Unigine::Math::quat Struct

Header:

#include <UnigineMathLibQuat.h>

This class represents a quaternion type. Quaternions represent a rotation. Typically, they are used for smooth interpolation between two angles, and for avoiding the gimbal lock problem that can occur with euler angles.

Quaternions add a fourth element to the [x, y, z] values that define a vector, resulting in arbitrary 4-D vectors. The following example illustrates how each element of a unit quaternion relates to an axis-angle rotation, where q represents a unit quaternion (x, y, z, w), axis is normalized, and theta is the desired counterclockwise (CCW) rotation around the axis:

q.x = sin(theta/2) * axis.x
q.y = sin(theta/2) * axis.y
q.z = sin(theta/2) * axis.z
q.w = cos(theta/2)

Usage Example#

The following example creates a quaternion for node rotation: 60 degrees per second along Z axis.

Notice

It's supposed that you have already created node instance to rotate.

Source code (C++)

// AppWorldLogic.cpp file

int AppWorldLogic::update()
{
	/* ... */

	// get delta time value
	float delta_time = Game::getIFps();

	// create quat for 60 degrees per second rotation along Z axis
	Unigine::Math::quat rotation_delta = Unigine::Math::quat(0.0f, 0.0f, 1.0f, 60 * delta_time);

	// rotate the node
	node->WorldRotate(delta_rotation);

	/* ... */
}

In the example above, the quaternion was initialized by using four values: 3 axis components (x,y,z) and angle (w component of the quaternion). 1 value of the Z axis component shows that the rotation will be performed along Z axis.

Methods:

Name	Description View: Sort by:
quat	Constructor.
set	Sets the quaternion using the given angle and axis coordinates.
get	Gets the quaternion: qq[0]=x, qq[1]=y, qq[2]=z, qq[3]=w.
getAngle	Returns the rotation angle of the quaternion for a given rotation axis.
getBinormal	Returns the quaternion binormal vector with respect to orientation.
getMat3	Returns the rotation matrix for the quaternion.
getNormal	Returns the quaternion normal vector.
getTangent	Returns the quaternion tangent vector.
getTangent4	Returns the quaternion tangent vector and binormal orientation as a four-component vec4 vector.
normalize	Returns normalized quaternion.
normalizeValid	Normalizes a quaternion, makes its magnitude equal to 1.
normalizeFast	Returns normalized quaternion, calculated using the fast inverse square root algorithm.
normalizeValidFast	Returns normalized quaternion, calculated using the fast inverse square root algorithm.
operator const float *	Performs type conversion to float void *.
operator const void *	Performs type conversion to const void *.
operator float *	Performs type conversion to float *.
operator void *	Performs type conversion to void *.
*operator =**	Performs quaternion multiplication.
operator +=	Performs quaternion addition.
operator -	Performs quaternion negation.
operator -=	Performs quaternion subtraction.
operator =	Sets the quaternion using a __m128 variable (128-bit) as a source.
operator []	Performs array access to the quaternion item reference by using given item index.
set	Sets the quaternion using a given four-component vec4 source vector.

Variables:

Name	Description
quat_identity	Quaternion representing no rotation (0.0, 0.0, 0.0, 1.0).
quat_zero	Zero quaternion (0.0, 0.0, 0.0, 0.0).

quat Class

Members

quat ( const __m128& v ) #

Constructor. Initializes the quaternion using a given __m128 variable (128-bit).

NoticeWe do not recommend to use this method unless you have a clear understanding of SSE2.

Arguments

const __m128& v - 128-bit variable.

quat ( const mat3& m ) #

Constructor. Initializes the quaternion using a given mat3 source matrix (3x3).

Arguments

const mat3& m - Source matrix (3x3).

quat ( const vec4& v ) #

Constructor. Initializes the quaternion using a given four-component vec4 source vector.

Arguments

const vec4& v - Four-component source vector.

quat ( ) #

Default constructor. Produces an identity quaternion (0.0, 0.0, 0.0, 1.0).

quat ( const quat& q ) #

Constructor. Initializes the quaternion by copying a given source quaternion.

Arguments

const quat& q - Source quaternion.

quat ( const vec3& axis, float angle ) #

Constructor. Initializes the quaternion using given rotation axis and angle.

Arguments

const vec3& axis - Rotation axis.
float angle - Rotation angle, in degrees.

quat ( float angle_x, float angle_y, float angle_z ) #

Constructor. Initializes the quaternion using given angles for each axis.

Arguments

float angle_x - Rotation angle along the X axis, in degrees.
float angle_y - Rotation angle along the Y axis, in degrees.
float angle_z - Rotation angle along the Z axis, in degrees.

quat ( const vec3& col0, const vec3& col1, const vec3& col2 ) #

Constructor. Initializes the quaternion using three given matrix columns represented by vec3 vectors.

