mxvk::QuatType Class Reference

Quaternion used for 3D rotations. More...

#include <mxvk/include/mxvk/mxvk_math.h>

Public Member Functions
void	Conj ()
	Conjugate this quaternion in place.
void	Conj ()
	Conjugate this quaternion in place.
void	EulerZYX (float theta_x, float theta_y, float theta_z)
	Build a quaternion from Euler angles in ZYX order, with angles in degrees.
void	EulerZYX (float theta_x, float theta_y, float theta_z)
	Build a quaternion from Euler angles in ZYX order, with angles in degrees.
void	Inverse ()
	Invert this quaternion in place.
void	Inverse ()
	Invert this quaternion in place.
void	InverseNormal ()
	Invert a unit quaternion by conjugating it.
void	InverseNormal ()
	Invert a unit quaternion by conjugating it.
float	Norm () const
	Compute the norm.
float	Norm () const
	Compute the norm.
float	Norm2 () const
	Compute the squared norm.
float	Norm2 () const
	Compute the squared norm.
void	Normalize ()
	Normalize this quaternion in place, or reset it to identity if it is too small.
void	Normalize ()
	Normalize this quaternion in place, or reset it to identity if it is too small.
constexpr QuatType	operator* (const QuatType &q) const
	Multiply two quaternions.
constexpr QuatType	operator* (const QuatType &q) const
	Multiply two quaternions.
QuatType &	operator*= (const QuatType &q)
	Multiply this quaternion by another quaternion in place.
QuatType &	operator*= (const QuatType &q)
	Multiply this quaternion by another quaternion in place.
constexpr QuatType	operator+ (const QuatType &q) const
	Add two quaternions component-wise.
constexpr QuatType	operator+ (const QuatType &q) const
	Add two quaternions component-wise.
constexpr QuatType	operator- (const QuatType &q) const
	Subtract two quaternions component-wise.
constexpr QuatType	operator- (const QuatType &q) const
	Subtract two quaternions component-wise.
void	QuatToVec3D (float *theta_degrees, vec3D &axis) const
	Convert this quaternion to axis-angle form.
void	QuatToVec3D (float *theta_degrees, vec3D &axis) const
	Convert this quaternion to axis-angle form.
constexpr	QuatType ()
	Construct the identity quaternion.
constexpr	QuatType ()
	Construct the identity quaternion.
constexpr	QuatType (float x_value, float y_value, float z_value, float w_value)
	Construct from explicit quaternion components.
constexpr	QuatType (float x_value, float y_value, float z_value, float w_value)
	Construct from explicit quaternion components.
void	Scale (float f)
	Scale all quaternion components in place.
void	Scale (float f)
	Scale all quaternion components in place.
QuatType	TripleProduct (const QuatType &p1, const QuatType &p2) const
	Return the quaternion product (*this * p1) * p2.
QuatType	TripleProduct (const QuatType &p1, const QuatType &p2) const
	Return the quaternion product (*this * p1) * p2.
void	vec3DthetaQuat (float theta_degrees, const vec3D &axis)
	Build a quaternion from an axis and angle in degrees.
void	vec3DthetaQuat (float theta_degrees, const vec3D &axis)
	Build a quaternion from an axis and angle in degrees.
void	vec4DthetaQuat (float theta_degrees, const vec4D &axis)
	Build a quaternion from a 4D axis vector and angle in degrees.
void	vec4DthetaQuat (float theta_degrees, const vec4D &axis)
	Build a quaternion from a 4D axis vector and angle in degrees.

Public Attributes
float	w = 1.0f
	Scalar component.
float	x = 0.0f
	X component of the vector part.
float	y = 0.0f
	Y component of the vector part.
float	z = 0.0f
	Z component of the vector part.

Detailed Description

Quaternion used for 3D rotations.

Definition at line 1170 of file mxvk_math.h.

Constructor & Destructor Documentation

QuatType() [1/4]

mxvk::QuatType::QuatType ( )

inlineconstexpr

Construct the identity quaternion.

Definition at line 1185 of file mxvk_math.h.

: x(0.0f), y(0.0f), z(0.0f), w(1.0f) {}

QuatType() [2/4]

mxvk::QuatType::QuatType ( float x_value, float y_value, float z_value, float w_value )

inlineconstexpr

Construct from explicit quaternion components.

Definition at line 1188 of file mxvk_math.h.

: x(x_value), y(y_value), z(z_value), w(w_value) {}

QuatType() [3/4]

mxvk::QuatType::QuatType ( )

inlineconstexpr

Construct the identity quaternion.

Definition at line 1185 of file mxvk_math_eigen.hpp.

