# Copyright (C) 2024-present Naver Corporation. All rights reserved.
# Licensed under CC BY-NC-SA 4.0 (non-commercial use only).
#
# --------------------------------------------------------
# utilities for interpreting the DUST3R output
# --------------------------------------------------------
import numpy as np
import torch
from dust3r.utils.geometry import xy_grid

# 估计焦距f，即论文中的《3.3.Downstream Applications-Recovering intrinsics.》章节的公式
def estimate_focal_knowing_depth(pts3d, pp, focal_mode='median', min_focal=0.5, max_focal=3.5):
    """ Reprojection method, for when the absolute depth is known:
        1) estimate the camera focal using a robust estimator
        2) reproject points onto true rays, minimizing a certain error
    """
    B, H, W, THREE = pts3d.shape
    assert THREE == 3

    # pixels即论文中的图像坐标系下的坐标(i`,j`)：i` = i - W/2 , j` = j - H/2
    pixels = xy_grid(W, H, device=pts3d.device).view(1, -1, 2) - pp.view(-1, 1, 2)  # B,HW,2
    pts3d = pts3d.flatten(1, 2)  # (B, H*W, 3)

    if focal_mode == 'median':
        with torch.no_grad():
            # direct estimation of focal
            u, v = pixels.unbind(dim=-1)
            x, y, z = pts3d.unbind(dim=-1)
            fx_votes = (u * z) / x
            fy_votes = (v * z) / y

            # assume square pixels, hence same focal for X and Y
            f_votes = torch.cat((fx_votes.view(B, -1), fy_votes.view(B, -1)), dim=-1)
            focal = torch.nanmedian(f_votes, dim=-1).values

    elif focal_mode == 'weiszfeld': # 参考链接：https://blog.csdn.net/qianlinjun/article/details/53852306
        # init focal with l2 closed form
        # we try to find focal = argmin Sum | pixel - focal * (x,y)/z|
        xy_over_z = (pts3d[..., :2] / pts3d[..., 2:3]).nan_to_num(posinf=0, neginf=0)  # 转齐次坐标，即x，y除以z坐标
        # 1、初始化第一轮迭代时的focal
        dot_xy_px = (xy_over_z * pixels).sum(dim=-1)
        dot_xy_xy = xy_over_z.square().sum(dim=-1)

        focal = dot_xy_px.mean(dim=1) / dot_xy_xy.mean(dim=1)
        # 2、基于weiszfeld算法迭代
        # iterative re-weighted least-squares
        for iter in range(10):
            # re-weighting by inverse of distance
            dis = (pixels - focal.view(-1, 1, 1) * xy_over_z).norm(dim=-1) # norm：求第二范式
            # print(dis.nanmean(-1))
            w = dis.clip(min=1e-8).reciprocal() # 求倒数
            # update the scaling with the new weights
            focal = (w * dot_xy_px).mean(dim=1) / (w * dot_xy_xy).mean(dim=1)
    else:
        raise ValueError(f'bad {focal_mode=}')

    focal_base = max(H, W) / (2 * np.tan(np.deg2rad(60) / 2))  # size / 1.1547005383792515
    focal = focal.clip(min=min_focal*focal_base, max=max_focal*focal_base)
    # print(focal)
    return focal