,6 +521,7 @@ class Rect final : public ElementBase<internal::abstract::RectAdapter> {
   [[nodiscard]] Measure y() const;
   [[nodiscard]] Measure width() const;
   [[nodiscard]] Measure height() const;
+  [[nodiscard]] std::optional<DrawingTransform> transform() const;
 
   [[nodiscard]] GraphicStyle style() const;
 };
@@ -519,6 +535,7 @@ class Line final : public ElementBase<internal::abstract::LineAdapter> {
   [[nodiscard]] Measure y1() const;
   [[nodiscard]] Measure x2() const;
   [[nodiscard]] Measure y2() const;
+  [[nodiscard]] std::optional<DrawingTransform> transform() const;
 
   [[nodiscard]] GraphicStyle style() const;
 };
@@ -532,6 +549,7 @@ class Circle final : public ElementBase<internal::abstract::CircleAdapter> {
   [[nodiscard]] Measure y() const;
   [[nodiscard]] Measure width() const;
   [[nodiscard]] Measure height() const;
+  [[nodiscard]] std::optional<DrawingTransform> transform() const;
 
   [[nodiscard]] GraphicStyle style() const;
 };
@@ -546,6 +564,7 @@ class CustomShape final
   [[nodiscard]] std::optional<Measure> y() const;
   [[nodiscard]] Measure width() const;
   [[nodiscard]] Measure height() const;
+  [[nodiscard]] std::optional<DrawingTransform> transform() const;
 
   [[nodiscard]] GraphicStyle style() const;
 };
diff --git a/src/odr/internal/abstract/document.hpp b/src/odr/internal/abstract/document.hpp
index a24139762..130f3a13f 100644
--- a/src/odr/internal/abstract/document.hpp
+++ b/src/odr/internal/abstract/document.hpp
@@ -28,6 +28,7 @@ struct TableCellStyle;
 struct TextStyle;
 struct ParagraphStyle;
 struct GraphicStyle;
+struct DrawingTransform;
 } // namespace odr
 
 namespace odr::internal::abstract {
@@ -442,6 +443,8 @@ class FrameAdapter {
   frame_height(ElementIdentifier element_id) const = 0;
   [[nodiscard]] virtual std::optional<std::int32_t>
   frame_z_index(ElementIdentifier element_id) const = 0;
+  [[nodiscard]] virtual std::optional<DrawingTransform>
+  frame_transform(ElementIdentifier element_id) const = 0;
 
   [[nodiscard]] virtual GraphicStyle
   frame_style(ElementIdentifier element_id) const = 0;
@@ -457,6 +460,8 @@ class RectAdapter {
   rect_width(ElementIdentifier element_id) const = 0;
   [[nodiscard]] virtual Measure
   rect_height(ElementIdentifier element_id) const = 0;
+  [[nodiscard]] virtual std::optional<DrawingTransform>
+  rect_transform(ElementIdentifier element_id) const = 0;
 
   [[nodiscard]] virtual GraphicStyle
   rect_style(ElementIdentifier element_id) const = 0;
@@ -470,6 +475,8 @@ class LineAdapter {
   [[nodiscard]] virtual Measure line_y1(ElementIdentifier element_id) const = 0;
   [[nodiscard]] virtual Measure line_x2(ElementIdentifier element_id) const = 0;
   [[nodiscard]] virtual Measure line_y2(ElementIdentifier element_id) const = 0;
+  [[nodiscard]] virtual std::optional<DrawingTransform>
+  line_transform(ElementIdentifier element_id) const = 0;
 
   [[nodiscard]] virtual GraphicStyle
   line_style(ElementIdentifier element_id) const = 0;
@@ -487,6 +494,8 @@ class CircleAdapter {
   circle_width(ElementIdentifier element_id) const = 0;
   [[nodiscard]] virtual Measure
   circle_height(ElementIdentifier element_id) const = 0;
+  [[nodiscard]] virtual std::optional<DrawingTransform>
+  circle_transform(ElementIdentifier element_id) const = 0;
 
   [[nodiscard]] virtual GraphicStyle
   circle_style(ElementIdentifier element_id) const = 0;
@@ -504,6 +513,8 @@ class CustomShapeAdapter {
   custom_shape_width(ElementIdentifier element_id) const = 0;
   [[nodiscard]] virtual Measure
   custom_shape_height(ElementIdentifier element_id) const = 0;
+  [[nodiscard]] virtual std::optional<DrawingTransform>
+  custom_shape_transform(ElementIdentifier element_id) const = 0;
 
