# Copyright (c) 2020-2022 NVIDIA CORPORATION & AFFILIATES. All rights reserved. 
#
# NVIDIA CORPORATION, its affiliates and licensors retain all intellectual
# property and proprietary rights in and to this material, related
# documentation and any modifications thereto. Any use, reproduction, 
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# without an express license agreement from NVIDIA CORPORATION or 
# its affiliates is strictly prohibited.

import torch
import nvdiffrast.torch as dr

from . import util
from . import mesh

######################################################################################
# Computes the image gradient, useful for kd/ks smoothness losses
######################################################################################
def image_grad(buf, std=0.01):
    t, s = torch.meshgrid(torch.linspace(-1.0 + 1.0 / buf.shape[1], 1.0 - 1.0 / buf.shape[1], buf.shape[1], device="cuda"), 
                          torch.linspace(-1.0 + 1.0 / buf.shape[2], 1.0 - 1.0 / buf.shape[2], buf.shape[2], device="cuda"),
                          indexing='ij')
    tc   = torch.normal(mean=0, std=std, size=(buf.shape[0], buf.shape[1], buf.shape[2], 2), device="cuda") + torch.stack((s, t), dim=-1)[None, ...]
    tap  = dr.texture(buf, tc, filter_mode='linear', boundary_mode='clamp')
    return torch.abs(tap[..., :-1] - buf[..., :-1]) * tap[..., -1:] * buf[..., -1:]

######################################################################################
# Computes the avergage edge length of a mesh. 
# Rough estimate of the tessellation of a mesh. Can be used e.g. to clamp gradients
######################################################################################
def avg_edge_length(v_pos, t_pos_idx):
    e_pos_idx = mesh.compute_edges(t_pos_idx)
    edge_len  = util.length(v_pos[:, e_pos_idx[:, 0]] - v_pos[:, e_pos_idx[:, 1]])
    return torch.mean(edge_len)

######################################################################################
# Laplacian regularization using umbrella operator (Fujiwara / Desbrun).
# https://mgarland.org/class/geom04/material/smoothing.pdf
######################################################################################
def laplace_regularizer_const(v_pos, t_pos_idx):
    batch_size = v_pos.shape[0]

    term = torch.zeros_like(v_pos)
    norm = torch.zeros_like(v_pos[..., 0:1])

    v0 = v_pos[:, t_pos_idx[0, :, 0], :]
    v1 = v_pos[:, t_pos_idx[0, :, 1], :]
    v2 = v_pos[:, t_pos_idx[0, :, 2], :]

    term.scatter_add_(1, t_pos_idx[..., 0:1].repeat(batch_size, 1, 3), (v1 - v0) + (v2 - v0))
    term.scatter_add_(1, t_pos_idx[..., 1:2].repeat(batch_size, 1, 3), (v0 - v1) + (v2 - v1))
    term.scatter_add_(1, t_pos_idx[..., 2:3].repeat(batch_size, 1, 3), (v0 - v2) + (v1 - v2))

    two = torch.ones_like(v0) * 2.0
    norm.scatter_add_(1, t_pos_idx[..., 0:1].repeat(batch_size, 1, 3), two)
    norm.scatter_add_(1, t_pos_idx[..., 1:2].repeat(batch_size, 1, 3), two)
    norm.scatter_add_(1, t_pos_idx[..., 2:3].repeat(batch_size, 1, 3), two)

    term = term / torch.clamp(norm, min=1.0)

    return torch.mean(term ** 2)

######################################################################################
# Smooth vertex normals
######################################################################################
def normal_consistency(v_pos, t_pos_idx):
    # Compute face normals
    v0 = v_pos[:, t_pos_idx[0, :, 0]]
    v1 = v_pos[:, t_pos_idx[0, :, 1]]
    v2 = v_pos[:, t_pos_idx[0, :, 2]]

    face_normals = util.safe_normalize(torch.cross(v1 - v0, v2 - v0, dim=-1))

    tris_per_edge = mesh.compute_edge_to_face_mapping(t_pos_idx)

    # Fetch normals for both faces sharing an edge
    n0 = face_normals[:, tris_per_edge[:, 0], :]
    n1 = face_normals[:, tris_per_edge[:, 1], :]

    # Compute error metric based on normal difference
    term = torch.clamp(util.dot(n0, n1), min=-1.0, max=1.0)
    term = (1.0 - term) * 0.5

    return torch.mean(torch.abs(term))


def get_edge_length(v_pos, t_pos_idx):
    e_pos_idx = mesh.compute_edges(t_pos_idx)
    edge_len  = util.length(v_pos[:, e_pos_idx[:, 0]] - v_pos[:, e_pos_idx[:, 1]])
    return edge_len
