AxisAngle.hpp
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/**
* @file AxisAngle.hpp
*
* @author James Goppert <james.goppert@gmail.com>
*/
#pragma once
#include "math.hpp"
namespace matrix
{
template <typename Type>
class Dcm;
template <typename Type>
class Euler;
template <typename Type>
class AxisAngle;
/**
* AxisAngle class
*
* The rotation between two coordinate frames is
* described by this class.
*/
template<typename Type>
class AxisAngle : public Vector<Type, 3>
{
public:
using Matrix31 = Matrix<Type, 3, 1>;
/**
* Constructor from array
*
* @param data_ array
*/
explicit AxisAngle(const Type data_[3]) :
Vector<Type, 3>(data_)
{
}
/**
* Standard constructor
*/
AxisAngle() = default;
/**
* Constructor from Matrix31
*
* @param other Matrix31 to copy
*/
AxisAngle(const Matrix31 &other) :
Vector<Type, 3>(other)
{
}
/**
* Constructor from quaternion
*
* This sets the instance from a quaternion representing coordinate transformation from
* frame 2 to frame 1 where the rotation from frame 1 to frame 2 is described
* by a 3-2-1 intrinsic Tait-Bryan rotation sequence.
*
* @param q quaternion
*/
AxisAngle(const Quaternion<Type> &q)
{
AxisAngle &v = *this;
Type mag = q.imag().norm();
if (fabs(mag) >= Type(1e-10)) {
v = q.imag() * Type(Type(2) * atan2(mag, q(0)) / mag);
} else {
v = q.imag() * Type(Type(2) * Type(sign(q(0))));
}
}
/**
* Constructor from dcm
*
* Instance is initialized from a dcm representing coordinate transformation
* from frame 2 to frame 1.
*
* @param dcm dcm to set quaternion to
*/
AxisAngle(const Dcm<Type> &dcm)
{
AxisAngle &v = *this;
v = AxisAngle<Type>(Quaternion<Type>(dcm));
}
/**
* Constructor from euler angles
*
* This sets the instance to a quaternion representing coordinate transformation from
* frame 2 to frame 1 where the rotation from frame 1 to frame 2 is described
* by a 3-2-1 intrinsic Tait-Bryan rotation sequence.
*
* @param euler euler angle instance
*/
AxisAngle(const Euler<Type> &euler)
{
AxisAngle &v = *this;
v = AxisAngle<Type>(Quaternion<Type>(euler));
}
/**
* Constructor from 3 axis angle values (unit vector * angle)
*
* @param x r_x*angle
* @param y r_y*angle
* @param z r_z*angle
*/
AxisAngle(Type x, Type y, Type z)
{
AxisAngle &v = *this;
v(0) = x;
v(1) = y;
v(2) = z;
}
/**
* Constructor from axis and angle
*
* @param axis An axis of rotation, normalized if not unit length
* @param angle The amount to rotate
*/
AxisAngle(const Matrix31 & axis_, Type angle_)
{
AxisAngle &v = *this;
// make sure axis is a unit vector
Vector<Type, 3> a = axis_;
a = a.unit();
v(0) = a(0)*angle_;
v(1) = a(1)*angle_;
v(2) = a(2)*angle_;
}
Vector<Type, 3> axis() {
if (Vector<Type, 3>::norm() > 0) {
return Vector<Type, 3>::unit();
} else {
return Vector3<Type>(1, 0, 0);
}
}
Type angle() {
return Vector<Type, 3>::norm();
}
};
using AxisAnglef = AxisAngle<float>;
using AxisAngled = AxisAngle<double>;
} // namespace matrix
/* vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 : */