: x(0.0f), y(0.0f), z(0.0f), w(1.0f) {}

QuatType() [4/4]

mxvk::QuatType::QuatType ( float x_value, float y_value, float z_value, float w_value )

inlineconstexpr

Construct from explicit quaternion components.

Definition at line 1188 of file mxvk_math_eigen.hpp.

: x(x_value), y(y_value), z(z_value), w(w_value) {}

Member Function Documentation

Conj() [1/2]

void mxvk::QuatType::Conj ( )

inline

Conjugate this quaternion in place.

Definition at line 1215 of file mxvk_math.h.

                    {
            x = -x;
            y = -y;
            z = -z;
        }

Conj() [2/2]

void mxvk::QuatType::Conj ( )

inline

Conjugate this quaternion in place.

Definition at line 1215 of file mxvk_math_eigen.hpp.

                    {
            x = -x;
            y = -y;
            z = -z;
        }

EulerZYX() [1/2]

void mxvk::QuatType::EulerZYX ( float theta_x, float theta_y, float theta_z )

inline

Build a quaternion from Euler angles in ZYX order, with angles in degrees.

Definition at line 1293 of file mxvk_math.h.

                                                                   {
            const float hx = deg2rad(theta_x) * 0.5f;
            const float hy = deg2rad(theta_y) * 0.5f;
            const float hz = deg2rad(theta_z) * 0.5f;
            const float cx = std::cos(hx);
            const float sx = std::sin(hx);
            const float cy = std::cos(hy);
            const float sy = std::sin(hy);
            const float cz = std::cos(hz);
            const float sz = std::sin(hz);
            w = cz * cy * cx + sz * sy * sx;
            x = cz * cy * sx - sz * sy * cx;
            y = cz * sy * cx + sz * cy * sx;
            z = sz * cy * cx - cz * sy * sx;
        }

EulerZYX() [2/2]

void mxvk::QuatType::EulerZYX ( float theta_x, float theta_y, float theta_z )

inline

Build a quaternion from Euler angles in ZYX order, with angles in degrees.

Definition at line 1293 of file mxvk_math_eigen.hpp.

                                                                   {
            const float hx = deg2rad(theta_x) * 0.5f;
            const float hy = deg2rad(theta_y) * 0.5f;
            const float hz = deg2rad(theta_z) * 0.5f;
            const float cx = std::cos(hx);
            const float sx = std::sin(hx);
            const float cy = std::cos(hy);
            const float sy = std::sin(hy);
            const float cz = std::cos(hz);
            const float sz = std::sin(hz);
            w = cz * cy * cx + sz * sy * sx;
            x = cz * cy * sx - sz * sy * cx;
            y = cz * sy * cx + sz * cy * sx;
            z = sz * cy * cx - cz * sy * sx;
        }

Inverse() [1/2]

void mxvk::QuatType::Inverse ( )

inline

Invert this quaternion in place.

Definition at line 1251 of file mxvk_math.h.

                       {
            const float n2 = Norm2();
            if (n2 <= EPSILON) {
                x = y = z = 0.0f;
                w = 1.0f;
                return;
            }
            x = -x / n2;
            y = -y / n2;
            z = -z / n2;
            w = w / n2;
        }

Inverse() [2/2]

void mxvk::QuatType::Inverse ( )

inline

Invert this quaternion in place.

Definition at line 1251 of file mxvk_math_eigen.hpp.

                       {
            const float n2 = Norm2();
            if (n2 <= EPSILON) {
                x = y = z = 0.0f;
                w = 1.0f;
                return;
            }
            x = -x / n2;
            y = -y / n2;
            z = -z / n2;
            w = w / n2;
        }

InverseNormal() [1/2]

void mxvk::QuatType::InverseNormal ( )

inline

Invert a unit quaternion by conjugating it.

Definition at line 1265 of file mxvk_math.h.

                             {
            Conj();
        }

InverseNormal() [2/2]

void mxvk::QuatType::InverseNormal ( )

inline

Invert a unit quaternion by conjugating it.

Definition at line 1265 of file mxvk_math_eigen.hpp.

                             {
            Conj();
        }

Norm() [1/2]

float mxvk::QuatType::Norm ( ) const

inlinenodiscard

Compute the norm.

Definition at line 1235 of file mxvk_math.h.

                                         {
            return std::sqrt(Norm2());
        }

Norm() [2/2]

float mxvk::QuatType::Norm ( ) const

inlinenodiscard

Compute the norm.

Definition at line 1235 of file mxvk_math_eigen.hpp.

                                         {
            return std::sqrt(Norm2());
        }

Norm2() [1/2]

float mxvk::QuatType::Norm2 ( ) const

inlinenodiscard

Compute the squared norm.

Definition at line 1230 of file mxvk_math.h.

