diff --git a/src/libslic3r/PerimeterGenerator.cpp b/src/libslic3r/PerimeterGenerator.cpp
index 0a138834a7..1f1f1289e5 100644
--- a/src/libslic3r/PerimeterGenerator.cpp
+++ b/src/libslic3r/PerimeterGenerator.cpp
@@ -2256,13 +2256,45 @@ void PerimeterGenerator::process_no_bridge(Surfaces& all_surfaces, coord_t perim
 
 // ORCA:
 // Inner Outer Inner wall ordering mode perimeter order optimisation functions
+
+// Whether two Arachne lines touch: somewhere the gap between their centrelines is no more than the
+// touching distance there. Each junction of one line is measured against the segments of the other,
+// both ways, and the search stops at the first spot that touches.
+// Arachne varies line width to fill the region (e.g. the odd centre line of a narrow wall is wider
+// than nominal), so the touching distance is half the combined width at the closest points, not the
+// nominal spacing. Widths are taken locally so a line widened in one place (a wedge tip, a wall
+// transition) does not count as touching where it passes close to other perimeters. min_threshold keeps
+// the nominal spacing threshold as the lower bound.
+static bool arachne_lines_touch(const Arachne::ExtrusionLine &a, const Arachne::ExtrusionLine &b, double min_threshold)
+{
+    auto one_way = [min_threshold](const Arachne::ExtrusionLine &from, const Arachne::ExtrusionLine &to) {
+        for (const Arachne::ExtrusionJunction &j : from.junctions) {
+            const Vec2d p = j.p.cast<double>();
+            for (size_t k = 0; k + 1 < to.junctions.size(); ++k) {
+                const Arachne::ExtrusionJunction &j0 = to.junctions[k];
+                const Arachne::ExtrusionJunction &j1 = to.junctions[k + 1];
+                const Vec2d  s0  = j0.p.cast<double>();
+                const Vec2d  seg = j1.p.cast<double>() - s0;
+                const double l2  = seg.squaredNorm();
+                const double t   = l2 > 0. ? std::clamp((p - s0).dot(seg) / l2, 0., 1.) : 0.;
+                const double w   = double(j0.w) + t * double(j1.w - j0.w); // width of `to` at the closest point
+                const double touch_distance = std::max(min_threshold, 0.5 * (double(j.w) + w));
+                if ((s0 + t * seg - p).norm() <= touch_distance)
+                    return true;
+            }
+        }
+        return false;
+    };
+    return one_way(a, b) || one_way(b, a);
+}
+
 /**
  * @brief Finds all perimeters touching a given set of reference lines, given as indexes.
  *
  * @param entities The list of PerimeterGeneratorArachneExtrusion entities.
  * @param referenceIndices A set of indices representing the reference points.
- * @param threshold_external The distance threshold to consider for proximity for a reference perimeter with inset index 0
- * @param threshold_internal The distance threshold to consider for proximity for a reference perimeter with inset index 1+
+ * @param threshold_external The minimum touching distance for a reference perimeter with inset index 0 
+ * @param threshold_internal The minimum touching distance for a reference perimeter with inset index 1+ 
  * @param considered_inset_idx What perimeter inset index are we searching for (eg. if we are searching for first internal perimeters proximate to the current reference perimeter, this value should be set to 1 etc).
  * @return std::vector<int> A vector of indices representing the touching perimeters.
  */
@@ -2271,7 +2303,6 @@ std::vector<int> findAllTouchingPerimeters(const std::vector<PerimeterGeneratorA
 
     for (const int refIdx : referenceIndices) {
         const auto& referenceEntity = entities[refIdx];
-        Points referencePoints = Arachne::to_points(*referenceEntity.extrusion);
         for (size_t i = 0; i < entities.size(); ++i) {
             // Skip already considered references and the reference entity
             if (referenceIndices.count(i) > 0) continue;
@@ -2282,15 +2313,9 @@ std::vector<int> findAllTouchingPerimeters(const std::vector<PerimeterGeneratorA
                 continue; // skip if they dont match
             }
             
-            Points points = Arachne::to_points(*entity.extrusion);
-            double distance = MultiPoint::minimumDistanceBetweenLinesDefinedByPoints(referencePoints, points);
-            // Add to touchingIndices if within threshold distance
-            size_t threshold=0;
-            if(referenceEntity.extrusion->inset_idx == 0)
-                threshold = threshold_external;
-            else
-                threshold = threshold_internal;
-            if (distance <= threshold) {
+            // Add to touchingIndices if the lines touch.
+            const double threshold = double(referenceEntity.extrusion->inset_idx == 0 ? threshold_external : threshold_internal);
+            if (arachne_lines_touch(*referenceEntity.extrusion, *entity.extrusion, threshold)) {
                 touchingIndices.insert(i);
             }
         }