Arguments

const vec3& col0 - First matrix column.
const vec3& col1 - Second matrix column.
const vec3& col2 - Third matrix column.

quat ( ) #

Constructor. Initializes the quaternion.

explicit quat ( const mat4& m ) #

Constructor. Initializes the quaternion using a given mat4 source matrix (4x4).

Arguments

const mat4& m - Source matrix (4x4).

explicit quat ( const dmat4& m ) #

Constructor. Initializes the quaternion using a given dmat4 source matrix (3x4).

Arguments

const dmat4& m - Source matrix (3x4).

explicit quat ( const float* q ) #

Constructor. Initializes the vector using a given pointer to the quaternion.

Arguments

const float* q - Pointer to the quaternion.

quat ( float x_, float y_, float z_, float w_, ConstexprTag ) #

Constructor. Initializes the quaternion using given constant float values.

Arguments

float x_ - X component of the quaternion.
float y_ - Y component of the quaternion.
float z_ - Z component of the quaternion.
float w_ - W component of the quaternion.
ConstexprTag - Auxiliary tag.

void set ( float axis_x, float axis_y, float axis_z, float angle ) #

Sets the quaternion using the given angle and axis coordinates.

Arguments

float axis_x - X coordinate of the axis.
float axis_y - Y coordinate of the axis.
float axis_z - Z coordinate of the axis.
float angle - Angle value, in degrees.

Examples

Source code (UnigineScript)

quat(1.0, 2.0, 3.0, 60);
/*
Creates a quaternion (0.133, 0.267, 0.4, 0.688)
*/

void set ( const float* q ) #

Sets the quaternion using a given pointer to the source quaternion.

Arguments

const float* q - Pointer to the source quaternion.

void set ( const mat3& m ) #

Sets the quaternion using a given mat3 source matrix (3x3).

Arguments

const mat3& m - Source matrix (3x3).

void set ( const vec3& col0, const vec3& col1, const vec3& col2 ) #

Sets the quaternion using three given matrix columns represented by vec3 vectors.

Arguments

const vec3& col0 - First matrix column.
const vec3& col1 - Second matrix column.
const vec3& col2 - Third matrix column.

void set ( float angle_x, float angle_y, float angle_z ) #

Sets the quaternion using given angles for each axis.

Arguments

float angle_x - Rotation angle along the X axis, in degrees.
float angle_y - Rotation angle along the Y axis, in degrees.
float angle_z - Rotation angle along the Z axis, in degrees.

void set ( const vec3& axis, float angle ) #

Sets the quaternion using given rotation axis and angle.

Arguments

const vec3& axis - Rotation axis.
float angle - Rotation angle, in degrees.

void set ( const dmat4& m ) #

Sets the quaternion using a given dmat4 source matrix (3x4).

Arguments

const dmat4& m - Source matrix (3x4).

void set ( const mat4& m ) #

Sets the quaternion using a given mat4 source matrix (4x4).

Arguments

const mat4& m - Source matrix (4x4).

void get ( float* qq ) const#

Gets the quaternion: qq[0]=x, qq[1]=y, qq[2]=z, qq[3]=w.

Arguments

float* qq - Pointer to the quaternion.

float * get ( ) #

Returns a pointer to the quaternion.

Return value

Pointer to the quaternion.

const float * get ( ) const#

Returns a constant pointer to the quaternion.

Return value

Constant pointer to the quaternion.

void get ( vec3& axis, float& angle ) const#

Gets rotation axis and angle of the quaternion and puts the values to corresponding variables: axis.x = x, axis.y = y, axis.z = z, angle = w.

Arguments

vec3& axis - Rotation axis.
float& angle - Rotation angle, in degrees.

float getAngle ( const vec3& axis ) const#

Returns the rotation angle of the quaternion for a given rotation axis.

Arguments

const vec3& axis - Rotation axis.

Return value

Rotation angle, in degrees, within the [-180, 180] range.

vec3 getBinormal ( ) const#

Returns the quaternion binormal vector with respect to orientation.

Return value

Quaternion binormal vector.

mat3 getMat3 ( ) const#

Returns the rotation matrix for the quaternion.

Output

For the quaternion (x, y, z, w) the corresponding rotation matrix M is defined as follows:  		
    | 1 - 2y² - 2z²    2xy + 2wz      	2xz - 2wy     | 
M=  | 2xy - 2wz        1 - 2x² - 2z²    2yz + 2wx     |
    | 2xz + 2wy        2yz - 2wx        1 - 2x² - 2y² |

vec3 getNormal ( ) const#

Returns the quaternion normal vector.

Return value

Quaternion normal vector.

vec3 getTangent ( ) const#

Returns the quaternion tangent vector.

Return value

Quaternion tangent vector.

vec4 getTangent4 ( ) const#

Returns the quaternion tangent vector and binormal orientation as a four-component vec4 vector.

Return value

Four-component vector representing guaternion tangent vector and binormal orientation.

quat & normalize ( ) #

Returns normalized quaternion.