                                          {
            return w * w + x * x + y * y + z * z;
        }

Norm2() [2/2]

float mxvk::QuatType::Norm2 ( ) const

inlinenodiscard

Compute the squared norm.

Definition at line 1230 of file mxvk_math_eigen.hpp.

                                          {
            return w * w + x * x + y * y + z * z;
        }

Normalize() [1/2]

void mxvk::QuatType::Normalize ( )

inline

Normalize this quaternion in place, or reset it to identity if it is too small.

Definition at line 1240 of file mxvk_math.h.

                         {
            const float norm = Norm();
            if (norm <= EPSILON) {
                x = y = z = 0.0f;
                w = 1.0f;
                return;
            }
            Scale(1.0f / norm);
        }

Normalize() [2/2]

void mxvk::QuatType::Normalize ( )

inline

Normalize this quaternion in place, or reset it to identity if it is too small.

Definition at line 1240 of file mxvk_math_eigen.hpp.

                         {
            const float norm = Norm();
            if (norm <= EPSILON) {
                x = y = z = 0.0f;
                w = 1.0f;
                return;
            }
            Scale(1.0f / norm);
        }

operator*() [1/2]

QuatType mxvk::QuatType::operator* ( const QuatType & q ) const

inlinenodiscardconstexpr

Multiply two quaternions.

Definition at line 1201 of file mxvk_math.h.

                                                                            {
            return {w * q.x + x * q.w + y * q.z - z * q.y,
                    w * q.y - x * q.z + y * q.w + z * q.x,
                    w * q.z + x * q.y - y * q.x + z * q.w,
                    w * q.w - x * q.x - y * q.y - z * q.z};
        }

operator*() [2/2]

QuatType mxvk::QuatType::operator* ( const QuatType & q ) const

inlinenodiscardconstexpr

Multiply two quaternions.

Definition at line 1201 of file mxvk_math_eigen.hpp.

                                                                            {
            return {w * q.x + x * q.w + y * q.z - z * q.y,
                    w * q.y - x * q.z + y * q.w + z * q.x,
                    w * q.z + x * q.y - y * q.x + z * q.w,
                    w * q.w - x * q.x - y * q.y - z * q.z};
        }

operator*=() [1/2]

QuatType & mxvk::QuatType::operator*= ( const QuatType & q )

inline

Multiply this quaternion by another quaternion in place.

Definition at line 1209 of file mxvk_math.h.

                                              {
            *this = *this * q;
            return *this;
        }

operator*=() [2/2]

QuatType & mxvk::QuatType::operator*= ( const QuatType & q )

inline

Multiply this quaternion by another quaternion in place.

Definition at line 1209 of file mxvk_math_eigen.hpp.

                                              {
            *this = *this * q;
            return *this;
        }

operator+() [1/2]

QuatType mxvk::QuatType::operator+ ( const QuatType & q ) const

inlinenodiscardconstexpr

Add two quaternions component-wise.

Definition at line 1191 of file mxvk_math.h.

                                                                            {
            return {x + q.x, y + q.y, z + q.z, w + q.w};
        }

operator+() [2/2]

QuatType mxvk::QuatType::operator+ ( const QuatType & q ) const

inlinenodiscardconstexpr

Add two quaternions component-wise.

Definition at line 1191 of file mxvk_math_eigen.hpp.

                                                                            {
            return {x + q.x, y + q.y, z + q.z, w + q.w};
        }

operator-() [1/2]

QuatType mxvk::QuatType::operator- ( const QuatType & q ) const

inlinenodiscardconstexpr

Subtract two quaternions component-wise.

Definition at line 1196 of file mxvk_math.h.

                                                                            {
            return {x - q.x, y - q.y, z - q.z, w - q.w};
        }

operator-() [2/2]

QuatType mxvk::QuatType::operator- ( const QuatType & q ) const

inlinenodiscardconstexpr

Subtract two quaternions component-wise.

Definition at line 1196 of file mxvk_math_eigen.hpp.

                                                                            {
            return {x - q.x, y - q.y, z - q.z, w - q.w};
        }

QuatToVec3D() [1/2]

void mxvk::QuatType::QuatToVec3D ( float * theta_degrees, vec3D & axis ) const

inline

Convert this quaternion to axis-angle form.

Definition at line 1310 of file mxvk_math.h.

                                                                  {
            QuatType q = *this;
            q.Normalize();
            const float s = std::sqrt(std::max(0.0f, 1.0f - q.w * q.w));
            if (s <= EPSILON) {
                axis.Set(1.0f, 0.0f, 0.0f);
            } else {
                axis.Set(q.x / s, q.y / s, q.z / s);
            }
            if (theta_degrees != nullptr) {
                *theta_degrees = rad2deg(2.0f * std::acos(std::clamp(q.w, -1.0f, 1.0f)));
            }
        }

QuatToVec3D() [2/2]

void mxvk::QuatType::QuatToVec3D ( float * theta_degrees, vec3D & axis ) const

inline

Convert this quaternion to axis-angle form.

