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Math: renamed {rotationAngle, rotationAxis}() -> {rotation, angle, axis}(). 

DualQuaternion and DualComplex has now only rotation() which returns
full rotation part, rotationAngle() and rotationAxis() on Quaternion and
Complex were renamed to angle() and axis().
pull/278/head
Vladimír Vondruš 13 years ago
parent
73a4e9b18a
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3e0e91d7db
9 changed files with 58 additions and 69 deletions
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  1. 14
      doc/transformations.dox
  2. 6
      src/Math/Complex.h
  3. 13
      src/Math/DualComplex.h
  4. 31
      src/Math/DualQuaternion.h
  5. 15
      src/Math/Quaternion.h
  6. 6
      src/Math/Test/ComplexTest.cpp
  7. 11
      src/Math/Test/DualComplexTest.cpp
  8. 17
      src/Math/Test/DualQuaternionTest.cpp
  9. 14
      src/Math/Test/QuaternionTest.cpp

14
doc/transformations.dox
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@ -243,18 +243,18 @@ Matrix3 c = Matrix3::from(rotation, {1.0f, 3.0f});
@endcode
%Complex numbers and quaternions are far better in this regard and they allow
you to extract rotation angle using Complex::rotationAngle(), Quaternion::rotationAngle(),
DualComplex::rotationAngle() or DualQuaternion::rotationAngle(), and rotation
axis in 3D using Quaternion::rotationAxis() or DualQuaternion::rotationAxis().
It is also possible to extract translation from their dual versions using
DualComplex::translation() const and DualQuaternion::translation() const.
you to extract rotation angle using Complex::angle() or Quaternion::angle() or
rotation axis in 3D using Quaternion::axis(). Their dual versions allow to
extract both rotation and translation part using DualComplex::rotation() const,
DualQuaternion::rotation() const, DualComplex::translation() const and
DualQuaternion::translation() const.
@code
DualComplex a;
Rad rotation = a.rotationAngle();
Rad rotationAngle = a.rotation().angle();
Vector2 translation = a.translation();
Quaternion b;
Vector3 rotationAxis = b.rotationAxis();
Vector3 rotationAxis = b.axis();
@endcode
You can convert Complex and Quaternion to rotation matrix using Complex::toMatrix()

6
src/Math/Complex.h
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@ -90,7 +90,7 @@ template<class T> class Complex {
* @f[
* c = cos \theta + i sin \theta
* @f]
* @see rotationAngle(), Matrix3::rotation(), Quaternion::rotation()
* @see angle(), Matrix3::rotation(), Quaternion::rotation()
*/
inline static Complex<T> rotation(Rad<T> angle) {
return {std::cos(T(angle)), std::sin(T(angle))};
@ -182,9 +182,9 @@ template<class T> class Complex {
* @f[
* \theta = atan2(b, a)
* @f]
* @see rotation(), DualComplex::rotationAngle()
* @see rotation()
*/
inline Rad<T> rotationAngle() const {
inline Rad<T> angle() const {
return Rad<T>(std::atan2(_imaginary, _real));
}

13
src/Math/DualComplex.h
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@ -55,7 +55,7 @@ template<class T> class DualComplex: public Dual<Complex<T>> {
* @f[
* \hat c = (cos \theta + i sin \theta) + \epsilon (0 + i0)
* @f]
* @see rotationAngle(), Complex::rotation(), Matrix3::rotation(),
* @see angle(), Complex::rotation(), Matrix3::rotation(),
* DualQuaternion::rotation()
*/
inline static DualComplex<T> rotation(Rad<T> angle) {
@ -139,15 +139,12 @@ template<class T> class DualComplex: public Dual<Complex<T>> {
}
/**
* @brief Rotation angle of dual complex number
* @brief Rotation part of dual complex number
*
* @f[
* \theta = atan2(b_0, a_0)
* @f]
* @see rotation(), Complex::rotationAngle()
* @see Complex::angle()
*/
inline Rad<T> rotationAngle() const {
return this->real().rotationAngle();
inline constexpr Complex<T> rotation() const {
return this->real();
}
/**

