diff --git a/Sofa/framework/Geometry/src/sofa/geometry/Edge.h b/Sofa/framework/Geometry/src/sofa/geometry/Edge.h
index d6398f3b81f..00a1f4d13ed 100644
--- a/Sofa/framework/Geometry/src/sofa/geometry/Edge.h
+++ b/Sofa/framework/Geometry/src/sofa/geometry/Edge.h
@@ -292,8 +292,18 @@ struct Edge
                 return false;
             }
 
-            const T alpha = alphaNom / alphaDenom;
-            const T beta = (dCACD + alpha * dABCD) / dCDCD;
+            T alpha = alphaNom / alphaDenom;
+            T beta = (dCACD + alpha * dABCD) / dCDCD;
+
+            if (abs(alpha) < EQUALITY_THRESHOLD)
+                alpha = 0;
+            else if (alpha > (1 - EQUALITY_THRESHOLD) && alpha < (1+ EQUALITY_THRESHOLD))
+                alpha = 1;
+
+            if (abs(beta) < EQUALITY_THRESHOLD)
+                beta = 0;
+            else if (beta > (1 - EQUALITY_THRESHOLD) && beta < (1 + EQUALITY_THRESHOLD))
+                beta = 1;
 
             const Node pX = pA + alpha * AB;
             const Node pY = pC + beta * CD;