   [[nodiscard]] virtual GraphicStyle
   custom_shape_style(ElementIdentifier element_id) const = 0;
diff --git a/src/odr/internal/html/document_element.cpp b/src/odr/internal/html/document_element.cpp
index bb2ece79f..e5e8b2b5e 100644
--- a/src/odr/internal/html/document_element.cpp
+++ b/src/odr/internal/html/document_element.cpp
@@ -622,7 +622,8 @@ void html::translate_line(const Element &element, const WritingState &state) {
                      {"version", "1.1"},
                      {"overflow", "visible"}})
                  .set_style("z-index:-1;position:absolute;top:0;left:0;" +
-                            translate_drawing_style(style)));
+                            translate_drawing_style(style) +
+                            translate_drawing_transform(line.transform())));
 
   state.out().write_element_begin(
       "line",
diff --git a/src/odr/internal/html/document_style.cpp b/src/odr/internal/html/document_style.cpp
index 3da69f987..1eb761477 100644
--- a/src/odr/internal/html/document_style.cpp
+++ b/src/odr/internal/html/document_style.cpp
@@ -4,6 +4,7 @@
 #include <odr/style.hpp>
 
 #include <odr/internal/html/common.hpp>
+#include <odr/internal/util/number_util.hpp>
 #include <odr/internal/xml/xml_util.hpp>
 
 namespace odr::internal {
@@ -416,6 +417,45 @@ std::string html::translate_drawing_style(const GraphicStyle &graphic_style) {
   return result;
 }
 
+std::string html::translate_drawing_transform(
+    const std::optional<DrawingTransform> &transform) {
+  if (!transform.has_value()) {
+    return "";
+  }
+
+  const auto number = [](const double value) {
+    return util::number::to_string_significant(value, 7);
+  };
+
+  // Css applies the list right to left, so the linear part goes last.
+  std::string result;
+  if (transform->e.magnitude() != 0 || transform->f.magnitude() != 0) {
+    result.append("translate(")
+        .append(transform->e.to_string())
+        .append(",")
+        .append(transform->f.to_string())
+        .append(")");
+  }
+  if (transform->a != 1 || transform->b != 0 || transform->c != 0 ||
+      transform->d != 1) {
+    result.append(result.empty() ? "" : " ")
+        .append("matrix(")
+        .append(number(transform->a))
+        .append(",")
+        .append(number(transform->b))
+        .append(",")
+        .append(number(transform->c))
+        .append(",")
+        .append(number(transform->d))
+        .append(",0,0)");
+  }
+  if (result.empty()) {
+    return "";
+  }
+  // Css would otherwise turn the box about its centre.
+  return "transform:" + result + ";transform-origin:0 0;";
+}
+
 std::string html::translate_frame_properties(const Frame &frame) {
   const GraphicStyle style = frame.style();
 
@@ -510,6 +550,7 @@ std::string html::translate_frame_properties(const Frame &frame) {
       z_index.has_value()) {
     result += "z-index:" + std::to_string(*z_index) + ";";
   }
+  result += translate_drawing_transform(frame.transform());
   return result;
 }
 
@@ -520,6 +561,7 @@ std::string html::translate_rect_properties(const Rect &rect) {
   result += "top:" + rect.y().to_string() + ";";
   result += "width:" + rect.width().to_string() + ";";
   result += "height:" + rect.height().to_string() + ";";
+  result += translate_drawing_transform(rect.transform());
   return result;
 }
 
@@ -530,6 +572,7 @@ std::string html::translate_circle_properties(const Circle &circle) {
   result += "top:" + circle.y().to_string() + ";";
   result += "width:" + circle.width().to_string() + ";";
   result += "height:" + circle.height().to_string() + ";";
+  result += translate_drawing_transform(circle.transform());
   return result;
 }
 
@@ -549,6 +592,7 @@ html::translate_custom_shape_properties(const CustomShape &custom_shape) {
   }
   result += "width:" + custom_shape.width().to_string() + ";";
   result += "height:" + custom_shape.height().to_string() + ";";
+  result += translate_drawing_transform(custom_shape.transform());
   return result;
 }
 
diff --git a/src/odr/internal/html/document_style.hpp b/src/odr/internal/html/document_style.hpp
index e2a0245bd..433dd9a1b 100644
--- a/src/odr/internal/html/document_style.hpp
+++ b/src/odr/internal/html/document_style.hpp
@@ -1,5 +1,6 @@
 #pragma once
 
+#include <optional>
 #include <string>
 
 namespace odr {
@@ -22,6 +23,7 @@ struct TableColumnStyle;
 struct TableRowStyle;
 struct TableCellStyle;
 struct GraphicStyle;
+struct DrawingTransform;
 struct PageLayout;
 } // namespace odr
 
@@ -47,6 +49,9 @@ translate_table_column_style(const TableColumnStyle &table_column_style);
 std::string translate_table_row_style(const TableRowStyle &table_row_style);
 std::string translate_table_cell_style(const TableCellStyle &table_cell_style);
 std::string translate_drawing_style(const GraphicStyle &graphic_style);
+/// Empty for a transform that moves nothing.
+std::string
+translate_drawing_transform(const std::optional<DrawingTransform> &transform);
 
 std::string translate_frame_properties(const Frame &frame);
 std::string translate_rect_properties(const Rect &rect);
diff --git a/src/odr/internal/iwork/iwork_document.cpp b/src/odr/internal/iwork/iwork_document.cpp
index 404c3a885..245ab3055 100644
--- a/src/odr/internal/iwork/iwork_document.cpp
+++ b/src/odr/internal/iwork/iwork_document.cpp
@@ -365,6 +365,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return std::nullopt;
   }
+  [[nodiscard]] std::optional<DrawingTransform> frame_transform(
+      [[maybe_unused]] const ElementIdentifier element_id) const override {
+    return std::nullopt;
+  }
   [[nodiscard]] GraphicStyle frame_style(
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return {};
diff --git a/src/odr/internal/odf/PLAN.md b/src/odr/internal/odf/PLAN.md
index d5948cc18..553669ddc 100644
--- a/src/odr/internal/odf/PLAN.md
+++ b/src/odr/internal/odf/PLAN.md
@@ -94,12 +94,19 @@ leaves behind.
 
