diff options
Diffstat (limited to 'src/core')
| -rw-r--r-- | src/core/ao_quaternion.h | 33 |
1 files changed, 33 insertions, 0 deletions
diff --git a/src/core/ao_quaternion.h b/src/core/ao_quaternion.h index 1c0617c4..6a701a18 100644 --- a/src/core/ao_quaternion.h +++ b/src/core/ao_quaternion.h @@ -31,6 +31,39 @@ static inline void ao_quaternion_multiply(struct ao_quaternion *r, { struct ao_quaternion t; #define T(_a,_b) (((a)->_a) * ((b)->_b)) + +/* + * Quaternions + * + * ii = jj = kk = ijk = -1; + * + * kji = 1; + * + * ij = k; ji = -k; + * kj = -i; jk = i; + * ik = -j; ki = j; + * + * Multiplication p * q: + * + * (pr + ipx + jpy + kpz) (qr + iqx + jqy + kqz) = + * + * ( pr * qr + pr * iqx + pr * jqy + pr * kqz) + + * (ipx * qr + ipx * iqx + ipx * jqy + ipx * kqz) + + * (jpy * qr + jpy * iqx + jpy * jqy + jpy * kqz) + + * (kpz * qr + kpz * iqx + kpz * jqy + kpz * kqz) = + * + * + * (pr * qr) + i(pr * qx) + j(pr * qy) + k(pr * qz) + + * i(px * qr) - (px * qx) + k(px * qy) - j(px * qz) + + * j(py * qr) - k(py * qx) - (py * qy) + i(py * qz) + + * k(pz * qr) + j(pz * qx) - i(pz * qy) - (pz * qz) = + * + * 1 * ( (pr * qr) - (px * qx) - (py * qy) - (pz * qz) ) + + * i * ( (pr * qx) + (px * qr) + (py * qz) - (pz * qy) ) + + * j * ( (pr * qy) - (px * qz) + (py * qr) + (pz * qx) ) + + * k * ( (pr * qz) + (px * qy) - (py * qx) + (pz * qr); + */ + t.r = T(r,r) - T(x,x) - T(y,y) - T(z,z); t.x = T(r,x) + T(x,r) + T(y,z) - T(z,y); t.y = T(r,y) - T(x,z) + T(y,r) + T(z,x); |