# Copyright (c) 2018-present, Facebook, Inc.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#

import numpy as np
import torch

from common.utils import wrap
from common.quaternion import qrot, 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(qrot, np.tile(Rt, (*X.shape[:-1], 1)), X - t) # Rotate and translate

    
def camera_to_world(X, R, t):
    return wrap(qrot, 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)
    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

def project_to_2d_linear(X, camera_params):
    """
    Project 3D points to 2D using only linear parameters (focal length and principal point).
    
    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]
    
    XX = torch.clamp(X[..., :2] / X[..., 2:], min=-1, max=1)
    
    return f*XX + c