diff --git a/Detectors/Base/include/DetectorsBase/O2Tessellated.h b/Detectors/Base/include/DetectorsBase/O2Tessellated.h
index 0a1cee8b3e01f..7a1a3945c80d8 100644
--- a/Detectors/Base/include/DetectorsBase/O2Tessellated.h
+++ b/Detectors/Base/include/DetectorsBase/O2Tessellated.h
@@ -133,6 +133,14 @@ class O2Tessellated : public TGeoBBox
   template <bool closest_facet = false>
   Double_t SafetyKernel(const Double_t* point, bool in, int* closest_facet_id = nullptr) const;
 
+  // cached values for safety
+  mutable float mLast_x;
+  mutable float mLast_y;
+  mutable float mLast_z;
+  mutable float mCachedSafety;
+  mutable size_t cached_counter = 0;
+  mutable size_t call_counter = 0;
+
   ClassDefOverride(O2Tessellated, 1) // tessellated shape class
 };
 
diff --git a/Detectors/Base/src/O2Tessellated.cxx b/Detectors/Base/src/O2Tessellated.cxx
index 256a70e5a697a..5c52625841868 100644
--- a/Detectors/Base/src/O2Tessellated.cxx
+++ b/Detectors/Base/src/O2Tessellated.cxx
@@ -1349,8 +1349,30 @@ Double_t O2Tessellated::Safety(const Double_t* point, Bool_t in) const
   // we could use some caching here (in future) since queries to the solid will likely
   // be made with some locality
 
+  if (in) {
+    call_counter++;
+    // distance to last known evaluation
+    const auto xd = float(point[0]) - mLast_x;
+    const auto yd = float(point[1]) - mLast_y;
+    const auto zd = float(point[2]) - mLast_z;
+    const auto d2 = xd * xd + yd * yd + zd * zd;
+
+    if (d2 < mCachedSafety * mCachedSafety) {
+      // we moved less than known safety
+      cached_counter++;
+      return mCachedSafety - std::sqrt(d2);
+    }
+  }
+
   // fall-back to precise safety kernel
-  return SafetyKernel<false>(point, in);
+  const auto safety = SafetyKernel<false>(point, in);
+  if (in) {
+    mLast_x = point[0];
+    mLast_y = point[1];
+    mLast_z = point[2];
+    mCachedSafety = safety;
+  }
+  return safety;
 }
 
 ////////////////////////////////////////////////////////////////////////////////
@@ -1506,4 +1528,4 @@ void O2Tessellated::CalculateNormals()
   }
 }
 
-// NOLINTEND
\ No newline at end of file
+// NOLINTEND