diff --git a/lucene/spatial3d/src/java/org/apache/lucene/spatial3d/geom/Vector.java b/lucene/spatial3d/src/java/org/apache/lucene/spatial3d/geom/Vector.java
index 62b3f5ed4a1..1e6e27fbf36 100755
--- a/lucene/spatial3d/src/java/org/apache/lucene/spatial3d/geom/Vector.java
+++ b/lucene/spatial3d/src/java/org/apache/lucene/spatial3d/geom/Vector.java
@@ -48,6 +48,12 @@ public class Vector {
   /** The z value */
   public final double z;
 
+  /**
+    * Gram-Schmidt convergence envelope is a bit smaller than we really need because we don't want the math to fail afterwards in
+    * other places.
+    */
+  private static final double MINIMUM_GRAM_SCHMIDT_ENVELOPE = MINIMUM_RESOLUTION * 0.5;
+  
   /**
    * Construct from (U.S.) x,y,z coordinates.
    *@param x is the x value.
@@ -122,7 +128,7 @@ public class Vector {
     while (true) {
       final double currentDotProdA = AX * normalizeX + AY * normalizeY + AZ * normalizeZ;
       final double currentDotProdB = BX * normalizeX + BY * normalizeY + BZ * normalizeZ;
-      if (Math.abs(currentDotProdA) < MINIMUM_RESOLUTION && Math.abs(currentDotProdB) < MINIMUM_RESOLUTION) {
+      if (Math.abs(currentDotProdA) < MINIMUM_GRAM_SCHMIDT_ENVELOPE && Math.abs(currentDotProdB) < MINIMUM_GRAM_SCHMIDT_ENVELOPE) {
         break;
       }
       // Converge on the one that has largest dot product
@@ -231,7 +237,7 @@ public class Vector {
     while (true) {
       final double currentDotProdA = A.x * normalizeX + A.y * normalizeY + A.z * normalizeZ;
       final double currentDotProdB = B.x * normalizeX + B.y * normalizeY + B.z * normalizeZ;
-      if (Math.abs(currentDotProdA) < MINIMUM_RESOLUTION && Math.abs(currentDotProdB) < MINIMUM_RESOLUTION) {
+      if (Math.abs(currentDotProdA) < MINIMUM_GRAM_SCHMIDT_ENVELOPE && Math.abs(currentDotProdB) < MINIMUM_GRAM_SCHMIDT_ENVELOPE) {
         break;
       }
       // Converge on the one that has largest dot product
diff --git a/lucene/spatial3d/src/test/org/apache/lucene/spatial3d/geom/RandomPlaneTest.java b/lucene/spatial3d/src/test/org/apache/lucene/spatial3d/geom/RandomPlaneTest.java
index d7828bddceb..af47e918df5 100644
--- a/lucene/spatial3d/src/test/org/apache/lucene/spatial3d/geom/RandomPlaneTest.java
+++ b/lucene/spatial3d/src/test/org/apache/lucene/spatial3d/geom/RandomPlaneTest.java
@@ -70,10 +70,11 @@ public class RandomPlaneTest extends RandomGeo3dShapeGenerator {
       if (plane == null) {
         fail(msg);
       }
-      assertTrue(plane.evaluate(check) + " " + msg, plane.isWithin(check));
-      assertTrue(plane.evaluate(point1) + " " +msg, plane.isWithin(point3));
+      // This is not expected
+      //assertTrue(plane.evaluate(check) + " " + msg, plane.isWithin(check));
+      assertTrue(plane.evaluate(point1) + " " +msg, plane.isWithin(point1));
       assertTrue(plane.evaluate(point2) + " " +msg, plane.isWithin(point2));
-      assertTrue(plane.evaluate(point3) + " " +msg, plane.isWithin(point1));
+      assertTrue(plane.evaluate(point3) + " " +msg, plane.isWithin(point3));
     }
   }