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/* Copyright (c) 2012 Patrick Ruoff
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*/
#pragma once
#include <cmath>
class Quat {
private:
static constexpr double pi = 3.141592653;
static constexpr double r2d = 180./pi;
double a,b,c,d; // quaternion coefficients
public:
Quat() : a(1.),b(0.),c(0.),d(0.) {}
Quat(double yaw, double pitch, double roll) { *this = from_euler_rads(yaw, pitch, roll); }
Quat(double a, double b, double c, double d) : a(a),b(b),c(c),d(d) {}
Quat inv() const
{
return Quat(a,-b,-c, -d);
}
// conversions
// see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
static Quat from_euler_rads(double yaw, double pitch, double roll)
{
const double sin_phi = sin(roll/2.);
const double cos_phi = cos(roll/2.);
const double sin_the = sin(pitch/2.);
const double cos_the = cos(pitch/2.);
const double sin_psi = sin(yaw/2.);
const double cos_psi = cos(yaw/2.);
Quat q;
q.a = cos_phi*cos_the*cos_psi + sin_phi*sin_the*sin_psi;
q.b = sin_phi*cos_the*cos_psi - cos_phi*sin_the*sin_psi;
q.c = cos_phi*sin_the*cos_psi + sin_phi*cos_the*sin_psi;
q.d = cos_phi*cos_the*sin_psi - sin_phi*sin_the*cos_psi;
return q;
}
void to_euler_rads(double& yaw, double& pitch, double& roll) const
{
roll = atan2(2.*(a*b + c*d), 1. - 2.*(b*b + c*c));
pitch = asin(2.*(a*c - b*d));
yaw = atan2(2.*(a*d + b*c), 1. - 2.*(c*c + d*d));
}
void to_euler_degrees(double& yaw, double& pitch, double& roll) const
{
to_euler_rads(yaw, pitch, roll);
yaw *= r2d;
pitch *= r2d;
roll *= r2d;
}
const Quat operator*(const Quat& B) const
{
const Quat& A = *this;
return Quat(A.a*B.a - A.b*B.b - A.c*B.c - A.d*B.d, // quaternion multiplication
A.a*B.b + A.b*B.a + A.c*B.d - A.d*B.c,
A.a*B.c - A.b*B.d + A.c*B.a + A.d*B.b,
A.a*B.d + A.b*B.c - A.c*B.b + A.d*B.a);
}
};
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