Definition at line 1310 of file mxvk_math_eigen.hpp.

                                                                  {
            QuatType q = *this;
            q.Normalize();
            const float s = std::sqrt(std::max(0.0f, 1.0f - q.w * q.w));
            if (s <= EPSILON) {
                axis.Set(1.0f, 0.0f, 0.0f);
            } else {
                axis.Set(q.x / s, q.y / s, q.z / s);
            }
            if (theta_degrees != nullptr) {
                *theta_degrees = rad2deg(2.0f * std::acos(std::clamp(q.w, -1.0f, 1.0f)));
            }
        }

Scale() [1/2]

void mxvk::QuatType::Scale ( float f )

inline

Scale all quaternion components in place.

Definition at line 1222 of file mxvk_math.h.

                            {
            x *= f;
            y *= f;
            z *= f;
            w *= f;
        }

Scale() [2/2]

void mxvk::QuatType::Scale ( float f )

inline

Scale all quaternion components in place.

Definition at line 1222 of file mxvk_math_eigen.hpp.

                            {
            x *= f;
            y *= f;
            z *= f;
            w *= f;
        }

TripleProduct() [1/2]

QuatType mxvk::QuatType::TripleProduct ( const QuatType & p1, const QuatType & p2 ) const

inlinenodiscard

Return the quaternion product (*this * p1) * p2.

Definition at line 1270 of file mxvk_math.h.

                                                                                           {
            return (*this * p1) * p2;
        }

TripleProduct() [2/2]

QuatType mxvk::QuatType::TripleProduct ( const QuatType & p1, const QuatType & p2 ) const

inlinenodiscard

Return the quaternion product (*this * p1) * p2.

Definition at line 1270 of file mxvk_math_eigen.hpp.

                                                                                           {
            return (*this * p1) * p2;
        }

vec3DthetaQuat() [1/2]

void mxvk::QuatType::vec3DthetaQuat ( float theta_degrees, const vec3D & axis )

inline

Build a quaternion from an axis and angle in degrees.

Definition at line 1275 of file mxvk_math.h.

                                                                    {
            vec3D n = axis;
            n.Normalize();
            const float half = deg2rad(theta_degrees) * 0.5f;
            const float s = std::sin(half);
            x = s * n.x;
            y = s * n.y;
            z = s * n.z;
            w = std::cos(half);
        }

vec3DthetaQuat() [2/2]

void mxvk::QuatType::vec3DthetaQuat ( float theta_degrees, const vec3D & axis )

inline

Build a quaternion from an axis and angle in degrees.

Definition at line 1275 of file mxvk_math_eigen.hpp.

                                                                    {
            vec3D n = axis;
            n.Normalize();
            const float half = deg2rad(theta_degrees) * 0.5f;
            const float s = std::sin(half);
            x = s * n.x;
            y = s * n.y;
            z = s * n.z;
            w = std::cos(half);
        }

vec4DthetaQuat() [1/2]

void mxvk::QuatType::vec4DthetaQuat ( float theta_degrees, const vec4D & axis )

inline

Build a quaternion from a 4D axis vector and angle in degrees.

Definition at line 1287 of file mxvk_math.h.

                                                                    {
            vec3D n(axis.x, axis.y, axis.z);
            vec3DthetaQuat(theta_degrees, n);
        }

vec4DthetaQuat() [2/2]

void mxvk::QuatType::vec4DthetaQuat ( float theta_degrees, const vec4D & axis )

inline

Build a quaternion from a 4D axis vector and angle in degrees.

Definition at line 1287 of file mxvk_math_eigen.hpp.

                                                                    {
            vec3D n(axis.x, axis.y, axis.z);
            vec3DthetaQuat(theta_degrees, n);
        }

Member Data Documentation

w

float mxvk::QuatType::w = 1.0f

Scalar component.

Definition at line 1182 of file mxvk_math.h.

x

float mxvk::QuatType::x = 0.0f

X component of the vector part.

Definition at line 1173 of file mxvk_math.h.

y

float mxvk::QuatType::y = 0.0f

Y component of the vector part.

Definition at line 1176 of file mxvk_math.h.

z

float mxvk::QuatType::z = 0.0f

Z component of the vector part.

Definition at line 1179 of file mxvk_math.h.

---

The documentation for this class was generated from the following files:

• mxvk/include/mxvk/mxvk_math.h
• mxvk/include/mxvk/mxvk_math_eigen.hpp