def rotate_z(cls, angle, dtype=FLOAT) -> 'Transform':
m = np.eye(4, 4, dtype=dtype)
sin_t = np.sin(np.deg2rad(angle))
cos_t = np.cos(np.deg2rad(angle))
m[0][0] = cos_t
m[0][1] = -sin_t
m[1][0] = sin_t
m[1][1] = cos_t
return cls(m, m.T, dtype)
def slerp(t: FLOAT, q1: 'Quaternion', q2: 'Quaternion') -> 'Quaternion':
cos_theta = dot(q1, q2)
if (cos_theta > 1. - EPS):
return ((1. - t) * q1 + t * q2).normalized()
else:
theta = np.arccos(np.clip(cos_theta, -1., 1.))
thetap = theta * t
qperp = (q2 - q1 * cos_theta).normalized()
return q1 * np.cos(thetap) + qperp * np.sin(thetap)
def rotate(cls, angle, axis: 'geo.Vector', dtype=FLOAT) -> 'Transform':
a = geo.normalize(axis)
s = np.sin(np.deg2rad(angle))
c = np.cos(np.deg2rad(angle))
m = np.eye(4, 4, dtype=dtype)
m[0][0] = a.x * a.x + (1. - a.x * a.x) * c
m[0][1] = a.x * a.y * (1. - c) - a.z * s
m[0][2] = a.x * a.z * (1. - c) + a.y * s
m[1][0] = a.x * a.y * (1. - c) + a.z * s
m[1][1] = a.y * a.y + (1. - a.y * a.y) * c
m[1][2] = a.y * a.z * (1. - c) - a.x * s
m[2][0] = a.x * a.z * (1. - c) - a.y * s
m[2][1] = a.y * a.z * (1. - c) + a.x * s
m[2][2] = a.z * a.z + (1. - a.z * a.z) * c
return cls(m, m.T, dtype)