31
src/Math/DualQuaternion.h
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@ -54,9 +54,9 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
* Expects that the rotation axis is normalized. @f[
* \hat q = [\boldsymbol a \cdot sin \frac \theta 2, cos \frac \theta 2] + \epsilon [\boldsymbol 0, 0]
* @f]
* @see rotationAngle(), rotationAxis(), Quaternion::rotation(),
* Matrix4::rotation(), DualComplex::rotation(), Vector3::xAxis(),
* Vector3::yAxis(), Vector3::zAxis(), Vector::isNormalized()
* @see rotation() const, Quaternion::rotation(), Matrix4::rotation(),
* DualComplex::rotation(), Vector3::xAxis(), Vector3::yAxis(),
* Vector3::zAxis(), Vector::isNormalized()
*/
inline static DualQuaternion<T> rotation(Rad<T> angle, const Vector3<T>& normalizedAxis) {
return {Quaternion<T>::rotation(angle, normalizedAxis), {{}, T(0)}};
@ -145,29 +145,12 @@ template<class T> class DualQuaternion: public Dual<Quaternion<T>> {
}
/**
* @brief Rotation angle of unit dual quaternion
* @brief Rotation part of unit dual quaternion
*
* Expects that the real part of the quaternion is normalized. @f[
* \theta = 2 \cdot acos q_{S 0}
* @f]
* @see rotationAxis(), rotation(), Quaternion::rotationAngle()
*/
inline Math::Rad<T> rotationAngle() const {
return this->real().rotationAngle();
}
/**
* @brief Rotation axis of unit dual quaternion
*
* Expects that the quaternion is normalized. Returns either unit-length
* vector for valid rotation quaternion or NaN vector for
* default-constructed quaternion. @f[
* \boldsymbol a = \frac{\boldsymbol q_{V 0}}{\sqrt{1 - q_{S 0}^2}}
* @f]
* @see rotationAngle(), rotation(), Quaternion::rotationAxis()
* @see Quaternion::angle(), Quaternion::axis()
*/
inline Vector3<T> rotationAxis() const {
return this->real().rotationAxis();
inline constexpr Quaternion<T> rotation() const {
return this->real();
}
/**

15
src/Math/Quaternion.h
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@ -162,7 +162,7 @@ template<class T> class Quaternion {
* Expects that the rotation axis is normalized. @f[
* q = [\boldsymbol a \cdot sin \frac \theta 2, cos \frac \theta 2]
* @f]
* @see rotationAngle(), rotationAxis(), DualQuaternion::rotation(),
* @see angle(), axis(), DualQuaternion::rotation(),
* Matrix4::rotation(), Complex::rotation(), Vector3::xAxis(),
* Vector3::yAxis(), Vector3::zAxis(), Vector::isNormalized()
*/
@ -247,12 +247,11 @@ template<class T> class Quaternion {
* Expects that the quaternion is normalized. @f[
* \theta = 2 \cdot acos q_S
* @f]
* @see isNormalized(), rotationAxis(), rotation(),
* DualQuaternion::rotationAngle()
* @see isNormalized(), axis(), rotation()
*/
inline Rad<T> rotationAngle() const {
inline Rad<T> angle() const {
CORRADE_ASSERT(isNormalized(),
"Math::Quaternion::rotationAngle(): quaternion must be normalized",
"Math::Quaternion::angle(): quaternion must be normalized",
Rad<T>(std::numeric_limits<T>::quiet_NaN()));
return Rad<T>(T(2)*std::acos(_scalar));
}
@ -265,11 +264,11 @@ template<class T> class Quaternion {
* default-constructed quaternion. @f[
* \boldsymbol a = \frac{\boldsymbol q_V}{\sqrt{1 - q_S^2}}
* @f]
* @see isNormalized(), rotationAngle(), rotation()
* @see isNormalized(), angle(), rotation()
*/
inline Vector3<T> rotationAxis() const {
inline Vector3<T> axis() const {
CORRADE_ASSERT(isNormalized(),
"Math::Quaternion::rotationAxis(): quaternion must be normalized",
"Math::Quaternion::axis(): quaternion must be normalized",
{});
return _vector/std::sqrt(1-pow2(_scalar));
}

6
src/Math/Test/ComplexTest.cpp
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@ -273,15 +273,15 @@ void ComplexTest::rotation() {
Complex a = Complex::rotation(Deg(120.0f));
CORRADE_COMPARE(a.length(), 1.0f);
CORRADE_COMPARE(a, Complex(-0.5f, 0.8660254f));
CORRADE_COMPARE_AS(a.rotationAngle(), Deg(120.0f), Rad);
CORRADE_COMPARE_AS(a.angle(), Deg(120.0f), Rad);
/* Verify negative angle */
Complex b = Complex::rotation(Deg(-240.0f));
CORRADE_COMPARE(b, Complex(-0.5f, 0.8660254f));
CORRADE_COMPARE_AS(b.rotationAngle(), Deg(120.0f), Rad);
CORRADE_COMPARE_AS(b.angle(), Deg(120.0f), Rad);
/* Default-constructed complex number has zero angle */
CORRADE_COMPARE_AS(Complex().rotationAngle(), Deg(0.0f), Rad);
CORRADE_COMPARE_AS(Complex().angle(), Deg(0.0f), Rad);
}
void ComplexTest::matrix() {

