Orbital Aero Model: Quaternion Class

This is one of a series of posts for how orientations and rotations are handled in the orbital aero model (original post in series). This Quaternion class ties in with the Vector, Euler, and Matrix classes also posted.

Quaternion.h

#pragma once
// Math cobbled together from a variety of sources:
// Introduction into quaternions for spacecraft attitude representation
// Dipl. -Ing. Karsten Groÿekatthöfer, Dr. -Ing. Zizung Yoon, May 31, 2012
// Implementation for a generalized quaternion class - Angela Bennett, 1.25.00
// http://www.gamedev.net/topic/621943-quaternion-object-rotation/
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
// http://www.blitzmax.com/Community/posts.php?topic=66504
// https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions
// http://www.haroldserrano.com/blog/developing-a-math-engine-in-c-implementing-quaternions
// https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles

#include <iostream>
#include <math.h>

class Euler;
class Vector;
class Matrix;

class Quaternion
{
private:
public:

double w;
double x;
double y;
double z;

// Create a quaternion equivalent to euler (0,0,0).
Quaternion();

// Create a quaternion from 4 inputs.
Quaternion(const double newW, const double newX, const double newY, const double newZ);

// Create a quaternion matching to another quaternion.
Quaternion(const Quaternion &newQuaternion);

// Create a quaternion from euler angles (in radians).
Quaternion(const Euler &newEulerAngle);

// Destructor
~Quaternion();

// Sets the quaternion to another quaternion.
Quaternion operator = (const Quaternion &qToCopy);

// Adds the quaternion to another quaternion.
Quaternion operator + (const Quaternion &qToAdd) const;

// Subtracts the quaternion by another quaternion.
Quaternion operator - (const Quaternion &qToSubtract) const;

// Multiplies the quaternion by another quaternion.
Quaternion operator * (const Quaternion &qToMultiply) const;

// Divides the quaternion by another quaternion.
Quaternion operator / (const Quaternion &qToDivide) const;

// Divides the quaternion by a scalar.
Quaternion operator / (const double valueToDivide) const;

// Adds the quaternion to another quaternion.
Quaternion &operator += (const Quaternion &qToAdd);

// Subtracts the quaternion by another quaternion.
Quaternion &operator -= (const Quaternion &qToSubtract);

// Multiplies the quaternion by another quaternion.
Quaternion &operator *= (const Quaternion &qToMultiply);

// Divides the quaternion by another quaternion.
Quaternion &operator /= (const Quaternion &qToDivide);

// Divides the quaternion by a scalar.
Quaternion &operator /= (const double valueToDivide);

// Returns if two quaternions are not equal.
bool operator != (const Quaternion &qToCompare) const;

// Returns if two quaternions are equal.
bool operator == (const Quaternion &qToCompare) const;

// Set the quaternion to the equivalent of euler angle (0,0,0).
void clear();

// Get the norm of the quaternion.
double norm() const;

// Get a quaternion scaled by a given scalar.
Quaternion scaledBy(const double valueToScale) const;

// Get the inverse of the quaternion.
Quaternion inverse() const;

// Get the conjugate of the quaternion.
Quaternion conjugate() const;

// Get the unit (normalization) of the quaternion.
Quaternion unit() const;

// Normalize the quaternion.
void normalize();

// Set the quaternion from euler angles (in radians).
void fromEulerAngles(const Euler &newEulerAngle);

// Get the euler angles (in radians) of the quaternion.
Euler toEulerAngles() const;

//void Quaternion::FromPYR(float pitch_radians, float yaw_radians, float roll_radians);

// Set the quaternion based on a rotation about the X axis.
void fromXRotation(const double angle_radians);

// Set the quaternion based on a rotation about the Y axis.
void fromYRotation(const double angle_radians);

// Set the quaternion based on a rotation about the Z axis.
void fromZRotation(const double angle_radians);

// Get the transformation matrix for this quaternion orientation.
Matrix transformationMatrix() const;

//Quaternion fromYawPitchRoll(Euler ypr);

// Rotate the quaternion about the local axis by a pitch/roll/heading.
void rotateAboutLocalAxis(const Euler &rotationAngle_radians);

