Unigine::Math::quat Struct
| Header: | #include <UnigineMathLib.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::get()->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->setWorldRotation(node->getWorldRotation() * 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.
See Also
- An article on Quaternions and Spatial Rotation on Wikipedia.
- A video tutorial on moving and rotating the node by using quaternion (C++)
quat Class
Members
quat(const __m128 & v)
Constructor. Initializes the quaternion using a given __m128 variable (128-bit).Notice
We 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(const vec3 & v)
Constructor. Initializes the quaternion using a given three-component vec3 source vector.Arguments
- const vec3 & v - Thee-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(float x, float y, float z, float angle)
Constructor. Initializes the quaternion using given 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 angle - W component of 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.
void set(float x, float y, float z, float angle)
Sets the quaternion by components.Arguments
- float x - X component of the quaternion.
- float y - Y component of the quaternion.
- float z - Z component of the quaternion.
- float angle - W component of the quaternion.
Examples
Source code (UnigineScript)
quat(1.0, 2.0, 3.0, 60);
/*
Creates a quaternion (1.0, 2.0, 3.0, 60)
*/void set(const float * qq)
Sets the quaternion using a given pointer to the source quaternion.Arguments
- const float * qq - 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 vec3 & v)
Sets the quaternion using a given three-component vec3 source vector.Arguments
- const vec3 & v - Three-component source vector.
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)
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)
Returns the rotation angle of the quaternion for a given rotation axis.Arguments
- const vec3 & axis - Rotation axis.
Return value
Rotation angle, in degrees.vec3 getBinormal() const
Returns the quaternion binormal vector with respect to orientation.Return value
Quaternion binormal vector.mat3 getMat3()
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 & normalizeFast()
Returns normalized quaternion, calculated using the fast inverse square root algorithm.Return value
Normalized quaternion.__m128 operator __m128()
Performs type conversion to __m128.Notice
We do not recommend to use this method unless you have a clear understanding of SSE2.
const float * operator const float *()
Performs type conversion to float void *.const void * operator const void *()
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-()
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.Notice
We 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 & qq)
Performs quaternion assignment. Destination quaternion = Source quaternion.Arguments
- const quat & qq - 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.__m128 sse()
Returns quaternion components as a 128-bit variable.Notice
We do not recommend to use this method unless you have a clear understanding of SSE2.
Return value
128-bit variable.void sse(const __m128 & v)
Sets the quaternion components using a given 128-bit variable.Notice
We do not recommend to use this method unless you have a clear understanding of SSE2.
Arguments
- const __m128 & v - 128-bit variable.
int IDENTITY
Description
Quaternion representing no rotation (0.0, 0.0, 0.0, 1.0).int ZERO
Description
Zero quaternion (0.0, 0.0, 0.0, 0.0).Last update: 10.08.2018
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