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rot_utils.py
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rot_utils.py
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import torch
def dirup_to_rotmat(dir_vec, up_vec):
# We do not assume that the inputs are normalized nor orthogonal
# Debug dot_prod function
# dot_prod = lambda a, b : torch.sum(a[...,:]*b[...,:], dim=-1)
# debug = lambda label, tensor : print(f"{label}={tensor.shape}")
# Renormalize the inputs
up_vec_norm = up_vec / torch.sqrt(torch.sum(up_vec**2, dim=-1, keepdim=True))
dir_vec_norm = dir_vec / torch.sqrt(torch.sum(dir_vec**2, dim=-1, keepdim=True))
# Make up and dir orthogonal and create the side vector
side_vec_norm = torch.cross(up_vec_norm, dir_vec_norm, dim=-1)
up_vec_norm = torch.cross(dir_vec_norm, side_vec_norm, dim=-1)
# Those three vectors create the new rotation basis
flat_rot_mat = torch.cat((up_vec_norm,
dir_vec_norm,
side_vec_norm), dim=-1)
# Row-wise reshaping rot_mat=[up^t; dir^t; side^t]
rot_mat = flat_rot_mat.reshape(-1, 3, 3)
return rot_mat
def rotmat_to_euler(rot_mat):
# XYZ convention is used here
# debug = lambda label, tensor : print(f"{label}={tensor.shape}")
norm_ry = torch.sqrt(rot_mat[..., 0, 0]**2 + rot_mat[..., 1, 0]**2) # [num_rays]
isSingular = norm_ry < torch.tensor(1e-6) # [num_rays]
euler_ang = torch.where(isSingular[..., None],
torch.cat((torch.atan2(-rot_mat[..., 1, 2], rot_mat[..., 1, 1])[..., None],
torch.atan2(-rot_mat[..., 2, 0], norm_ry)[..., None],
torch.zeros_like(norm_ry[..., None])), dim=-1),
torch.cat((torch.atan2(rot_mat[..., 2, 1], rot_mat[..., 2, 2])[..., None],
torch.atan2(-rot_mat[..., 2, 0], norm_ry)[..., None],
torch.atan2(rot_mat[..., 1, 0], rot_mat[..., 0, 0])[..., None]), dim=-1)
)
return euler_ang
def rotmat_to_quaternion(rot_mat):
# Pseudo code:
# -------------------------------
# if (m22 < 0){
# if (m00 > m11) {
# t = 1 + m00 - m11 - m22;
# q = quat(t, m01 + m10, m20 + m02, m12 - m21);}
# else {
# t = 1 - m00 + m11 - m22;
# q = quat(m01 + m10, t, m12 + m21, m20 - m02);}
# }
# else{
# if (m00 < -m11){
# t = 1 - m00 - m11 + m22;
# q = quat(m20 + m02, m12 + m21, t, m01 - m10);}
# else{
# t = 1 + m00 + m11 + m22;
# q = quat(m12 - m21, m20 - m02, m01 - m10, t);}
# }
# q *= 0.5 / Sqrt(t);
# -------------------------------
r = rot_mat
q = 0.5 * torch.where(r[..., 2, 2] < 0,
torch.where(r[..., 0, 0] > r[..., 1, 1],
# case 1
torch.stack((1. + r[..., 0, 0] - r[..., 1, 1] - r[..., 2, 2],
r[..., 0, 1] + r[..., 1, 0],
r[..., 2, 0] + r[..., 0, 2],
r[..., 1, 2] - r[..., 2, 1]), dim=0) /
torch.sqrt(1. + r[..., 0, 0] - r[..., 1, 1] - r[..., 2, 2]),
# case 2
torch.stack((r[..., 0, 1] + r[..., 1, 0],
1. - r[..., 0, 0] + r[..., 1, 1] - r[..., 2, 2],
r[..., 1, 2] + r[..., 2, 1],
r[..., 2, 0] - r[..., 0, 2]), dim=0) /
torch.sqrt(1. - r[..., 0, 0] + r[..., 1, 1] - r[..., 2, 2]),),
torch.where(r[..., 0, 0] < -r[..., 1, 1],