// Rotate the quaternion about the world axis.
void Quaternion::rotateAboutWorldAxis(const Euler &rotationAngles_radians);
};

Quaternion.cpp

#include "math.h"
#include "Euler.h"
#include "Matrix.h"
#include "Quaternion.h"

// Create a quaternion equivalent to euler (0,0,0).
Quaternion::Quaternion()
{
// Equivalent of euler angle (0,0,0).
this->w = 1.0;
this->x = 0.0;
this->y = 0.0;
this->z = 0.0;
return;
}

// Create a quaternion from 4 inputs.
Quaternion::Quaternion(const double newW, const double newX, const double newY, const double newZ)
{
this->w = newW;
this->x = newX;
this->y = newY;
this->z = newZ;
return;
}

// Create a quaternion matching to another quaternion.
Quaternion::Quaternion(const Quaternion &newQuaternion)
{
this->w = newQuaternion.w;
this->x = newQuaternion.x;
this->y = newQuaternion.y;
this->z = newQuaternion.z;
return;
} 

// Create a quaternion from euler angles (in radians).
Quaternion::Quaternion(const Euler &newEulerAngle)
{
this->fromEulerAngles(newEulerAngle);
}

// Destructor
Quaternion::~Quaternion()
{
}

// Sets the quaternion to another quaternion.
Quaternion Quaternion::operator = (const Quaternion &qToCopy)
{
this->w = qToCopy.w;
this->x = qToCopy.x;
this->y = qToCopy.y;
this->z = qToCopy.z;
  
  return *this;
}

// Adds the quaternion to another quaternion.
Quaternion Quaternion::operator + (const Quaternion &qToAdd) const
{
return Quaternion(this->w + qToAdd.w, this->x + qToAdd.x, this->y + qToAdd.y, this->z + qToAdd.z);
}
  
// Subtracts the quaternion by another quaternion.
Quaternion Quaternion::operator - (const Quaternion &qToSubtract) const
{
return Quaternion(this->w - qToSubtract.w, this->x - qToSubtract.x, this->y - qToSubtract.y, this->z - qToSubtract.z);
}

// Multiplies the quaternion by another quaternion.
Quaternion Quaternion::operator * (const Quaternion &qToMultiply) const
{
return Quaternion((this->w * qToMultiply.w) - (this->x * qToMultiply.x) - (this->y * qToMultiply.y) - (this->z * qToMultiply.z),
 (this->w * qToMultiply.x) + (this->x * qToMultiply.w) + (this->y * qToMultiply.z) - (this->z * qToMultiply.y),
 (this->w * qToMultiply.y) + (this->y * qToMultiply.w) + (this->z * qToMultiply.x) - (this->x * qToMultiply.z),
 (this->w * qToMultiply.z) + (this->z * qToMultiply.w) + (this->x * qToMultiply.y) - (this->y * qToMultiply.x));
}

// Divides the quaternion by another quaternion.
Quaternion Quaternion::operator / (const Quaternion &qToDivide) const
{
return ((*this) * qToDivide.inverse());
}

// Divides the quaternion by a scalar.
Quaternion Quaternion::operator / (const double valueToDivide) const
{
if (valueToDivide != 0.0)
{
return Quaternion(this->w / valueToDivide, this->x / valueToDivide, this->y / valueToDivide, this->z / valueToDivide);
}
else
{
return Quaternion(this->w, this->x, this->y, this->z);
}
}

// Adds the quaternion to another quaternion.
Quaternion& Quaternion::operator += (const Quaternion &qToAdd)
{
this->w += qToAdd.w;
this->x += qToAdd.x;
this->y += qToAdd.y;
this->z += qToAdd.z;

  return (*this);
}

// Subtracts the quaternion by another quaternion.
Quaternion& Quaternion::operator -= (const Quaternion &qToSubtract)
{
this->w -= qToSubtract.w;
this->x -= qToSubtract.x;
this->y -= qToSubtract.y;
this->z -= qToSubtract.z;

