# Copyright (c) 2020-2022 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
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# documentation and any modifications thereto. Any use, reproduction,
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# without an express license agreement from NVIDIA CORPORATION or
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import torch
import nvdiffrast.torch as dr
import pytorch3d.ops
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):
term = torch.zeros_like(v_pos)
norm = torch.zeros_like(v_pos[..., 0:1])
v0 = v_pos[t_pos_idx[:, 0], :]
v1 = v_pos[t_pos_idx[:, 1], :]
v2 = v_pos[t_pos_idx[:, 2], :]
term.scatter_add_(0, t_pos_idx[:, 0:1].repeat(1,3), (v1 - v0) + (v2 - v0))
term.scatter_add_(0, t_pos_idx[:, 1:2].repeat(1,3), (v0 - v1) + (v2 - v1))
term.scatter_add_(0, t_pos_idx[:, 2:3].repeat(1,3), (v0 - v2) + (v1 - v2))
two = torch.ones_like(v0) * 2.0
norm.scatter_add_(0, t_pos_idx[:, 0:1], two)
norm.scatter_add_(0, t_pos_idx[:, 1:2], two)
norm.scatter_add_(0, t_pos_idx[:, 2:3], two)
term = term / torch.clamp(norm, min=1.0)
return torch.mean(term**2)
def scale_dependent_relative_laplace_regularizer_const(v_pos, v_pos_abs, t_pos_idx):
term = torch.zeros_like(v_pos)
norm = torch.zeros_like(v_pos[..., 0:1])
v0 = v_pos[t_pos_idx[:, 0], :]
v1 = v_pos[t_pos_idx[:, 1], :]
v2 = v_pos[t_pos_idx[:, 2], :]
v0_abs = v_pos_abs[t_pos_idx[:, 0], :]
v1_abs = v_pos_abs[t_pos_idx[:, 1], :]
v2_abs = v_pos_abs[t_pos_idx[:, 2], :]
eps = 1e-8
deformable_dist = False
if deformable_dist:
raise NotImplementedError
else:
## The original distance; does not account for the
v01_dist = ((v0_abs - v1_abs).pow(2).sum(-1, keepdim=True) + eps).sqrt()
v12_dist = ((v1_abs - v2_abs).pow(2).sum(-1, keepdim=True) + eps).sqrt()
v20_dist = ((v2_abs - v0_abs).pow(2).sum(-1, keepdim=True) + eps).sqrt()
term.scatter_add_(0, t_pos_idx[:, 0:1].repeat(1,3), (v1 - v0) / v01_dist + (v2 - v0) / v20_dist)
term.scatter_add_(0, t_pos_idx[:, 1:2].repeat(1,3), (v0 - v1) / v01_dist + (v2 - v1) / v12_dist)
term.scatter_add_(0, t_pos_idx[:, 2:3].repeat(1,3), (v0 - v2) / v20_dist + (v1 - v2) / v12_dist)
return torch.mean(term**2)
def scale_dependent_laplace_regularizer_const(v_pos, t_pos_idx):
term = torch.zeros_like(v_pos)
norm = torch.zeros_like(v_pos[..., 0:1])
v0 = v_pos[t_pos_idx[:, 0], :]
v1 = v_pos[t_pos_idx[:, 1], :]
v2 = v_pos[t_pos_idx[:, 2], :]
eps = 1e-8
v01_dist = ((v0 - v1).pow(2).sum(-1, keepdim=True) + eps).sqrt()
v12_dist = ((v1 - v2).pow(2).sum(-1, keepdim=True) + eps).sqrt()
v20_dist = ((v2 - v0).pow(2).sum(-1, keepdim=True) + eps).sqrt()
stopgd = True
if stopgd:
v01_dist = v01_dist.detach()
v12_dist = v12_dist.detach()
v20_dist = v20_dist.detach()
