diff --git a/CHANGES.md b/CHANGES.md
index b19c37bda547..514dda84cfae 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -20,6 +20,7 @@ Change Log
 * Added a [new Sandcastle example](https://cesiumjs.org/Cesium/Build/Apps/Sandcastle/?src=Time%20Dynamic%20Wheels.html) on using `nodeTransformations` to rotate a model's wheels based on its velocity. [#7361](https://github.com/AnalyticalGraphicsInc/cesium/pull/7361)
 * Added `EllipsoidRhumbLine` class as a rhumb line counterpart to `EllipsoidGeodesic`. [#7484](https://github.com/AnalyticalGraphicsInc/cesium/pull/7484)
 * Added rhumb line support to `PolygonGeometry`, `PolygonOutlineGeometry`, `PolylineGeometry`, `GroundPolylineGeometry`, and `SimplePolylineGeometry`. [#7492](https://github.com/AnalyticalGraphicsInc/cesium/pull/7492)
+* Improved the performance of `QuantizedMeshTerrainData.interpolateHeight`.  [#7508](https://github.com/AnalyticalGraphicsInc/cesium/pull/7508)
 
 ##### Fixes :wrench:
 * Fixed 3D Tiles performance regression. [#7482](https://github.com/AnalyticalGraphicsInc/cesium/pull/7482)
diff --git a/Source/Core/QuantizedMeshTerrainData.js b/Source/Core/QuantizedMeshTerrainData.js
index ed582ce13649..7040125f2ef6 100644
--- a/Source/Core/QuantizedMeshTerrainData.js
+++ b/Source/Core/QuantizedMeshTerrainData.js
@@ -498,6 +498,14 @@ define([
         return interpolateMeshHeight(this, u, v);
     };
 
+    function pointInBoundingBox(u, v, u0, v0, u1, v1, u2, v2) {
+        var minU = Math.min(u0, u1, u2);
+        var maxU = Math.max(u0, u1, u2);
+        var minV = Math.min(v0, v1, v2);
+        var maxV = Math.max(v0, v1, v2);
+        return (u >= minU && u <= maxU && v >= minV && v <= maxV);
+    }
+
     var texCoordScratch0 = new Cartesian2();
     var texCoordScratch1 = new Cartesian2();
     var texCoordScratch2 = new Cartesian2();
@@ -517,12 +525,14 @@ define([
             var uv1 = encoding.decodeTextureCoordinates(vertices, i1, texCoordScratch1);
             var uv2 = encoding.decodeTextureCoordinates(vertices, i2, texCoordScratch2);
 
-            var barycentric = Intersections2D.computeBarycentricCoordinates(u, v, uv0.x, uv0.y, uv1.x, uv1.y, uv2.x, uv2.y, barycentricCoordinateScratch);
-            if (barycentric.x >= -1e-15 && barycentric.y >= -1e-15 && barycentric.z >= -1e-15) {
-                var h0 = encoding.decodeHeight(vertices, i0);
-                var h1 = encoding.decodeHeight(vertices, i1);
-                var h2 = encoding.decodeHeight(vertices, i2);
-                return barycentric.x * h0 + barycentric.y * h1 + barycentric.z * h2;
+            if (pointInBoundingBox(u, v, uv0.x, uv0.y, uv1.x, uv1.y, uv2.x, uv2.y)) {
+                var barycentric = Intersections2D.computeBarycentricCoordinates(u, v, uv0.x, uv0.y, uv1.x, uv1.y, uv2.x, uv2.y, barycentricCoordinateScratch);
+                if (barycentric.x >= -1e-15 && barycentric.y >= -1e-15 && barycentric.z >= -1e-15) {
+                    var h0 = encoding.decodeHeight(vertices, i0);
+                    var h1 = encoding.decodeHeight(vertices, i1);
+                    var h2 = encoding.decodeHeight(vertices, i2);
+                    return barycentric.x * h0 + barycentric.y * h1 + barycentric.z * h2;
+                }
             }
         }
 
@@ -549,12 +559,14 @@ define([
             var v1 = vBuffer[i1];
             var v2 = vBuffer[i2];
 
-            var barycentric = Intersections2D.computeBarycentricCoordinates(u, v, u0, v0, u1, v1, u2, v2, barycentricCoordinateScratch);
-            if (barycentric.x >= -1e-15 && barycentric.y >= -1e-15 && barycentric.z >= -1e-15) {
-                var quantizedHeight = barycentric.x * heightBuffer[i0] +
-                                      barycentric.y * heightBuffer[i1] +
-                                      barycentric.z * heightBuffer[i2];
-                return CesiumMath.lerp(terrainData._minimumHeight, terrainData._maximumHeight, quantizedHeight / maxShort);
+            if (pointInBoundingBox(u, v, u0, v0, u1, v1, u2, v2)) {
+                var barycentric = Intersections2D.computeBarycentricCoordinates(u, v, u0, v0, u1, v1, u2, v2, barycentricCoordinateScratch);
+                if (barycentric.x >= -1e-15 && barycentric.y >= -1e-15 && barycentric.z >= -1e-15) {
+                    var quantizedHeight = barycentric.x * heightBuffer[i0] +
+                                          barycentric.y * heightBuffer[i1] +
+                                          barycentric.z * heightBuffer[i2];
+                    return CesiumMath.lerp(terrainData._minimumHeight, terrainData._maximumHeight, quantizedHeight / maxShort);
+                }
             }
         }