import numpy as np
import torch

from tools.utils import wrap
from common.quaternion import qort, qinverse


def normalize_screen_coordinates(X, w, h):
    assert X.shape[-1] == 2

    # Normalize so that [0, w] is mapped to [-1, 1], while preserving the aspect ratio
    return X/w*2 - [1, h/w]


def image_coordinates(X, w, h):
    assert X.shape[-1] == 2

    # Reverse camera frame normalization
    return (X + [1, h/w]) * w / 2


def world_to_camera(X, R, t):
    Rt = wrap(qinverse, R)  # Invert rotation
    return wrap(qort, np.tile(Rt, (*X.shape[:-1], 1)), X - t)  # Rotate and translate


def camera_to_world(X, R, t):
    return wrap(qort, np.tile(R, (*X.shape[:-1], 1)), X) + t


def project_to_2d(X, camera_params):
    """
    Project 3D points to 2D using the Human3.6M camera projection function.
    This is a differentiable and batched reimplementation of the original MATLAB script.

    Arguments:
    X -- 3D points in *camera space* to transform (N, *, 3)
    camera_params -- intrinsic parameteres (N, 2+2+3+2=9)
    """
    assert X.shape[-1] == 3
    assert len(camera_params.shape) == 2
    assert camera_params.shape[-1] == 9
    assert X.shape[0] == camera_params.shape[0]

    while len(camera_params.shape) < len(X.shape):
        camera_params = camera_params.unsqueeze(1)

    f = camera_params[..., :2]
    c = camera_params[..., 2:4]
    k = camera_params[..., 4:7]
    p = camera_params[..., 7:]

    # XX = torch.clamp(X[..., :2] / X[..., 2:], min=-1, max=1)
    XX = X[..., :2] / X[..., 2:]
    r2 = torch.sum(XX[..., :2]**2, dim=len(XX.shape)-1, keepdim=True)

    radial = 1 + torch.sum(k * torch.cat((r2, r2**2, r2**3), dim=len(r2.shape)-1), dim=len(r2.shape)-1, keepdim=True)
    tan = torch.sum(p*XX, dim=len(XX.shape)-1, keepdim=True)

    XXX = XX*(radial + tan) + p*r2

    return f*XXX + c