diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
index de339b172e..6e8030c797 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
@@ -40,6 +40,7 @@ SourceFiles
 #include "tensor.H"
 #include "pointHit.H"
 #include "Random.H"
+#include "cachedRandom.H"
 #include "FixedList.H"
 #include "UList.H"
 #include "linePointRef.H"
@@ -162,6 +163,10 @@ public:
             //  distribution
             inline Point randomPoint(Random& rndGen) const;
 
+            //- Return a random point on the triangle from a uniform
+            //  distribution
+            inline Point randomPoint(cachedRandom& rndGen) const;
+
             //- Calculate the barycentric coordinates of the given
             //  point, in the same order as a, b, c.  Returns the
             //  determinant of the solution.
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H
index 1f4465637f..fbc5a14286 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H
@@ -244,6 +244,25 @@ inline Point Foam::triangle<Point, PointRef>::randomPoint(Random& rndGen) const
 }
 
 
+template<class Point, class PointRef>
+inline Point Foam::triangle<Point, PointRef>::randomPoint
+(
+    cachedRandom& rndGen
+) const
+{
+    // Generating Random Points in Triangles
+    // by Greg Turk
+    // from "Graphics Gems", Academic Press, 1990
+    // http://tog.acm.org/GraphicsGems/gems/TriPoints.c
+
+    scalar s = rndGen.sample01<scalar>();
+
+    scalar t = sqrt(rndGen.sample01<scalar>());
+
+    return (1 - t)*a_ + (1 - s)*t*b_ + s*t*c_;
+}
+
+
 template<class Point, class PointRef>
 Foam::scalar Foam::triangle<Point, PointRef>::barycentric
 (