From df12190955e05f5bc15e71427ce8db6d860e3df3 Mon Sep 17 00:00:00 2001
From: Robin Christ <robin@rchrist.io>
Date: Mon, 3 Nov 2025 23:52:26 +0100
Subject: [PATCH 1/2] EmbeddedGeometryInterface: Add face centroids as managed
 quantity

---
 .../surface/embedded_geometry_interface.h     |  8 ++++++++
 src/surface/embedded_geometry_interface.cpp   | 20 +++++++++++++++++++
 2 files changed, 28 insertions(+)

diff --git a/include/geometrycentral/surface/embedded_geometry_interface.h b/include/geometrycentral/surface/embedded_geometry_interface.h
index 64d2710d..fed68671 100644
--- a/include/geometrycentral/surface/embedded_geometry_interface.h
+++ b/include/geometrycentral/surface/embedded_geometry_interface.h
@@ -28,6 +28,11 @@ class EmbeddedGeometryInterface : public ExtrinsicGeometryInterface {
   void requireVertexPositions();
   void unrequireVertexPositions();
 
+  // Face centroids
+  FaceData<Vector3> faceCentroids;
+  void requireFaceCentroids();
+  void unrequireFaceCentroids();
+
   // Face normal
   FaceData<Vector3> faceNormals;
   void requireFaceNormals();
@@ -116,6 +121,9 @@ class EmbeddedGeometryInterface : public ExtrinsicGeometryInterface {
   DependentQuantityD<VertexData<Vector3>> vertexPositionsQ;
   virtual void computeVertexPositions() = 0;
 
+  DependentQuantityD<FaceData<Vector3>> faceCentroidsQ;
+  virtual void computeFaceCentroids();
+
   DependentQuantityD<FaceData<Vector3>> faceNormalsQ;
   virtual void computeFaceNormals();
 
diff --git a/src/surface/embedded_geometry_interface.cpp b/src/surface/embedded_geometry_interface.cpp
index a32035b3..9b0dbd48 100644
--- a/src/surface/embedded_geometry_interface.cpp
+++ b/src/surface/embedded_geometry_interface.cpp
@@ -13,6 +13,7 @@ EmbeddedGeometryInterface::EmbeddedGeometryInterface(SurfaceMesh& mesh_) :
   ExtrinsicGeometryInterface(mesh_),
 
   vertexPositionsQ                (&vertexPositions,                std::bind(&EmbeddedGeometryInterface::computeVertexPositions, this),                quantities),
+  faceCentroidsQ                  (&faceCentroids,                  std::bind(&EmbeddedGeometryInterface::computeFaceCentroids, this),                  quantities),
   faceNormalsQ                    (&faceNormals,                    std::bind(&EmbeddedGeometryInterface::computeFaceNormals, this),                    quantities),
   vertexNormalsQ                  (&vertexNormals,                  std::bind(&EmbeddedGeometryInterface::computeVertexNormals, this),                  quantities),
   faceTangentBasisQ               (&faceTangentBasis,               std::bind(&EmbeddedGeometryInterface::computeFaceTangentBasis, this),               quantities),
@@ -76,6 +77,25 @@ void EmbeddedGeometryInterface::computeEdgeDihedralAngles() {
 void EmbeddedGeometryInterface::requireVertexPositions() { vertexPositionsQ.require(); }
 void EmbeddedGeometryInterface::unrequireVertexPositions() { vertexPositionsQ.unrequire(); }
 
+// Face centroids
+void EmbeddedGeometryInterface::computeFaceCentroids() {
+  vertexPositionsQ.ensureHave();
+
+  faceCentroids = FaceData<Vector3>(mesh);
+
+  for (Face f : mesh.faces()) {
+    Vector3 centroid = Vector3::zero();
+    size_t n = 0;
+    for (Vertex v : f.adjacentVertices()) {
+      centroid += vertexPositions[v];
+      n++;
+    }
+    centroid /= static_cast<double>(n);
+    faceCentroids[f] = centroid;
+  }
+}
+void EmbeddedGeometryInterface::requireFaceCentroids() { faceCentroidsQ.require(); }
+void EmbeddedGeometryInterface::unrequireFaceCentroids() { faceCentroidsQ.unrequire(); }
 
 void EmbeddedGeometryInterface::computeFaceNormals() {
   vertexPositionsQ.ensureHave();

From 4717575f5d94f1049ecc8e7785387211acdd1b94 Mon Sep 17 00:00:00 2001
From: Nicholas Sharp <nmwsharp@gmail.com>
Date: Sun, 26 Apr 2026 12:35:03 -0700
Subject: [PATCH 2/2] add docs for face centroids

---
 docs/docs/surface/geometry/quantities.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/docs/docs/surface/geometry/quantities.md b/docs/docs/surface/geometry/quantities.md
index aeed7489..2557aa47 100644
--- a/docs/docs/surface/geometry/quantities.md
+++ b/docs/docs/surface/geometry/quantities.md
@@ -734,6 +734,16 @@ These quantities depend explicitly on an embedding in 3D space (better known as
     - **require:** `void EmbeddedGeometryInterface::requireVertexPositions()`
 
 
+??? func "face centroid"
+
+    ##### face centroid
+
+    The centroid (geometric center) of each face, computed as the average of its adjacent vertex positions. Works for faces of any degree (triangles, quads, polygons, etc.).
+
+    - **member:** `FaceData<Vector3> EmbeddedGeometryInterface::faceCentroids`
+    - **require:** `void EmbeddedGeometryInterface::requireFaceCentroids()`
+
+
 ??? func "face normal"
 
     ##### face normal