quaternion
The quaternion w + xi + yj + zk. Arithmetic stays exact when the parts are.
w(number) --x(number) --y(number) --z(number) --
Quaternions
norm
|q| = sqrt(w^2 + x^2 + y^2 + z^2), exact. Also works on tensors.
q(quaternion) --
normSq
|q|^2, exact.
q(quaternion) --
inverse
q^-1 = conjugate(q) / |q|^2, exact.
q(quaternion) --
isUnit
True if |q| = 1.
q(quaternion) --
scalarPart
w, the real part.
q(quaternion) --
vectorPart
(x, y, z) as a vector.
q(quaternion) --
axisAngle
The unit quaternion rotating by angle (radians) about the axis (ax, ay, az).
ax(number) --ay(number) --az(number) --angle(number) -- radians
toAxisAngle
The rotation axis and angle of a unit quaternion.
q(quaternion) --
fromEuler
The rotation quaternion for roll, pitch, yaw (radians).
roll(number) --pitch(number) --yaw(number) --
compose
The rotation q1 followed by q2 (q2 * q1).
q2(quaternion) --q1(quaternion) --
rotationMatrix
The 3x3 rotation matrix of q.
q(quaternion) --
qexp
e^q.
q(quaternion) --
qlog
The natural logarithm of q.
q(quaternion) --
qpow
q^t for a real t.
q(quaternion) --t(number) --
slerp
Spherical linear interpolation from q0 (t = 0) to q1 (t = 1).
q0(quaternion) --q1(quaternion) --t(number) --