  return (*this);
}

// Multiplies the quaternion by another quaternion.
Quaternion& Quaternion::operator *= (const Quaternion &qToMultiply)
{
double newW = (this->w * qToMultiply.w) - (this->x * qToMultiply.x) - (this->y * qToMultiply.y) - (this->z * qToMultiply.z);
double newX = (this->w * qToMultiply.x) + (this->x * qToMultiply.w) + (this->y * qToMultiply.z) - (this->z * qToMultiply.y);
double newY = (this->w * qToMultiply.y) + (this->y * qToMultiply.w) + (this->z * qToMultiply.x) - (this->x * qToMultiply.z);
double newZ = (this->w * qToMultiply.z) + (this->z * qToMultiply.w) + (this->x * qToMultiply.y) - (this->y * qToMultiply.x);
  
this->w = newW;
this->x = newX;
this->y = newY;
this->z = newZ;

return (*this);
}

// Divides the quaternion by another quaternion.
Quaternion& Quaternion::operator /= (const Quaternion &qToDivide)
{
(*this) = (*this) * qToDivide.inverse();
return (*this);
}

// Divides the quaternion by a scalar.
Quaternion& Quaternion::operator /= (const double valueToDivide)
{
this->w /= valueToDivide;
this->x /= valueToDivide;
this->y /= valueToDivide;
this->z /= valueToDivide;
return (*this);
}

// Returns if two quaternions are not equal.
bool Quaternion::operator != (const Quaternion &qToCompare) const
{
if ((this->w != qToCompare.w) || (this->x != qToCompare.x) || (this->y != qToCompare.y) || (this->z != qToCompare.z))
{
return true;
}
else
{
return false;
}
}

// Returns if two quaternions are equal.
bool Quaternion::operator == (const Quaternion &qToCompare) const
{
if ((this->w == qToCompare.w) && (this->x == qToCompare.x) && (this->y == qToCompare.y) && (this->z == qToCompare.z))
{
return true;
}
else
{
return false;
}
}  

// Set the quaternion to the equivalent of euler angle (0,0,0).
void Quaternion::clear()
{
// Equivalent of euler angle (0,0,0).
this->w = 1.0;
this->x = 0.0;
this->y = 0.0;
this->z = 0.0;
return;
}

// Get the norm of the quaternion.
double Quaternion::norm() const
{
// |q| = sqrt(w*w + x*x + y*y + z*z)
return sqrt( (this->w * this->w) + (this->x * this->x) + (this->y * this->y) + (this->z * this->z) );
}

// Get a quaternion scaled by a given scalar.
Quaternion Quaternion::scaledBy(const double valueToScale) const
{
return Quaternion(this->w * valueToScale, this->x * valueToScale, this->y * valueToScale, this->z * valueToScale);
}

// Get the inverse of the quaternion.
Quaternion Quaternion::inverse() const
{
// q^-1 = q* / |q|
double quatNorm = this->norm();
return (this->conjugate() / (quatNorm * quatNorm));
}

// Get the conjugate of the quaternion.
Quaternion Quaternion::conjugate() const
{
// q* = [w, -x , -y, -z]
return Quaternion(this->w, -this->x, -this->y, -this->z);
}

// Get the unit (normalization) of the quaternion.
Quaternion Quaternion::unit() const
{
// Unit: ||q|| = q / |q|
return ((*this) / this->norm());
}

// Normalize the quaternion.
void Quaternion::normalize()
{
// Unit: ||q|| = q / |q|
(*this) /= this->norm();
return;
}

// Set the quaternion from euler angles (in radians).
void Quaternion::fromEulerAngles(const Euler &newEulerAngle)
{
double halfPsi = newEulerAngle.psi * 0.5;
double halfTheta = newEulerAngle.theta * -0.5;
double halfPhi = newEulerAngle.phi * 0.5;

double cosPsi = cos(halfPsi);
double cosTheta = cos(halfTheta);
double cosPhi = cos(halfPhi);

double sinPsi = sin(halfPsi);
double sinTheta = sin(halfTheta);
double sinPhi = sin(halfPhi);

double cosPsiCosPhi = cosPsi * cosPhi;
double cosPsiSinPhi = cosPsi * sinPhi;
double sinPsiCosPhi = sinPsi * cosPhi;
double sinPsiSinPhi = sinPsi * sinPhi;

