[BALL] Fix Quaternion_test

When constructing axis-angles from quaternions, Eigen flips the rotation
axis if the real component of the quaternion is negative. Since this
does not affect the validity of the rotation, the result is still
correct. The test case has been adjusted to also accept the alternative
representation with flipped axis and modified angle of (2\pi -
old_angle).

Author: tkemmer

test/Quaternion_test.C

@@ -193,10 +193,24 @@ CHECK(void toAxisAngle(TVector3<T>& axis, T& angle))
 	Quaternion q(v1, a);	
 	q.toAxisAngle(v2, ang);
 	v1.normalize();
-	TEST_REAL_EQUAL(ang, a)
-	TEST_REAL_EQUAL(v2.x, v1.x)
-	TEST_REAL_EQUAL(v2.y, v1.y)
-	TEST_REAL_EQUAL(v2.z, v1.z)
+	/*
+	 * There are two valid axis-angle representations for the same
+	 * rotation, namely (v, a) and (-v, 2\pi-a). Since the actual
+	 * result depends on the eigen3 version used, we have to test
+	 * both versions here.
+	 */
+	if(v2.x < 0) {
+		TEST_REAL_EQUAL(ang, 2 * BALL::Constants::PI - a)
+		TEST_REAL_EQUAL(v2.x, -v1.x)
+		TEST_REAL_EQUAL(v2.y, -v1.y)
+		TEST_REAL_EQUAL(v2.z, -v1.z)
+	}
+	else {
+		TEST_REAL_EQUAL(ang, a)
+		TEST_REAL_EQUAL(v2.x, v1.x)
+		TEST_REAL_EQUAL(v2.y, v1.y)
+		TEST_REAL_EQUAL(v2.z, v1.z)
+	}
 RESULT
 
 CHECK(void toEulerAngles(T& yaw, T& pitch, T& roll))
@@ -217,17 +231,26 @@ RESULT
 
 CHECK(T getAngle() const)
 	Quaternion q(v,a);
-	TEST_REAL_EQUAL(q.getAngle(),a) 
+	// see toAxisAngle check
+	TEST_EQUAL((abs(q.getAngle()-a) < 1e-4 || abs(q.getAngle() - 2 * BALL::Constants::PI + a) < 1e-4), true)
 RESULT
 
 CHECK(TVector3<T> getAxis())
 	Quaternion q(v,a);
 	Vector3 v1(v);
 	v1.normalize();
 	Vector3 v2 = q.getAxis();
-	TEST_REAL_EQUAL(v2.x, v1.x)
-	TEST_REAL_EQUAL(v2.y, v1.y)
-	TEST_REAL_EQUAL(v2.z, v1.z)
+	// see toAxisAngle check
+	if(v2.x < 0) {
+		TEST_REAL_EQUAL(v2.x, -v1.x)
+		TEST_REAL_EQUAL(v2.y, -v1.y)
+		TEST_REAL_EQUAL(v2.z, -v1.z)
+	}
+	else {
+		TEST_REAL_EQUAL(v2.x, v1.x)
+		TEST_REAL_EQUAL(v2.y, v1.y)
+		TEST_REAL_EQUAL(v2.z, v1.z)
+	}
 RESULT
 
 CHECK(TMatrix4x4<T>& getRotationMatrix(TMatrix4x4<T>& m) const throw())