quaternion_mul

gs_nyx.nyx_py_sdk.quaternion_mul(a: gs_nyx.nyx_py_sdk.quaternion, b: gs_nyx.nyx_py_sdk.quaternion) → gs_nyx.nyx_py_sdk.quaternion

Return the Hamilton product a * b of two quaternions.

Example

The Hamilton product composes rotations right-to-left, so quaternion_mul(b, a) rotates first by a and then by b (the same ordering as 4×4 matrix multiplication on column vectors):

import math
import gs_nyx.nyx_py_sdk as nps

# 45° rotation about +Z, written as a unit quaternion in (x, y, z, w).
half_w = math.cos(math.radians(22.5))
half_z = math.sin(math.radians(22.5))
q45 = nps.quaternion(0.0, 0.0, half_z, half_w)

# Composing two 45° rotations yields a 90° rotation about the same axis.
q90 = nps.quaternion_mul(q45, q45)
# q90.w ≈ cos(45°) ≈ 0.70710678
# q90.z ≈ sin(45°) ≈ 0.70710678

Note

quaternion_mul does not renormalise its result. After many chained compositions, divide each component by sqrt(w² + x² + y² + z²) to keep numerical drift in check; renormalisation matters because quaternion_conjugate() only inverts unit quaternions.