11
src/Math/Test/DualComplexTest.cpp
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@ -207,7 +207,12 @@ void DualComplexTest::rotation() {
DualComplex a = DualComplex::rotation(Deg(120.0f));
CORRADE_COMPARE(a.length(), 1.0f);
CORRADE_COMPARE(a, DualComplex({-0.5f, 0.8660254f}, {0.0f, 0.0f}));
CORRADE_COMPARE_AS(a.rotationAngle(), Deg(120.0f), Rad);
CORRADE_COMPARE_AS(a.rotation().angle(), Deg(120.0f), Rad);
/* Constexpr access to rotation */
constexpr DualComplex b({-1.0f, 2.0f}, {});
constexpr Complex c = b.rotation();
CORRADE_COMPARE(c, Complex(-1.0f, 2.0f));
}
void DualComplexTest::translation() {
@ -223,8 +228,8 @@ void DualComplexTest::combinedTransformParts() {
DualComplex a = DualComplex::translation(translation)*DualComplex::rotation(Deg(23.0f));
DualComplex b = DualComplex::rotation(Deg(23.0f))*DualComplex::translation(translation);
CORRADE_COMPARE_AS(a.rotationAngle(), Deg(23.0f), Rad);
CORRADE_COMPARE_AS(b.rotationAngle(), Deg(23.0f), Rad);
CORRADE_COMPARE_AS(a.rotation().angle(), Deg(23.0f), Rad);
CORRADE_COMPARE_AS(b.rotation().angle(), Deg(23.0f), Rad);
CORRADE_COMPARE(a.translation(), translation);
CORRADE_COMPARE(b.translation(), Complex::rotation(Deg(23.0f)).transformVector(translation));
}

17
src/Math/Test/DualQuaternionTest.cpp
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@ -210,8 +210,13 @@ void DualQuaternionTest::rotation() {
DualQuaternion q = DualQuaternion::rotation(Deg(120.0f), axis);
CORRADE_COMPARE(q.length(), 1.0f);
CORRADE_COMPARE(q, DualQuaternion({Vector3(0.5f, 0.5f, 0.5f), 0.5f}, {{}, 0.0f}));
CORRADE_COMPARE_AS(q.rotationAngle(), Deg(120.0f), Deg);
CORRADE_COMPARE(q.rotationAxis(), axis);
CORRADE_COMPARE_AS(q.rotation().angle(), Deg(120.0f), Deg);
CORRADE_COMPARE(q.rotation().axis(), axis);
/* Constexpr access to rotation */
constexpr DualQuaternion b({{-1.0f, 2.0f, 3.0f}, 4.0f}, {});
constexpr Quaternion c = b.rotation();
CORRADE_COMPARE(c, Quaternion({-1.0f, 2.0f, 3.0f}, 4.0f));
}
void DualQuaternionTest::translation() {
@ -227,10 +232,10 @@ void DualQuaternionTest::combinedTransformParts() {
DualQuaternion a = DualQuaternion::translation(translation)*DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis());
DualQuaternion b = DualQuaternion::rotation(Deg(23.0f), Vector3::xAxis())*DualQuaternion::translation(translation);
CORRADE_COMPARE(a.rotationAxis(), Vector3::xAxis());
CORRADE_COMPARE(b.rotationAxis(), Vector3::xAxis());
CORRADE_COMPARE_AS(a.rotationAngle(), Deg(23.0f), Rad);
CORRADE_COMPARE_AS(b.rotationAngle(), Deg(23.0f), Rad);
CORRADE_COMPARE(a.rotation().axis(), Vector3::xAxis());
CORRADE_COMPARE(b.rotation().axis(), Vector3::xAxis());
CORRADE_COMPARE_AS(a.rotation().angle(), Deg(23.0f), Rad);
CORRADE_COMPARE_AS(b.rotation().angle(), Deg(23.0f), Rad);
CORRADE_COMPARE(a.translation(), translation);
CORRADE_COMPARE(b.translation(), Quaternion::rotation(Deg(23.0f), Vector3::xAxis()).transformVector(translation));

14
src/Math/Test/QuaternionTest.cpp
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@ -255,19 +255,19 @@ void QuaternionTest::rotation() {
Quaternion q = Quaternion::rotation(Deg(120.0f), axis);
CORRADE_COMPARE(q.length(), 1.0f);
CORRADE_COMPARE(q, Quaternion(Vector3(0.5f, 0.5f, 0.5f), 0.5f));
CORRADE_COMPARE_AS(q.rotationAngle(), Deg(120.0f), Deg);
CORRADE_COMPARE(q.rotationAxis(), axis);
CORRADE_COMPARE(q.rotationAxis().length(), 1.0f);
CORRADE_COMPARE_AS(q.angle(), Deg(120.0f), Deg);
CORRADE_COMPARE(q.axis(), axis);
CORRADE_COMPARE(q.axis().length(), 1.0f);
/* Verify negative angle */
Quaternion q2 = Quaternion::rotation(Deg(-120.0f), axis);
CORRADE_COMPARE(q2, Quaternion(Vector3(-0.5f, -0.5f, -0.5f), 0.5f));
CORRADE_COMPARE_AS(q2.rotationAngle(), Deg(120.0f), Deg);
CORRADE_COMPARE(q2.rotationAxis(), -axis);
CORRADE_COMPARE_AS(q2.angle(), Deg(120.0f), Deg);
CORRADE_COMPARE(q2.axis(), -axis);
/* Default-constructed quaternion has zero angle and NaN axis */
CORRADE_COMPARE_AS(Quaternion().rotationAngle(), Deg(0.0f), Deg);
CORRADE_VERIFY(Quaternion().rotationAxis() != Quaternion().rotationAxis());
CORRADE_COMPARE_AS(Quaternion().angle(), Deg(0.0f), Deg);
CORRADE_VERIFY(Quaternion().axis() != Quaternion().axis());
}
void QuaternionTest::angle() {

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