Return value

Normalized quaternion.

quat & normalizeValid ( ) #

Normalizes a quaternion, makes its magnitude equal to 1. When normalized, a quaternion keeps the same direction but its length is equal to 1. Check for the zero quaternion is performed: if the argument is a zero quaternion, then a zero quaternion is returned.

Return value

Normalized quaternion.

quat & normalizeFast ( ) #

Returns normalized quaternion, calculated using the fast inverse square root algorithm.

Return value

Normalized quaternion.

quat & normalizeValidFast ( ) #

Returns normalized quaternion, calculated using the fast inverse square root algorithm. Check for the zero quaternion is performed: if the argument is a zero quaternion, then a zero quaternion is returned.

Return value

Normalized quaternion.

const float * operator const float * ( ) const#

Performs type conversion to float void *.

const void * operator const void * ( ) const#

Performs type conversion to const void *.

float * operator float * ( ) #

Performs type conversion to float *.

void * operator void * ( ) #

Performs type conversion to void *.

quat & operator*= ( const quat& q ) #

Performs quaternion multiplication.

Arguments

const quat& q - Quaternion.

Return value

Resulting quaternion.

quat & operator*= ( float v ) #

Performs scalar multiplication.

Arguments

float v - Scalar value.

Return value

Resulting quaternion.

quat & operator+= ( const quat& q ) #

Performs quaternion addition.

Arguments

const quat& q - Quaternion.

Return value

Resulting quaternion.

quat operator- ( ) const#

Performs quaternion negation. The sign of each component of the quaternion is flipped.

Return value

Resulting quaternion.

quat & operator-= ( const quat& q ) #

Performs quaternion subtraction.

Arguments

const quat& q - Quaternion.

Return value

Resulting quaternion.

quat & operator= ( const __m128& v ) #

Sets the quaternion using a __m128 variable (128-bit) as a source.

NoticeWe do not recommend to use this method unless you have a clear understanding of SSE2.

Arguments

const __m128& v - 128-bit variable.

Return value

Resulting quaternion.

quat & operator= ( const quat& q ) #

Performs quaternion assignment. Destination quaternion = Source quaternion.

Arguments

const quat& q - Source quaternion.

Return value

Result.

float & operator[] ( int i ) #

Performs array access to the quaternion item reference by using given item index.

Arguments

int i - Quaternion item index.

Return value

Quaternion item reference.

float operator[] ( int i ) const#

Performs array access to the quaternion item by using given item index.

Arguments

int i - Quaternion item index.

Return value

Quaternion item.

void set ( const vec4& v ) #

Sets the quaternion using a given four-component vec4 source vector.

Arguments

const vec4& v - Source vector.

void set ( const quat& v ) #

Sets the quaternion using the source quaternion.

Arguments

const quat& v - Source quaternion.

Last update: 2022-02-04

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Unigine::Math::quat Struct

Usage Example#

See Also#

Methods:

Variables:

quat Class

Members

quat ( const __m128& v ) #

Arguments

quat ( const mat3& m ) #

Arguments

quat ( const vec4& v ) #

Arguments

quat ( ) #

quat ( const quat& q ) #

Arguments

quat ( const vec3& axis, float angle ) #

Arguments

quat ( float angle_x, float angle_y, float angle_z ) #

Arguments

quat ( const vec3& col0, const vec3& col1, const vec3& col2 ) #

Arguments

quat ( ) #

explicit quat ( const mat4& m ) #

Arguments

explicit quat ( const dmat4& m ) #

Arguments

explicit quat ( const float* q ) #

Arguments

quat ( float x_, float y_, float z_, float w_, ConstexprTag ) #

Arguments

void set ( float axis_x, float axis_y, float axis_z, float angle ) #

Arguments

Examples

void set ( const float* q ) #

Arguments

void set ( const mat3& m ) #

Arguments

void set ( const vec3& col0, const vec3& col1, const vec3& col2 ) #

Arguments

void set ( float angle_x, float angle_y, float angle_z ) #

Arguments

void set ( const vec3& axis, float angle ) #

Arguments

void set ( const dmat4& m ) #

Arguments

void set ( const mat4& m ) #

Arguments

void get ( float* qq ) const#

Arguments

float * get ( ) #

Return value

const float * get ( ) const#

Return value

void get ( vec3& axis, float& angle ) const#

Arguments

float getAngle ( const vec3& axis ) const#

Arguments

Return value

vec3 getBinormal ( ) const#

Return value

mat3 getMat3 ( ) const#

vec3 getNormal ( ) const#

Return value

vec3 getTangent ( ) const#

Return value

vec4 getTangent4 ( ) const#

Return value

quat & normalize ( ) #

Return value

quat & normalizeValid ( ) #

Return value

quat & normalizeFast ( ) #

Return value

quat & normalizeValidFast ( ) #

Return value

const float * operator const float * ( ) const#

const void * operator const void * ( ) const#

float * operator float * ( ) #

void * operator void * ( ) #