 Each stage is one pull request, stacked on the one before.
 
-### 1 — `draw:transform`
+### 1 — `draw:transform` — landed
 
 `DrawingTransform` in the public header; `transform()` on `Frame`, `Rect`,
-`Line`, `Circle` and `CustomShape`; the odf adapter reads and composes the
+`Line`, `Circle` and `CustomShape`; `odf_geometry.cpp` reads and composes the
 attribute; the renderer writes `transform` + `transform-origin:0 0`.
-Visible on 4 files. Closes the `transform` box in `README.md`.
+
+Two things the spec text does not settle, both fixed against libreoffice's own
+svg export of `style-drawing-1.odp`: the list applies to the shape **left to
+right**, so a `translate` after a `rotate` is not itself rotated, and `rotate`
+is **counter-clockwise** for a positive angle — libreoffice writes svg's
+`rotate(-19.4°)` for the file's `rotate (0.34 rad)`. Composing both readings
+and comparing against the bounding box libreoffice reports (`x=23084`, exact)
+is what decided it.
 
 ### 2 — the missing shape elements
 
diff --git a/src/odr/internal/odf/README.md b/src/odr/internal/odf/README.md
index b46f54fed..c3fadd692 100644
--- a/src/odr/internal/odf/README.md
+++ b/src/odr/internal/odf/README.md
@@ -66,7 +66,8 @@ Roughly ordered by importance.
   - [x] custom shapes (bounding box, fill/stroke) #159
     - [ ] enhanced geometry / shape path rendering
   - [x] graphic style: stroke width/color, fill color, vertical align, text wrap
-  - [ ] transform (e.g. flip, rotate)
+  - [x] transform (`draw:transform`, its operation list composed to one matrix)
+  - [ ] mirror (`style:mirror`, `draw:mirror-horizontal` / `-vertical`)
 - [x] page layout (size, orientation, margins)
 - [ ] annotations (`office:annotation`)
 