term.scatter_add_(0, t_pos_idx[:, 0:1].repeat(1,3), (v1 - v0) / v01_dist + (v2 - v0) / v20_dist)
term.scatter_add_(0, t_pos_idx[:, 1:2].repeat(1,3), (v0 - v1) / v01_dist + (v2 - v1) / v12_dist)
term.scatter_add_(0, t_pos_idx[:, 2:3].repeat(1,3), (v0 - v2) / v20_dist + (v1 - v2) / v12_dist)
return torch.mean(term**2)
def mesh_repulsion(v_pos, t_pos_idx):
term = torch.zeros_like(v_pos)
v0 = v_pos[t_pos_idx[:, 0], :]
v1 = v_pos[t_pos_idx[:, 1], :]
v2 = v_pos[t_pos_idx[:, 2], :]
eps = 1e-8
v01_dist = ((v0 - v1).pow(2).sum(-1, keepdim=True) + eps).sqrt()
v12_dist = ((v1 - v2).pow(2).sum(-1, keepdim=True) + eps).sqrt()
v20_dist = ((v2 - v0).pow(2).sum(-1, keepdim=True) + eps).sqrt()
term.scatter_add_(0, t_pos_idx[:, 0:1], v01_dist)
term.scatter_add_(0, t_pos_idx[:, 1:2], v12_dist)
term.scatter_add_(0, t_pos_idx[:, 2:3], v20_dist)
return term**2
def laplace_regularizer_const_adaptive(v_pos, t_pos_idx):
term = torch.zeros_like(v_pos)
norm = torch.zeros_like(v_pos[..., 0:1])
v0 = v_pos[t_pos_idx[:, 0], :]
v1 = v_pos[t_pos_idx[:, 1], :]
v2 = v_pos[t_pos_idx[:, 2], :]
term.scatter_add_(0, t_pos_idx[:, 0:1].repeat(1,3), (v1 - v0) + (v2 - v0))
term.scatter_add_(0, t_pos_idx[:, 1:2].repeat(1,3), (v0 - v1) + (v2 - v1))
term.scatter_add_(0, t_pos_idx[:, 2:3].repeat(1,3), (v0 - v2) + (v1 - v2))
two = torch.ones_like(v0) * 2.0
norm.scatter_add_(0, t_pos_idx[:, 0:1], two)
norm.scatter_add_(0, t_pos_idx[:, 1:2], two)
norm.scatter_add_(0, t_pos_idx[:, 2:3], two)
term = term / torch.clamp(norm, min=1.0)
v_pos = v_pos.unsqueeze(0) * 64
with torch.no_grad():
scale = (pytorch3d.ops.knn.knn_points(v_pos, v_pos, K=2).dists[0, :, -1].detach()).sqrt().pow(1.5) ## K=2 because dist(self, self)=0
dist = term.pow(2).mean(-1) ### since the vanilla one uses mean
return torch.mean(dist * scale)
# def laplace_regularizer_const_sec_order(v_pos, t_pos_idx):
# term = torch.zeros_like(v_pos)
# norm = torch.zeros_like(v_pos[..., 0:1])
# v0 = v_pos[t_pos_idx[:, 0], :]
# v1 = v_pos[t_pos_idx[:, 1], :]
# v2 = v_pos[t_pos_idx[:, 2], :]
# term.scatter_add_(0, t_pos_idx[:, 0:1].repeat(1,3), (v1 - v0) + (v2 - v0))
# term.scatter_add_(0, t_pos_idx[:, 1:2].repeat(1,3), (v0 - v1) + (v2 - v1))
# term.scatter_add_(0, t_pos_idx[:, 2:3].repeat(1,3), (v0 - v2) + (v1 - v2))
# two = torch.ones_like(v0) * 2.0
# norm.scatter_add_(0, t_pos_idx[:, 0:1], two)
# norm.scatter_add_(0, t_pos_idx[:, 1:2], two)
# norm.scatter_add_(0, t_pos_idx[:, 2:3], 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], :]
v1 = v_pos[t_pos_idx[:, 1], :]
v2 = v_pos[t_pos_idx[:, 2], :]
face_normals = util.safe_normalize(torch.cross(v1 - v0, v2 - v0))
tris_per_edge = mesh.compute_edge_to_face_mapping(t_pos_idx)
# Fetch normals for both faces sharind 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))