Quaternion

Quaternion inherits Object

Construction: Quaternion newObj = Quaternion();

Clone: Quaternion newObj = Quaternion(other);

A Quaternion is a four-valued mathematical construct, an alternative to three Euler rotation angles or a Direction Cosine Matrix (DCM) as a way to represent the orientation of a solid body in 3-D space. It has the advantage of not producing a mathematical singularity at pitch angles of +/- 90 degrees. Euler rotation angles are performed in the following order:

• Psi = Yaw Rotation(+Z)

• Theta = Pitch Rotation(+Y)

• Phi = Roll Rotation(+X)

Static Methods

static Quaternion Construct(double aPsi, double aTheta, double aPhi)

Return a new quaternion with the provided Euler rotation angles given in degrees.

static Quaternion Construct(double aA, double aI, double aJ, double aK)

Return a new quaternion with the provided initial values for angle and vector.

static Quaternion Multiply(Quaternion aOrientation1, Quaternion aOrientation2)

Returns the product of the two given quaternions.

static Quaternion Slerp(Quaternion aOrientation1, Quaternion aOrientation2, double aInterpolationCoefficient)

Returns the spherical linear interpolation result given two quaternions and an interpolation coefficient [0..1]. An interpolation coefficient of 0 corresponds to the aOrientation1 quaternion and an interpolation coefficient of 1 corresponds to the aOrientation2 quaternion. (https://en.wikipedia.org/wiki/Slerp#Quaternion_Slerp)

Methods

void Normalize()

Re-normalizes the quaternion.

Note

A quaternion orientation should always have a magnitude of one, so after constructing and/or extended time propagation, it should be re-normalized.

void SetRate(Quaternion aOrientation, Vec3 aBodyRate)

Sets a Quaternion to a Rate, from an orientation and local body rates. The aBodyRate vector is (X,Y,Z) body-axis rates, in degrees per second.

Note

Do not re-normalize this vector before use, as it is an incremental change value, with non-unity magnitude.

void Set(double aPsi, double aTheta, double aPhi)

Set the quaternion as an orientation with the given Euler angles in degrees.

Vec3 Rotate(Vec3 aVector)

Rotate a vector by this quaternion. The quaternion is assumed to be normalized.

Vec3 ReverseRotate(Vec3 aVector)

Reverse, or de-rotate a vector by this quaternion. The quaternion is assumed to be normalized.

Quaternion Rotate(Vec3 aBodyRates, double aDeltaT)

Propagate the body-relative rotation rates forward to a new orientation. The aBodyRate vector is (X,Y,Z) body-axis rates, in degrees per second, and aDeltaT specifies the amount of time over which to integrate the body rates.

..note:: This function degrades in accuracy at larger time steps with higher rotation rates; the context is assumed to be digital forward integration of platform motion state in small steps.

double Psi()

Return the psi Euler angle equivalent (in degrees) represented by this quaternion.

double Theta()

Return the theta Euler angle equivalent (in degrees) represented by this quaternion.

double Phi()

Return the phi Euler angle equivalent (in degrees) represented by this quaternion.