diff --git a/src/odr/internal/odf/odf_document.cpp b/src/odr/internal/odf/odf_document.cpp
index 3f5d32814..2c987fa44 100644
--- a/src/odr/internal/odf/odf_document.cpp
+++ b/src/odr/internal/odf/odf_document.cpp
@@ -9,6 +9,7 @@
 #include <odr/internal/common/table_cursor.hpp>
 #include <odr/internal/crypto/crypto_util.hpp>
 #include <odr/internal/odf/odf_element_registry.hpp>
+#include <odr/internal/odf/odf_geometry.hpp>
 #include <odr/internal/odf/odf_list.hpp>
 #include <odr/internal/odf/odf_parser.hpp>
 #include <odr/internal/odf/odf_table.hpp>
@@ -838,6 +839,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
     }
     return static_cast<std::int32_t>(attribute.as_int());
   }
+  [[nodiscard]] std::optional<DrawingTransform>
+  frame_transform(const ElementIdentifier element_id) const override {
+    return read_transform(get_node(element_id));
+  }
   [[nodiscard]] GraphicStyle
   frame_style(const ElementIdentifier element_id) const override {
     return get_intermediate_style(element_id).graphic_style;
@@ -859,6 +864,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
   rect_height(const ElementIdentifier element_id) const override {
     return read_measure_or_zero(get_node(element_id).attribute("svg:height"));
   }
+  [[nodiscard]] std::optional<DrawingTransform>
+  rect_transform(const ElementIdentifier element_id) const override {
+    return read_transform(get_node(element_id));
+  }
   [[nodiscard]] GraphicStyle
   rect_style(const ElementIdentifier element_id) const override {
     return get_intermediate_style(element_id).graphic_style;
@@ -880,6 +889,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
   line_y2(const ElementIdentifier element_id) const override {
     return read_measure_or_zero(get_node(element_id).attribute("svg:y2"));
   }
+  [[nodiscard]] std::optional<DrawingTransform>
+  line_transform(const ElementIdentifier element_id) const override {
+    return read_transform(get_node(element_id));
+  }
   [[nodiscard]] GraphicStyle
   line_style(const ElementIdentifier element_id) const override {
     return get_intermediate_style(element_id).graphic_style;
@@ -901,6 +914,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
   circle_height(const ElementIdentifier element_id) const override {
     return read_measure_or_zero(get_node(element_id).attribute("svg:height"));
   }
+  [[nodiscard]] std::optional<DrawingTransform>
+  circle_transform(const ElementIdentifier element_id) const override {
+    return read_transform(get_node(element_id));
+  }
   [[nodiscard]] GraphicStyle
   circle_style(const ElementIdentifier element_id) const override {
     return get_intermediate_style(element_id).graphic_style;
@@ -922,6 +939,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
   custom_shape_height(const ElementIdentifier element_id) const override {
     return read_measure_or_zero(get_node(element_id).attribute("svg:height"));
   }
+  [[nodiscard]] std::optional<DrawingTransform>
+  custom_shape_transform(const ElementIdentifier element_id) const override {
+    return read_transform(get_node(element_id));
+  }
   [[nodiscard]] GraphicStyle
   custom_shape_style(const ElementIdentifier element_id) const override {
     return get_intermediate_style(element_id).graphic_style;
diff --git a/src/odr/internal/odf/odf_geometry.cpp b/src/odr/internal/odf/odf_geometry.cpp
new file mode 100644
index 000000000..f961da6a6
--- /dev/null
+++ b/src/odr/internal/odf/odf_geometry.cpp
@@ -0,0 +1,262 @@
+#include <odr/internal/odf/odf_geometry.hpp>
+
+#include <odr/document_element.hpp>
+
+#include <odr/internal/util/math_util.hpp>
+
+#include <cmath>
+#include <cstddef>
+#include <cstdlib>
+#include <string>
+
+namespace odr::internal::odf {
+
+namespace {
+
+/// Zero for a unit that is not an absolute length.
+double centimetres_per(const std::string_view unit) {
+  if (unit == "cm") {
+    return 1.0;
+  }
+  if (unit == "mm") {
+    return 0.1;
+  }
+  if (unit == "in") {
+    return 2.54;
+  }
+  if (unit == "pt") {
+    return 2.54 / 72.0;
+  }
+  if (unit == "pc") {
+    return 2.54 / 6.0;
+  }
+  if (unit == "px") {
+    return 2.54 / 96.0;
+  }
+  return 0.0;
+}
+
+/// Composes the operation list, holding the translation in centimetres. The
+/// remaining input bounds every read, so nothing here depends on a terminator.
+class TransformParser {
+public:
+  explicit TransformParser(const std::string_view value) : m_rest{value} {}
+
+  [[nodiscard]] std::optional<DrawingTransform> parse() {
+    while (true) {
+      skip_separators();
+      if (m_rest.empty()) {
+        break;
+      }
+      if (!parse_operation()) {
+        return {};
+      }
+    }
+
+    const double scale = m_unit.empty() ? 1.0 : centimetres_per(m_unit);
+    const DynamicUnit unit{m_unit};
+    return DrawingTransform{
+        .a = m_transform.a,
+        .b = m_transform.b,
+        .c = m_transform.c,
+        .d = m_transform.d,
+        .e = Measure(m_transform.e / scale, unit),
+        .f = Measure(m_transform.f / scale, unit),
+    };
+  }
+
+private:
+  static bool is_separator(const char c) {
