Quaternion

Detailed Description

Functions
Quaternion	QSlerp (const Quaternion &q1, const Quaternion &q2, Float64 alfa)
Quaternion	QSquad (const Quaternion &q0, const Quaternion &q1, const Quaternion &q2, const Quaternion &q3, Float64 alfa)
Quaternion	QBlend (const Quaternion &q1, const Quaternion &q2, const Float64 r)
Quaternion	QSpline (const Quaternion &qn_m1, const Quaternion &qn, const Quaternion &qn_p1, const Quaternion &qn_p2, Float64 t)
Quaternion	QSmoothCubic (const Quaternion &qn_m1, const Quaternion &qn, const Quaternion &qn_p1, Float64 t)
Quaternion	QNorm (const Quaternion &q)
Quaternion	QMul (const Quaternion &q1, const Quaternion &q2)
Quaternion	QMul (const Quaternion &q, Float64 s)
Quaternion	QAdd (const Quaternion &q1, const Quaternion &q2)
Quaternion	QSub (const Quaternion &q1, const Quaternion &q2)
Quaternion	QInvert (const Quaternion &q)
Float64	QDot (const Quaternion &q1, const Quaternion &q2)
Quaternion	QDeriv (const Quaternion &q, const Vector64 &w)
Quaternion	QLogN (const Quaternion &q)
Quaternion	QExpQ (const Quaternion &q)

Function Documentation

QSlerp()

Quaternion QSlerp	(	const Quaternion &	q1,
		const Quaternion &	q2,
		Float64	alfa
	)

Linear interpolates the quaternions q1 and q2 with the parameter alpha.

Parameters

[in]	q1	The first quaternion.
[in]	q2	The second quaternion.
[in]	alfa	The interpolation parameter. Between 0.0 (q1) and 1.0 (q2).

Returns

The interpolated quaternion.

QSquad()

Quaternion QSquad	(	const Quaternion &	q0,
		const Quaternion &	q1,
		const Quaternion &	q2,
		const Quaternion &	q3,
		Float64	alfa
	)

Cubic interpolates the quaternions q1 and q2 with parameter alpha using spherical quadrangle interpolation. q0 and q3 are used to provide C1-continuity at the borders (tangents): q0 = i-1, q1 = i, q2 = i+1, q3 = i+2

Parameters

[in]	q0	The first quaternion to provide continuity.
[in]	q1	The first quaternion to interpolate from.
[in]	q2	The second quaternion to interpolate from.
[in]	q3	The second quaternion to provide continuity.
[in]	alfa	The interpolation parameter. Between 0.0 (q1) and 1.0 (q2).

Returns

The interpolated quaternion.

QBlend()

Quaternion QBlend	(	const Quaternion &	q1,
		const Quaternion &	q2,
		const Float64	r
	)

Smooth interpolates the quaternions q1 and q2 with parameter r.

Parameters

[in]	q1	The first quaternion.
[in]	q2	The second quaternion.
[in]	r	The blending parameter. Between 0.0 (q1) and 1.0 (q2).

Returns

The interpolated quaternion.

QSpline()

Quaternion QSpline	(	const Quaternion &	qn_m1,
		const Quaternion &	qn,
		const Quaternion &	qn_p1,
		const Quaternion &	qn_p2,
		Float64	t
	)

Smooth blends the quaternions qn and qn_p1 using spherical spline interpolation with parameter t.
qn_m1 (-1) and qn_p2 (-1+2) are used to provide C1-continuity at the borders (tangents).

Parameters

[in]	qn_m1	The first quaternion (-1) to provide continuity.
[in]	qn	The first quaternion to interpolate from.
[in]	qn_p1	The second quaternion to interpolate from.
[in]	qn_p2	The second quaternion (+2) to provide continuity.
[in]	t	The blending parameter. Between 0.0 (qn) and 1.0 (qn_p1).

Returns

The interpolated quaternion.

QSmoothCubic()

Quaternion QSmoothCubic	(	const Quaternion &	qn_m1,
		const Quaternion &	qn,
		const Quaternion &	qn_p1,
		Float64	t
	)

Smooth blends the quaternions qn and qn_p1 using Cubic interpolation with parameter t.
qn_m1 (-1) and qn_p2 (-1+2) are used to provide C1-continuity at the borders (tangents).

Since

R18

Parameters

[in]	qn_m1	The first quaternion (-1) to provide continuity.
[in]	qn	The first quaternion to interpolate from.
[in]	qn_p1	The second quaternion to interpolate from.
[in]	t	The blending parameter. Between 0.0 (qn) and 1.0 (qn_p1).

Returns

The interpolated quaternion.

QNorm()

Quaternion QNorm

(

const Quaternion &

q

)

Gets a normalized copy of quaternion q.

Parameters

[in]

q

The quaternion to normalize.

Returns

A normalized copy of q.

QMul() [1/2]

Quaternion QMul	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

Calculates the quaternion product of quaternions q1 and q2.

Parameters

[in]	q1	The first quaternion.
[in]	q2	The second quaternion.

Returns

The quaternion product of q1 and q2.

QMul() [2/2]

Quaternion QMul	(	const Quaternion &	q,
		Float64	s
	)

Calculates the product of quaternion q with scalar s.

Parameters

[in]	q	The quaternion.
[in]	s	The scalar.

Returns

The product of q with s.

QAdd()

Quaternion QAdd	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

Calculates the quaternion addition of quaternions q1 and q2.

Parameters

[in]	q1	The first quaternion.
[in]	q2	The second quaternion.

Returns

The quaternion addition of q1 and q2.

QSub()

Quaternion QSub	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

Calculates the quaternion subtraction of quaternions q1 and q2.

Parameters

[in]	q1	The first quaternion.
[in]	q2	The second quaternion.

Returns

The quaternion subtraction of q1 and q2.

QInvert()

Quaternion QInvert

(

const Quaternion &

q

)

Calculates the inverse of quaternion q.

Parameters

[in]

q

The quaternion.

Returns

The quaternion inverse of q.

QDot()

Float64 QDot	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

Calculates the Dot Product between q1 and q2.

Since

R18

Parameters

[in]	q1	The first quaternion.
[in]	q2	The second quaternion.

Returns

The Dot Product of q1 and q2.

QDeriv()

Quaternion QDeriv	(	const Quaternion &	q,
		const Vector64 &	w
	)

Calculates the derivative of quaternion q by vector w.

Parameters

[in]	q	The quaternion.
[in]	w	The vector.

Returns

The quaternion derivative of q by w.

QLogN()

Quaternion QLogN

(

const Quaternion &

q

)

Calculates the natural logarithm of quaternion q.

Parameters

[in]

q

The quaternion.

Returns

The natural logarithm of q.

QExpQ()

Quaternion QExpQ

(

const Quaternion &

q

)

Calculates the exponential of quaternion q.

Parameters

[in]

q

The quaternion.

Returns

The exponential of q.