# Copyright (c) OpenMMLab. All rights reserved.
import torch
from torch.nn import functional as F


def rot6d_to_rotmat(x):
    """Convert 6D rotation representation to 3x3 rotation matrix.

    Based on Zhou et al., "On the Continuity of Rotation
    Representations in Neural Networks", CVPR 2019
    Input:
        (B,6) Batch of 6-D rotation representations
    Output:
        (B,3,3) Batch of corresponding rotation matrices
    """
    x = x.view(-1, 3, 2)
    a1 = x[:, :, 0]
    a2 = x[:, :, 1]
    b1 = F.normalize(a1)
    b2 = F.normalize(a2 - torch.einsum('bi,bi->b', b1, a2).unsqueeze(-1) * b1)
    b3 = torch.cross(b1, b2)
    return torch.stack((b1, b2, b3), dim=-1)


def batch_rodrigues(theta):
    """Convert axis-angle representation to rotation matrix.
    Args:
        theta: size = [B, 3]
    Returns:
        Rotation matrix corresponding to the quaternion
            -- size = [B, 3, 3]
    """
    l2norm = torch.norm(theta + 1e-8, p=2, dim=1)
    angle = torch.unsqueeze(l2norm, -1)
    normalized = torch.div(theta, angle)
    angle = angle * 0.5
    v_cos = torch.cos(angle)
    v_sin = torch.sin(angle)
    quat = torch.cat([v_cos, v_sin * normalized], dim=1)
    return quat_to_rotmat(quat)


def quat_to_rotmat(quat):
    """Convert quaternion coefficients to rotation matrix.
    Args:
        quat: size = [B, 4] 4 <===>(w, x, y, z)
    Returns:
        Rotation matrix corresponding to the quaternion
            -- size = [B, 3, 3]
    """
    norm_quat = quat
    norm_quat = norm_quat / norm_quat.norm(p=2, dim=1, keepdim=True)
    w, x, y, z = norm_quat[:, 0], norm_quat[:, 1],\
        norm_quat[:, 2], norm_quat[:, 3]

    B = quat.size(0)

    w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2)
    wx, wy, wz = w * x, w * y, w * z
    xy, xz, yz = x * y, x * z, y * z

    rotMat = torch.stack([
        w2 + x2 - y2 - z2, 2 * xy - 2 * wz, 2 * wy + 2 * xz, 2 * wz + 2 * xy,
        w2 - x2 + y2 - z2, 2 * yz - 2 * wx, 2 * xz - 2 * wy, 2 * wx + 2 * yz,
        w2 - x2 - y2 + z2
    ],
                         dim=1).view(B, 3, 3)
    return rotMat