+    return c == ' ' || c == '\t' || c == '\r' || c == '\n' || c == ',';
+  }
+  static bool is_letter(const char c) {
+    return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');
+  }
+  /// A superset of what a number is made of, to bound the run `std::strtod`
+  /// then reads properly.
+  static bool is_number_char(const char c) {
+    return (c >= '0' && c <= '9') || c == '+' || c == '-' || c == '.' ||
+           c == 'e' || c == 'E';
+  }
+
+  std::string_view m_rest;
+
+  util::math::Transform2D m_transform;
+  /// What every length agreed on, or `cm` where they did not; empty until one
+  /// is seen, which keeps a list of pure rotations unitless.
+  std::string m_unit;
+
+  /// The next character, or `\0` where the input ended.
+  [[nodiscard]] char peek() const {
+    return m_rest.empty() ? '\0' : m_rest.front();
+  }
+
+  /// The leading run of characters @p accept admits, left in place.
+  [[nodiscard]] std::string_view peek_while(bool (*accept)(char)) const {
+    std::size_t length = 0;
+    while (length < m_rest.size() && accept(m_rest[length])) {
+      ++length;
+    }
+    return m_rest.substr(0, length);
+  }
+
+  /// The same run, consumed.
+  [[nodiscard]] std::string_view take_while(bool (*accept)(char)) {
+    const std::string_view taken = peek_while(accept);
+    m_rest.remove_prefix(taken.size());
+    return taken;
+  }
+
+  void skip_separators() {
+    while (is_separator(peek())) {
+      m_rest.remove_prefix(1);
+    }
+  }
+
+  [[nodiscard]] std::string_view read_name() { return take_while(is_letter); }
+
+  [[nodiscard]] bool consume(const char c) {
+    skip_separators();
+    if (peek() != c) {
+      return false;
+    }
+    m_rest.remove_prefix(1);
+    return true;
+  }
+
+  /// `std::strtod` wants a terminator, so the run the view bounds is copied
+  /// out rather than read in place: libc++ has no floating-point
+  /// `std::from_chars` until llvm 20, which the ndk, emscripten and xcode 16
+  /// are all short of.
+  [[nodiscard]] std::optional<double> read_number() {
+    skip_separators();
+    const std::string number(peek_while(is_number_char));
+    char *end = nullptr;
+    const double value = std::strtod(number.c_str(), &end);
+    if (end == number.c_str()) {
+      return {};
+    }
+    // `strtod` may stop short of the run, on a trailing `e` say
+    m_rest.remove_prefix(static_cast<std::size_t>(end - number.c_str()));
+    return value;
+  }
+
+  /// Reduced to centimetres.
+  [[nodiscard]] std::optional<double> read_length() {
+    const std::optional<double> value = read_number();
+    if (!value.has_value()) {
+      return {};
+    }
+    const std::string_view unit =
+        take_while([](const char c) { return is_letter(c) || c == '%'; });
+
+    // A zero needs no unit.
+    if (unit.empty()) {
+      return *value == 0.0 ? std::optional<double>(0.0) : std::nullopt;
+    }
+    const double scale = centimetres_per(unit);
+    if (scale == 0.0) {
+      return {};
+    }
+    if (m_unit.empty()) {
+      m_unit = unit;
+    } else if (m_unit != unit) {
+      m_unit = "cm";
+    }
+    return *value * scale;
+  }
+
+  /// The list applies left to right, so a `translate` after a `rotate` is not
+  /// itself rotated.
+  void compose(const util::math::Transform2D &operation) {
+    m_transform = m_transform * operation;
+  }
+
+  [[nodiscard]] bool parse_operation() {
+    const std::string_view name = read_name();
+    if (name.empty() || !consume('(')) {
+      return false;
+    }
+
+    if (name == "matrix") {
+      const std::optional<double> a = read_number();
+      const std::optional<double> b = read_number();
+      const std::optional<double> c = read_number();
+      const std::optional<double> d = read_number();
+      const std::optional<double> e = read_length();
+      const std::optional<double> f = read_length();
+      if (!a || !b || !c || !d || !e || !f) {
+        return false;
+      }
+      compose({*a, *b, *c, *d, *e, *f});
+    } else if (name == "translate") {
+      const std::optional<double> x = read_length();
+      if (!x) {
+        return false;
+      }
+      const std::optional<double> y =
+          peek_argument() ? read_length() : std::optional<double>(0);
+      if (!y) {
+        return false;
+      }
+      compose(util::math::Transform2D::translation(*x, *y));
+    } else if (name == "scale") {
+      const std::optional<double> x = read_number();
+      if (!x) {
+        return false;
+      }
+      const std::optional<double> y = peek_argument() ? read_number() : x;
+      if (!y) {
+        return false;
+      }
+      compose(util::math::Transform2D::scaling(*x, *y));
+    } else if (name == "rotate" || name == "skewX" || name == "skewY") {
+      const std::optional<double> angle = read_number();
+      if (!angle) {
+        return false;
+      }
+      // Radians, counter-clockwise, so the sine changes sign against svg's
+      // `rotate` in the same y-down space; the skews take that handedness. No
+      // corpus file skews measurably.
