diff --git a/Source/Core/CorridorGeometryLibrary.js b/Source/Core/CorridorGeometryLibrary.js
index d937443a23c1..418fcf3d3573 100644
--- a/Source/Core/CorridorGeometryLibrary.js
+++ b/Source/Core/CorridorGeometryLibrary.js
@@ -219,7 +219,7 @@ define([
             Cartesian3.subtract(backward, backwardProjection, backwardProjection);
             Cartesian3.normalize(backwardProjection, backwardProjection);
 
-            var doCorner = !CesiumMath.equalsEpsilon(Math.abs(Cartesian3.dot(forwardProjection, backwardProjection)), 1.0, CesiumMath.EPSILON1);
+            var doCorner = !CesiumMath.equalsEpsilon(Math.abs(Cartesian3.dot(forwardProjection, backwardProjection)), 1.0, CesiumMath.EPSILON7);
 
             if (doCorner) {
                 cornerDirection = Cartesian3.cross(cornerDirection, normal, cornerDirection);
diff --git a/Source/Core/PolylineVolumeGeometryLibrary.js b/Source/Core/PolylineVolumeGeometryLibrary.js
index 9df76e151611..39e5733aaeba 100644
--- a/Source/Core/PolylineVolumeGeometryLibrary.js
+++ b/Source/Core/PolylineVolumeGeometryLibrary.js
@@ -350,7 +350,7 @@ define([
             Cartesian3.subtract(backward, backwardProjection, backwardProjection);
             Cartesian3.normalize(backwardProjection, backwardProjection);
 
-            var doCorner = !CesiumMath.equalsEpsilon(Math.abs(Cartesian3.dot(forwardProjection, backwardProjection)), 1.0, CesiumMath.EPSILON1);
+            var doCorner = !CesiumMath.equalsEpsilon(Math.abs(Cartesian3.dot(forwardProjection, backwardProjection)), 1.0, CesiumMath.EPSILON7);
 
             if (doCorner) {
                 cornerDirection = Cartesian3.cross(cornerDirection, surfaceNormal, cornerDirection);
diff --git a/Specs/Core/CorridorGeometrySpec.js b/Specs/Core/CorridorGeometrySpec.js
index e531decff19b..58ea955b6a55 100644
--- a/Specs/Core/CorridorGeometrySpec.js
+++ b/Specs/Core/CorridorGeometrySpec.js
@@ -180,6 +180,24 @@ defineSuite([
         expect(m.indices.length).toEqual(3 * 8);
     });
 
+    it('computes sharp turns', function() {
+        var m = CorridorGeometry.createGeometry(new CorridorGeometry({
+            vertexFormat : VertexFormat.POSITION_ONLY,
+            positions : Cartesian3.fromDegreesArray([
+                 2.00571672577652,52.7781459942399,
+                 1.99188457974115,52.7764958852886,
+                 2.01325961458495,52.7674170680511,
+                 1.98708058340534,52.7733979856253,
+                 2.00634853946644,52.7650460748473
+            ]),
+            cornerType: CornerType.BEVELED,
+            width : 100
+        }));
+
+        expect(m.attributes.position.values.length).toEqual(3 * 13);
+        expect(m.indices.length).toEqual(3 * 11);
+    });
+
     it('computes straight corridors', function() {
         var m = CorridorGeometry.createGeometry(new CorridorGeometry({
             vertexFormat : VertexFormat.POSITION_ONLY,
diff --git a/Specs/Core/PolylineVolumeGeometrySpec.js b/Specs/Core/PolylineVolumeGeometrySpec.js
index de819ab2a7bc..a8cec93e6a27 100644
--- a/Specs/Core/PolylineVolumeGeometrySpec.js
+++ b/Specs/Core/PolylineVolumeGeometrySpec.js
@@ -169,6 +169,24 @@ defineSuite([
         expect(m.indices.length).toEqual(3 * (8 * 2 + 4 * 7 * 2 + 4));
     });
 
+    it('computes sharp turns', function() {
+        var m = PolylineVolumeGeometry.createGeometry(new PolylineVolumeGeometry({
+            vertexFormat : VertexFormat.POSITION_ONLY,
+            polylinePositions : Cartesian3.fromDegreesArrayHeights([
+                 2.00571672577652, 52.7781459942399, 500,
+                 1.99188457974115, 52.7764958852886, 500,
+                 2.01325961458495, 52.7674170680511, 500,
+                 1.98708058340534, 52.7733979856253, 500,
+                 2.00634853946644, 52.7650460748473, 500
+            ]),
+            cornerType: CornerType.BEVELED,
+            shapePositions: shape
+        }));
+
+        expect(m.attributes.position.values.length).toEqual(360);
+        expect(m.indices.length).toEqual(324);
+    });
+
     it('computes straight volume', function() {
         var m = PolylineVolumeGeometry.createGeometry(new PolylineVolumeGeometry({
             vertexFormat : VertexFormat.POSITION_ONLY,