j3259の日記: Quaternion (四元数)
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j3259
A quaternion q = (qv, w) = ai + bj + ck + w = qv + w,
qv = ai + bj + ck = (a, b, c),
i2 = j2 = k2 = -1, jk = -kj = i, ki = -ik = j, ij = -ji = k
Addtion
q + r = (qv + rv, qw + rw)
Multiplication
qr = (qv CROSS rv + rwqv + qwrv, qwrw - qv DOT rv)
Conjugate
q* = (-qv, qw)
Norm
n(q) = sqrt(q q*) = sqrt(q* q) = sqrt(qv DOT qv + qwqw)
Identity
i = (0, 1)
Inverse
q-1 = (1 / n(q)2) q*