+      if (name == "rotate") {
+        const double sin = std::sin(*angle);
+        const double cos = std::cos(*angle);
+        compose({cos, -sin, sin, cos, 0, 0});
+      } else if (name == "skewX") {
+        compose({1, 0, -std::tan(*angle), 1, 0, 0});
+      } else {
+        compose({1, -std::tan(*angle), 0, 1, 0, 0});
+      }
+    } else {
+      return false;
+    }
+
+    return consume(')');
+  }
+
+  [[nodiscard]] bool peek_argument() {
+    skip_separators();
+    return peek() != ')' && peek() != '\0';
+  }
+};
+
+} // namespace
+
+} // namespace odr::internal::odf
+
+namespace odr::internal {
+
+std::optional<DrawingTransform> odf::read_transform(const pugi::xml_node node) {
+  const pugi::xml_attribute attribute = node.attribute("draw:transform");
+  if (!attribute) {
+    return {};
+  }
+  return parse_transform(attribute.value());
+}
+
+std::optional<DrawingTransform>
+odf::parse_transform(const std::string_view value) {
+  return odf::TransformParser(value).parse();
+}
+
+} // namespace odr::internal
diff --git a/src/odr/internal/odf/odf_geometry.hpp b/src/odr/internal/odf/odf_geometry.hpp
new file mode 100644
index 000000000..9e98f4d50
--- /dev/null
+++ b/src/odr/internal/odf/odf_geometry.hpp
@@ -0,0 +1,23 @@
+#pragma once
+
+#include <optional>
+#include <string_view>
+
+#include <pugixml.hpp>
+
+namespace odr {
+struct DrawingTransform;
+}
+
+namespace odr::internal::odf {
+
+/// `draw:transform` (19.228) off @p node, its operation list composed into one
+/// transform. Nothing where the attribute is absent or unreadable.
+[[nodiscard]] std::optional<DrawingTransform>
+read_transform(pugi::xml_node node);
+
+/// Angles are radians; the list applies left to right.
+[[nodiscard]] std::optional<DrawingTransform>
+parse_transform(std::string_view value);
+
+} // namespace odr::internal::odf
diff --git a/src/odr/internal/oldms/presentation/ppt_document.cpp b/src/odr/internal/oldms/presentation/ppt_document.cpp
index d6a1a1154..475079959 100644
--- a/src/odr/internal/oldms/presentation/ppt_document.cpp
+++ b/src/odr/internal/oldms/presentation/ppt_document.cpp
@@ -215,6 +215,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
   frame_z_index(const ElementIdentifier /*element_id*/) const override {
     return std::nullopt;
   }
+  [[nodiscard]] std::optional<DrawingTransform>
+  frame_transform(const ElementIdentifier /*element_id*/) const override {
+    return std::nullopt;
+  }
   [[nodiscard]] GraphicStyle
   frame_style(const ElementIdentifier /*element_id*/) const override {
     return {};
diff --git a/src/odr/internal/ooxml/presentation/ooxml_presentation_document.cpp b/src/odr/internal/ooxml/presentation/ooxml_presentation_document.cpp
index 8d28da329..078a21903 100644
--- a/src/odr/internal/ooxml/presentation/ooxml_presentation_document.cpp
+++ b/src/odr/internal/ooxml/presentation/ooxml_presentation_document.cpp
@@ -496,6 +496,11 @@ class ElementAdapter final : public abstract::ElementAdapter,
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return std::nullopt;
   }
+  [[nodiscard]] std::optional<DrawingTransform> frame_transform(
+      [[maybe_unused]] const ElementIdentifier element_id) const override {
+    // TODO the rotation `a:xfrm` carries
+    return std::nullopt;
+  }
   [[nodiscard]] GraphicStyle
   frame_style(const ElementIdentifier element_id) const override {
     const pugi::xml_node node = get_node(element_id);
diff --git a/src/odr/internal/ooxml/spreadsheet/ooxml_spreadsheet_document.cpp b/src/odr/internal/ooxml/spreadsheet/ooxml_spreadsheet_document.cpp
index 58e3e412a..7cc761986 100644
--- a/src/odr/internal/ooxml/spreadsheet/ooxml_spreadsheet_document.cpp
+++ b/src/odr/internal/ooxml/spreadsheet/ooxml_spreadsheet_document.cpp
@@ -393,6 +393,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return std::nullopt;
   }
+  [[nodiscard]] std::optional<DrawingTransform> frame_transform(
+      [[maybe_unused]] const ElementIdentifier element_id) const override {
+    return std::nullopt;
+  }
   [[nodiscard]] GraphicStyle frame_style(
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return {};
diff --git a/src/odr/internal/ooxml/text/ooxml_text_document.cpp b/src/odr/internal/ooxml/text/ooxml_text_document.cpp
index 9095afea9..fc3e6f5df 100644
--- a/src/odr/internal/ooxml/text/ooxml_text_document.cpp
+++ b/src/odr/internal/ooxml/text/ooxml_text_document.cpp
@@ -547,6 +547,10 @@ class ElementAdapter final : public abstract::ElementAdapter,
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return std::nullopt;
   }
+  [[nodiscard]] std::optional<DrawingTransform> frame_transform(
+      [[maybe_unused]] const ElementIdentifier element_id) const override {
+    return std::nullopt;
+  }
   [[nodiscard]] GraphicStyle frame_style(
       [[maybe_unused]] const ElementIdentifier element_id) const override {
     return {};
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 19f618cc8..a451a1b6b 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -74,6 +74,7 @@ add_executable(odr_test
         "src/internal/rtf/rtf_tokenizer_test.cpp"
 
