From 759a28ef45f3b01de4672698ce797ed9e3b471df Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Thu, 11 Jul 2013 14:41:42 +0200
Subject: [PATCH] Math: improved documentation for *::isNormalized().

---
 src/Math/Complex.h        | 2 +-
 src/Math/DualComplex.h    | 1 +
 src/Math/DualQuaternion.h | 1 +
 src/Math/Quaternion.h     | 2 +-
 src/Math/Vector.h         | 2 +-
 5 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/src/Math/Complex.h b/src/Math/Complex.h
index 8e54f03b7..88f2338f7 100644
--- a/src/Math/Complex.h
+++ b/src/Math/Complex.h
@@ -150,7 +150,7 @@ template<class T> class Complex {
          * @brief Whether the complex number is normalized
          *
          * Complex number is normalized if it has unit length: @f[
-         *      |c|^2 = |c| = 1
+         *      |c \cdot c - 1| < 2 \epsilon + \epsilon^2 \cong 2 \epsilon
          * @f]
          * @see dot(), normalized()
          */
diff --git a/src/Math/DualComplex.h b/src/Math/DualComplex.h
index 024563d2f..95ed5e7fb 100644
--- a/src/Math/DualComplex.h
+++ b/src/Math/DualComplex.h
@@ -133,6 +133,7 @@ template<class T> class DualComplex: public Dual<Complex<T>> {
          *      |c_0|^2 = |c_0| = 1
          * @f]
          * @see Complex::dot(), normalized()
+         * @todoc Improve the equation as in Complex::isNormalized()
          */
         bool isNormalized() const {
             return Implementation::isNormalizedSquared(lengthSquared());
diff --git a/src/Math/DualQuaternion.h b/src/Math/DualQuaternion.h
index 6411c9fa7..e3ef06f26 100644
--- a/src/Math/DualQuaternion.h
+++ b/src/Math/DualQuaternion.h
@@ -139,6 +139,7 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
          *      |\hat q|^2 = |\hat q| = 1 + \epsilon 0
          * @f]
          * @see lengthSquared(), normalized()
+         * @todoc Improve the equation as in Quaternion::isNormalized()
          */
         bool isNormalized() const {
             /* Comparing dual part classically, as comparing sqrt() of it would
diff --git a/src/Math/Quaternion.h b/src/Math/Quaternion.h
index d17c3e627..65c3f9408 100644
--- a/src/Math/Quaternion.h
+++ b/src/Math/Quaternion.h
@@ -164,7 +164,7 @@ template<class T> class Quaternion {
          * @brief Whether the quaternion is normalized
          *
          * Quaternion is normalized if it has unit length: @f[
-         *      |q|^2 = |q| = 1
+         *      |q \cdot q - 1| < 2 \epsilon + \epsilon^2 \cong 2 \epsilon
          * @f]
          * @see dot(), normalized()
          */
diff --git a/src/Math/Vector.h b/src/Math/Vector.h
index 353986936..42aaac41c 100644
--- a/src/Math/Vector.h
+++ b/src/Math/Vector.h
@@ -224,7 +224,7 @@ template<std::size_t size, class T> class Vector {
          * @brief Whether the vector is normalized
          *
          * The vector is normalized if it has unit length: @f[
-         *      |\boldsymbol a|^2 = |\boldsymbol a| = 1
+         *      |\boldsymbol a \cdot \boldsymbol a - 1| < 2 \epsilon + \epsilon^2 \cong 2 \epsilon
          * @f]
          * @see dot(), normalized()
          */