# case 3
torch.stack((r[..., 2, 0] + r[..., 0, 2],
r[..., 1, 2] + r[..., 2, 1],
1. - r[..., 0, 0] - r[..., 1, 1] + r[..., 2, 2],
r[..., 0, 1] - r[..., 1, 0]), dim=0) /
torch.sqrt(1. - r[..., 0, 0] - r[..., 1, 1] + r[..., 2, 2]),
# case 4
torch.stack((r[..., 1, 2] - r[..., 2, 1],
r[..., 2, 0] - r[..., 0, 2],
r[..., 0, 1] - r[..., 1, 0],
1. + r[..., 0, 0] + r[..., 1, 1] + r[..., 2, 2]), dim=0) /
torch.sqrt(1. + r[..., 0, 0] + r[..., 1, 1] + r[..., 2, 2]),))
return q.permute(1, 0)
def rotmat_to_pseudoquat(rot_mat):
# ad = 0.25*(r32-r23)
# bd = 0.25*(r13-r31)
# cd = 0.25*(r21-r12)
# dd = 0.25*(1+r11+r22+r33)
r = rot_mat
dd = 0.25 * (1 + r[..., 0, 0] + r[..., 1, 1] + r[..., 2, 2]) # has nothing to do with r
eps = 1e-3
q = torch.where(dd >= eps ** 2,
torch.stack((0.25 * (r[..., 2, 1] - r[..., 1, 2]),
0.25 * (r[..., 0, 2] - r[..., 2, 0]),
0.25 * (r[..., 1, 0] - r[..., 0, 1]),
dd), dim=0
),
torch.stack((0.5 * eps * torch.sign(r[..., 2, 1] - r[..., 1, 2]) * torch.sqrt(r[..., 0, 0] - r[..., 1, 1] - r[..., 2, 2] + 1),
0.5 * eps * torch.sign(r[..., 0, 2] - r[..., 2, 0]) * torch.sqrt(-r[..., 0, 0] + r[..., 1, 1] - r[..., 2, 2] + 1),
0.5 * eps * torch.sign(r[..., 1, 0] - r[..., 0, 1]) * torch.sqrt(-r[..., 0, 0] - r[..., 1, 1] + r[..., 2, 2] + 1),
eps * torch.sqrt(dd)), dim=0
))
return q.permute(1, 0)
def pseudoquat_to_rotmat(q):
# pseudo quat = [a r, b r, c r, d r]
# rotmat = [a2-b2-c2+d2, 2(ab-cd), 2(ac+bd),
# 2(ab+cd), b2-c2-a2+d2, 2(bc-ad),
# 2(ac-bd), 2(bc+ad), c2-a2-b2-d2]
ad_ = q[..., 0]
bd_ = q[..., 1]
cd_ = q[..., 2]
dd_ = q[..., 3]
sxd2 = ad_**2 + bd_**2 + cd_**2 + dd_**2
# Products
a2 = ad_ ** 2 / sxd2
b2 = bd_ ** 2 / sxd2
c2 = cd_ ** 2 / sxd2
d2 = dd_ ** 2 / sxd2
ab = ad_*bd_ / sxd2
ac = ad_*cd_ / sxd2
cd = cd_*dd_ / sxd2
bd = bd_*dd_ / sxd2
bc = bd_*cd_ / sxd2
ad = ad_*dd_ / sxd2
rot_mat = torch.cat((a2-b2-c2+d2, 2*(ab-cd), 2*(ac+bd),
2*(ab+cd), b2-c2-a2+d2, 2*(bc-ad),
2*(ac-bd), 2*(bc+ad), c2-a2-b2-d2), dim=-1).reshape(-1, 3, 3)
return rot_mat
def dist_between_rotmats(rot1, rot2_transpose):
diff_rot = rot1.matmul(rot2_transpose)
return torch.acos(.5*(torch.trace(diff_rot)-1.))
# Unit test here
def main():
# euler = [ x: 0.8, y: -0.9, z: -0.6 ] (XYZ convention)
# = [ x: 1.122394, y: -0.045392, z: -1.0314609 ] (ZYX convention)
# quaternion = [ 0.4533835, -0.2791119, -0.4069129, 0.742268 ] (x,y,z,w)
rot_mat = torch.tensor([[0.5130368, 0.3509874, -0.7833269],
[-0.8571663, 0.2577305, -0.4459157],
[0.0453765, 0.9002126, 0.4330798]],
dtype=torch.float32).unsqueeze(0).permute(0, 2, 1)
print(f"rot_mat=\n{rot_mat}")
euler = rotmat_to_euler(rot_mat)
print(f"euler=\n{euler}")
quaternion = rotmat_to_quaternion(rot_mat)
print(f"quaternion=\n{quaternion}")
pseudoquat = rotmat_to_pseudoquat(rot_mat)
print(f"pseudoquat=\n{pseudoquat}")
rot_mat_rec = pseudoquat_to_rotmat(pseudoquat)
print(f"rec_rot_mat=\n{rot_mat_rec}")
if __name__ == '__main__':
main()