         "src/internal/odf/odf_flat_file_test.cpp"
+        "src/internal/odf/odf_geometry_test.cpp"
         "src/internal/odf/odf_sheet_repeat_test.cpp"
         "src/internal/odf/odf_table_test.cpp"
 
diff --git a/test/data.cmake b/test/data.cmake
index fda352b4e..a437e3f16 100644
--- a/test/data.cmake
+++ b/test/data.cmake
@@ -17,9 +17,9 @@ odr_test_data(
 odr_test_data(
         PATH "reference-output/odr-public"
         URL "https://github.com/opendocument-app/OpenDocument.test.output.git"
-        REVISION "05441f24b4fcc9398b5115718a7d812ab4d63cea")
+        REVISION "b8560b554a01d66f6b41bcd70569578da5ae408b")
 
 odr_test_data(
         PATH "reference-output/odr-private"
         URL "https://github.com/opendocument-app/OpenDocument.test-private.output.git"
-        REVISION "931589fe01472f0f02eae8423c713afa4db90bd8")
+        REVISION "dfb67a4683d60b519602760d3702f3df210ddbb3")
diff --git a/test/src/internal/html/document_style_test.cpp b/test/src/internal/html/document_style_test.cpp
index eaf1aedb7..85349e261 100644
--- a/test/src/internal/html/document_style_test.cpp
+++ b/test/src/internal/html/document_style_test.cpp
@@ -1,3 +1,4 @@
+#include <odr/document_element.hpp>
 #include <odr/quantity.hpp>
 #include <odr/style.hpp>
 
