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# jerome.duriez@inrae.fr
def spaceRot(index=0, nTot=10):
'''Returns the rotation (as a quaternion) that transforms z-axis into some other direction vector, chosen from an adequate set of direction vectors that cover the whole 3D space
:param int index: from 0 to nTot-1, to pick among that adequate set
:param int nTot: how many different image directions / rotations to consider in total'''
phiMult = pi * (3 - 5.**0.5) # same spiral path as in polyhedralBall
phi = index * phiMult
theta = acos(-1. + (2. * index + 1.) / nTot)
vec = Vector3(sin(theta) * cos(phi), sin(theta) * sin(phi), cos(theta)) # the direction in space, image of z through the desired rotation
vecRot = (Vector3.UnitZ).cross(vec) # the vector carrying the rotation
return Quaternion(vecRot.normalized(), theta) # the angle is the oriented angle (vecZ,vec) = theta, basically
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