Merge pull request #14 from WorldWindEarth/determinantFix

Determinant fix

Author: caller

src/gov/nasa/worldwind/geom/Matrix.java

@@ -2061,7 +2061,7 @@ public final double getDeterminant()
                 + this.m24 * (this.m31 * this.m42 - this.m41 * this.m32));
         // Columns 1, 2, 3.
         result -= this.m14 *
-            (this.m21 * (this.m32 * this.m43 - this.m42 - this.m33)
+            (this.m21 * (this.m32 * this.m43 - this.m42 * this.m33)
                 - this.m22 * (this.m31 * this.m43 - this.m41 * this.m33)
                 + this.m23 * (this.m31 * this.m42 - this.m41 * this.m32));
         return result;

test/gov/nasa/worldwind/geom/MatrixTest.java

@@ -136,6 +136,26 @@ public void testInverseOfNearSingular()
         Matrix identity = m.multiply(mInv);
         assertTrue("Matrix inverse is incorrect", equals(identity, Matrix.IDENTITY, NEAR_SINGULAR_EQUALITY_TOLERANCE));
     }
+    
+    @Test
+    public void testDeterminantEqualToDeterminantOfTranspose()
+    {
+        // Create random matrix.
+        Matrix matrix = new Matrix(
+            random.nextDouble(), random.nextDouble(), random.nextDouble(), random.nextDouble(),
+            random.nextDouble(), random.nextDouble(), random.nextDouble(), random.nextDouble(),
+            random.nextDouble(), random.nextDouble(), random.nextDouble(), random.nextDouble(),
+            random.nextDouble(), random.nextDouble(), random.nextDouble(), random.nextDouble());
+        
+        // Calculate the determinant.
+        double determinant = matrix.getDeterminant();
+        
+        // Transpose the matrix.
+        Matrix transpose = matrix.getTranspose();
+        
+        // The determinant and the determinant of the transpose should be equal.
+        assertEquals(determinant, transpose.getDeterminant(), EQUALITY_TOLERANCE);
+    }
 
     //**************************************************************//
     //********************  Helper Methods  ************************//