@@ -5,6 +6,8 @@
 
 #include <gtest/gtest.h>
 
+#include <optional>
+
 using namespace odr;
 namespace ihtml = odr::internal::html;
 
@@ -17,6 +20,26 @@ PageLayout a4_page_layout() {
   return page_layout;
 }
 
+DrawingTransform identity() {
+  return DrawingTransform{.a = 1,
+                          .b = 0,
+                          .c = 0,
+                          .d = 1,
+                          .e = Measure(0, DynamicUnit()),
+                          .f = Measure(0, DynamicUnit())};
+}
+
+/// A quarter turn counter-clockwise, the shape of every rotation the corpus
+/// carries.
+DrawingTransform quarter_turn() {
+  DrawingTransform transform = identity();
+  transform.a = 0;
+  transform.b = 1;
+  transform.c = -1;
+  transform.d = 0;
+  return transform;
+}
+
 } // namespace
 
 TEST(html_document_style, outer_page_style_fixes_both_dimensions) {
@@ -70,3 +93,35 @@ TEST(html_document_style, block_font_style_leaves_what_paints_to_the_run) {
 TEST(html_document_style, block_font_style_of_a_style_naming_no_font) {
   EXPECT_EQ(ihtml::translate_block_font_style(TextStyle()), "");
 }
+
+TEST(html_document_style, drawing_transform_of_nothing_is_nothing) {
+  EXPECT_EQ(ihtml::translate_drawing_transform(std::nullopt), "");
+}
+
+TEST(html_document_style, drawing_transform_of_the_identity_is_nothing) {
+  EXPECT_EQ(ihtml::translate_drawing_transform(identity()), "");
+}
+
+TEST(html_document_style, drawing_transform_of_a_translation_writes_no_matrix) {
+  DrawingTransform transform = identity();
+  transform.e = Measure(1, DynamicUnit("cm"));
+  transform.f = Measure(2, DynamicUnit("cm"));
+  EXPECT_EQ(ihtml::translate_drawing_transform(transform),
+            "transform:translate(1cm,2cm);transform-origin:0 0;");
+}
+
+TEST(html_document_style, drawing_transform_of_a_rotation_writes_no_translate) {
+  EXPECT_EQ(ihtml::translate_drawing_transform(quarter_turn()),
+            "transform:matrix(0,1,-1,0,0,0);transform-origin:0 0;");
+}
+
+TEST(html_document_style, drawing_transform_writes_the_linear_part_last) {
+  // Css applies the list right to left, so the shape turns about its own
+  // origin and is moved after, which is what the composed matrix means.
+  DrawingTransform transform = quarter_turn();
+  transform.e = Measure(1, DynamicUnit("cm"));
+  transform.f = Measure(2, DynamicUnit("cm"));
+  EXPECT_EQ(ihtml::translate_drawing_transform(transform),
+            "transform:translate(1cm,2cm) matrix(0,1,-1,0,0,0);"
+            "transform-origin:0 0;");
+}
diff --git a/test/src/internal/odf/odf_geometry_test.cpp b/test/src/internal/odf/odf_geometry_test.cpp
new file mode 100644
index 000000000..6f54675b0
--- /dev/null
+++ b/test/src/internal/odf/odf_geometry_test.cpp
@@ -0,0 +1,162 @@
+#include <odr/internal/odf/odf_geometry.hpp>
+
+#include <odr/document_element.hpp>
+
+#include <gtest/gtest.h>
+
+#include <cmath>
+#include <string>
+#include <string_view>
+
+using namespace odr;
+using namespace odr::internal::odf;
+
+namespace {
+
+void expect_linear(const DrawingTransform &transform, const double a,
+                   const double b, const double c, const double d) {
+  EXPECT_NEAR(a, transform.a, 1e-9);
+  EXPECT_NEAR(b, transform.b, 1e-9);
+  EXPECT_NEAR(c, transform.c, 1e-9);
+  EXPECT_NEAR(d, transform.d, 1e-9);
+}
+
+} // namespace
+
+TEST(OdfTransform, empty_list_is_the_identity) {
+  const std::optional<DrawingTransform> transform = parse_transform("");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 1, 0, 0, 1);
+  EXPECT_EQ(Measure(0, DynamicUnit()), transform->e);
+  EXPECT_EQ(Measure(0, DynamicUnit()), transform->f);
+}
+
+TEST(OdfTransform, translate_keeps_the_unit_it_was_written_in) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate (23.084cm 2.415cm)");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 1, 0, 0, 1);
+  EXPECT_EQ(Measure(23.084, DynamicUnit("cm")), transform->e);
+  EXPECT_EQ(Measure(2.415, DynamicUnit("cm")), transform->f);
+}
+
+TEST(OdfTransform, translate_defaults_its_second_coordinate_to_zero) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate (4in)");
+  ASSERT_TRUE(transform.has_value());
+  EXPECT_EQ(Measure(4, DynamicUnit("in")), transform->e);
+  EXPECT_EQ(Measure(0, DynamicUnit("in")), transform->f);
+}
+
+TEST(OdfTransform, rotate_is_counter_clockwise_and_in_radians) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("rotate (0.340164671213695)");
+  ASSERT_TRUE(transform.has_value());
+  const double angle = 0.340164671213695;
+  expect_linear(*transform, std::cos(angle), -std::sin(angle), std::sin(angle),
+                std::cos(angle));
+}
+
+TEST(OdfTransform, a_translate_after_a_rotate_is_not_itself_rotated) {
+  const std::optional<DrawingTransform> transform = parse_transform(
+      "rotate (0.340164671213695) translate (23.084cm 2.415cm)");
+  ASSERT_TRUE(transform.has_value());
+  EXPECT_EQ(Measure(23.084, DynamicUnit("cm")), transform->e);
+  EXPECT_EQ(Measure(2.415, DynamicUnit("cm")), transform->f);
+}
+
+TEST(OdfTransform, a_rotate_after_a_translate_turns_the_translation_too) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate (1cm 0cm) rotate (1.5707963267948966)");
+  ASSERT_TRUE(transform.has_value());
+  // A quarter turn counter-clockwise sends (1cm, 0) to (0, -1cm).
+  EXPECT_NEAR(0, transform->e.magnitude(), 1e-9);
+  EXPECT_NEAR(-1, transform->f.magnitude(), 1e-9);
+}
+
+TEST(OdfTransform, matrix_is_taken_as_written) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("matrix (2 0 0 3 1cm 2cm)");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 2, 0, 0, 3);
+  EXPECT_EQ(Measure(1, DynamicUnit("cm")), transform->e);
+  EXPECT_EQ(Measure(2, DynamicUnit("cm")), transform->f);
+}
+
+TEST(OdfTransform, scale_takes_one_factor_for_both_axes) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("scale (2)");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 2, 0, 0, 2);
+}
+
+TEST(OdfTransform, lengths_that_disagree_on_a_unit_reduce_to_centimetres) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate (1in 0cm) translate (1cm 0cm)");
+  ASSERT_TRUE(transform.has_value());
+  EXPECT_EQ(DynamicUnit("cm"), transform->e.unit());
+  EXPECT_NEAR(3.54, transform->e.magnitude(), 1e-9);
+}
+
+TEST(OdfTransform, a_skew_composes_with_the_rest) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("skewX (0.5) translate (1cm 0cm)");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 1, 0, -std::tan(0.5), 1);
+  EXPECT_EQ(Measure(1, DynamicUnit("cm")), transform->e);
+}
+
+TEST(OdfTransform, separators_may_be_commas) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate(1cm,2cm),scale(2,3)");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 2, 0, 0, 3);
+  EXPECT_EQ(Measure(2, DynamicUnit("cm")), transform->e);
+  EXPECT_EQ(Measure(6, DynamicUnit("cm")), transform->f);
+}
+
+TEST(OdfTransform, an_unreadable_list_is_dropped_whole) {
+  EXPECT_FALSE(parse_transform("rotate").has_value());
+  EXPECT_FALSE(parse_transform("rotate (").has_value());
+  EXPECT_FALSE(parse_transform("wobble (1)").has_value());
+  EXPECT_FALSE(parse_transform("translate (1cm 2cm").has_value());
+}
+
+TEST(OdfTransform, a_length_in_a_relative_unit_is_not_a_length) {
+  EXPECT_FALSE(parse_transform("translate (1em 2em)").has_value());
+  EXPECT_FALSE(parse_transform("translate (50% 0%)").has_value());
+  EXPECT_FALSE(parse_transform("translate (1 2)").has_value());
+}
+
+TEST(OdfTransform, a_leading_plus_is_a_sign) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate (+1cm +2cm)");
+  ASSERT_TRUE(transform.has_value());
+  EXPECT_EQ(Measure(1, DynamicUnit("cm")), transform->e);
+  EXPECT_EQ(Measure(2, DynamicUnit("cm")), transform->f);
+}
+
+TEST(OdfTransform, an_exponent_is_a_number) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("skewX (-5.59465989067396E-017)");
+  ASSERT_TRUE(transform.has_value());
+  expect_linear(*transform, 1, 0, 5.59465989067396E-017, 1);
+}
+
+TEST(OdfTransform, the_view_ends_the_list) {
+  // Nothing here reads for a terminator, so the operation the view cuts off is
+  // not seen.
+  const std::string_view value = "translate (1cm 2cm) translate (4cm 8cm)";
+  const std::optional<DrawingTransform> transform =
+      parse_transform(value.substr(0, 19));
+  ASSERT_TRUE(transform.has_value());
+  EXPECT_EQ(Measure(1, DynamicUnit("cm")), transform->e);
+  EXPECT_EQ(Measure(2, DynamicUnit("cm")), transform->f);
+}
+
+TEST(OdfTransform, a_zero_needs_no_unit) {
+  const std::optional<DrawingTransform> transform =
+      parse_transform("translate (0 0)");
+  ASSERT_TRUE(transform.has_value());
+  EXPECT_EQ(Measure(0, DynamicUnit()), transform->e);
+}