this->w = (cosTheta * cosPsiCosPhi) + (sinTheta * sinPsiSinPhi);
this->x = (cosTheta * cosPsiSinPhi) - (sinTheta * sinPsiCosPhi);
this->y = -(cosTheta * sinPsiSinPhi) - (sinTheta * cosPsiCosPhi);
this->z = (cosTheta * sinPsiCosPhi) - (sinTheta * cosPsiSinPhi);

return;
}

// Get the euler angles (in radians) of the quaternion.
Euler Quaternion::toEulerAngles() const
{
Euler newEulerAngle;
double xw = this->x * this->w;
double yw = this->y * this->w;
double zw = this->z * this->w;

double xz = this->x * this->z;
double yz = this->y * this->z;
double xy = this->x * this->y;

double xx = this->x * this->x;
double yy = this->y * this->y;
double zz = this->z * this->z;

newEulerAngle.phi = atan2((2 * (xw + yz)), (1 - 2 * (xx + yy)));
newEulerAngle.theta = asin(2 * (yw - xz));
newEulerAngle.psi = atan2((2 * (zw + xy)), (1 - 2 * (yy + zz)));

while (newEulerAngle.psi < 0.0)
{
newEulerAngle.psi += 2 * 3.1415926;
}
return newEulerAngle;
}

// Set the quaternion based on a rotation about the X axis.
void Quaternion::fromXRotation(const double angle_radians)
{
this->w = cos(angle_radians / 2);
this->x = sin(angle_radians / 2);
this->y = 0.0;
this->z = 0.0;
return;
}

// Set the quaternion based on a rotation about the Y axis.
void Quaternion::fromYRotation(const double angle_radians)
{
this->w = cos(angle_radians / 2);
this->x = 0.0;
this->y = sin(angle_radians / 2);
this->z = 0.0;
return;
}

// Set the quaternion based on a rotation about the Z axis.
void Quaternion::fromZRotation(const double angle_radians)
{
this->w = cos(angle_radians / 2);
this->x = 0.0;
this->y = 0.0;
this->z = sin(angle_radians / 2);
return;
}

// Get the transformation matrix for this quaternion orientation.
Matrix Quaternion::transformationMatrix() const
{
double xx = this->x * this->x;
double xy = this->x * this->y;
double xz = this->x * this->z;
double xw = this->x * this->w;

double yy = this->y * this->y;
double yz = this->y * this->z;
double yw = this->y * this->w;

double zz = this->z * this->z;
double zw = this->z * this->w;

Matrix rotationMatrix;
rotationMatrix.value[0][0] = 1 - 2 * (yy + zz);
rotationMatrix.value[1][0] = 2 * (xy - zw);
rotationMatrix.value[2][0] = 2 * (xz + yw);

rotationMatrix.value[0][1] = 2 * (xy + zw);
rotationMatrix.value[1][1] = 1 - 2 * (xx + zz);
rotationMatrix.value[2][1] = 2 * (yz - xw);

rotationMatrix.value[0][2] = 2 * (xz - yw);
rotationMatrix.value[1][2] = 2 * (yz + xw);
rotationMatrix.value[2][2] = 1 - 2 * (xx + yy);

return rotationMatrix;
}

// Rotate the quaternion about the local axis by a pitch/roll/heading.
void Quaternion::rotateAboutLocalAxis(const Euler &rotationAngles_radians)
{
(*this) *= Quaternion(rotationAngles_radians);

return;
}

// Rotate the quaternion about the world axis.
void Quaternion::rotateAboutWorldAxis(const Euler &rotationAngles_radians)
{
Quaternion xOffset = Quaternion();
Quaternion yOffset = Quaternion();
Quaternion zOffset = Quaternion();

xOffset.fromXRotation(rotationAngles_radians.phi);
yOffset.fromYRotation(rotationAngles_radians.theta);
zOffset.fromZRotation(rotationAngles_radians.psi);
(*this) = xOffset * yOffset * zOffset * (*this);

this->normalize();

return;
}

Copyright (c) 2017 Clinton Kam
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