From 3515d218163ad4743b4dc92d162d5b9e86fd434f Mon Sep 17 00:00:00 2001
From: Symmetricity <184246+Symmetricity@users.noreply.github.com>
Date: Mon, 18 May 2026 18:25:08 +0200
Subject: [PATCH 1/2] Stabilize polylabel centroid seed

Compute the polygon centroid seed relative to a local ring origin before translating it back to map coordinates.

This isolates the centroid-origin change from the distance-key ordering candidate so it can be tested independently against the submitted PR stack.
---
 include/polylabel.h | 16 +++++++++++-----
 1 file changed, 11 insertions(+), 5 deletions(-)

diff --git a/include/polylabel.h b/include/polylabel.h
index 5d3805eb..894795e1 100644
--- a/include/polylabel.h
+++ b/include/polylabel.h
@@ -111,18 +111,24 @@ Cell getCentroidCell(const Polygon& polygon) {
     double area = 0;
     double cx = 0, cy = 0;
     const auto& ring = polygon.outer();
+    const Point& origin = ring.at(0);
+    const double ox = origin.get<0>();
+    const double oy = origin.get<1>();
 
     for (std::size_t i = 0, len = ring.size(), j = len - 1; i < len; j = i++) {
         const Point& a = ring[i];
         const Point& b = ring[j];
-        auto f = a.get<0>() * b.get<1>() - b.get<0>() * a.get<1>();
-        cx += (a.get<0>() + b.get<0>()) * f;
-        cy += (a.get<1>() + b.get<1>()) * f;
+        const double ax = a.get<0>() - ox;
+        const double ay = a.get<1>() - oy;
+        const double bx = b.get<0>() - ox;
+        const double by = b.get<1>() - oy;
+        auto f = ax * by - bx * ay;
+        cx += (ax + bx) * f;
+        cy += (ay + by) * f;
         area += f * 3;
     }
 
-    Point c { cx, cy };
-    return Cell(area == 0 ? ring.at(0) : Point { cx / area, cy / area }, 0, polygon);
+    return Cell(area == 0 ? ring.at(0) : Point { ox + cx / area, oy + cy / area }, 0, polygon);
 }
 
 } // namespace detail

From f85385bb6a55fd6fbe545a8543ee0c4f8a39140d Mon Sep 17 00:00:00 2001
From: Symmetricity <184246+Symmetricity@users.noreply.github.com>
Date: Mon, 18 May 2026 19:11:44 +0200
Subject: [PATCH 2/2] Stabilize polylabel queue ties

Break exact priority-queue ties with existing cell geometry values so equivalent cells are not left to implementation-specific heap ordering.

This keeps the local-origin centroid candidate isolated from the broader distance-key ordering change while testing whether the remaining macOS versus Linux/Windows point drift is caused by queue ordering alone.
---
 include/polylabel.h | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/include/polylabel.h b/include/polylabel.h
index 894795e1..de3a8bc7 100644
--- a/include/polylabel.h
+++ b/include/polylabel.h
@@ -150,7 +150,11 @@ Point polylabel(const Polygon& polygon, double precision = 0.00001, bool debug =
 
     // a priority queue of cells in order of their "potential" (max distance to polygon)
     auto compareMax = [] (const Cell& a, const Cell& b) {
-        return a.max < b.max;
+        if (a.max != b.max) return a.max < b.max;
+        if (a.d != b.d) return a.d < b.d;
+        if (a.h != b.h) return a.h > b.h;
+        if (a.c.get<0>() != b.c.get<0>()) return a.c.get<0>() > b.c.get<0>();
+        return a.c.get<1>() > b.c.get<1>();
     };
     using Queue = std::priority_queue<Cell, std::vector<Cell>, decltype(compareMax)>;
     Queue cellQueue(compareMax);