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# SPDX-FileCopyrightText: Copyright (c) 2023 - 2025 NVIDIA CORPORATION & AFFILIATES.
# SPDX-FileCopyrightText: All rights reserved.
# SPDX-License-Identifier: Apache-2.0
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import List, Tuple
import numpy as np
import torch
from torch import Tensor
def latlon2xyz(latlon: Tensor, radius: float = 1, unit: str = "deg") -> Tensor:
"""
Converts latlon in degrees to xyz
Based on: https://stackoverflow.com/questions/1185408
- The x-axis goes through long,lat (0,0);
- The y-axis goes through (0,90);
- The z-axis goes through the poles.
Parameters
----------
latlon : Tensor
Tensor of shape (N, 2) containing latitudes and longitudes
radius : float, optional
Radius of the sphere, by default 1
unit : str, optional
Unit of the latlon, by default "deg"
Returns
-------
Tensor
Tensor of shape (N, 3) containing x, y, z coordinates
"""
if unit == "deg":
latlon = deg2rad(latlon)
elif unit == "rad":
pass
else:
raise ValueError("Not a valid unit")
lat, lon = latlon[:, 0], latlon[:, 1]
x = radius * torch.cos(lat) * torch.cos(lon)
y = radius * torch.cos(lat) * torch.sin(lon)
z = radius * torch.sin(lat)
return torch.stack((x, y, z), dim=1)
def xyz2latlon(xyz: Tensor, radius: float = 1, unit: str = "deg") -> Tensor:
"""
Converts xyz to latlon in degrees
Based on: https://stackoverflow.com/questions/1185408
- The x-axis goes through long,lat (0,0);
- The y-axis goes through (0,90);
- The z-axis goes through the poles.
Parameters
----------
xyz : Tensor
Tensor of shape (N, 3) containing x, y, z coordinates
radius : float, optional
Radius of the sphere, by default 1
unit : str, optional
Unit of the latlon, by default "deg"
Returns
-------
Tensor
Tensor of shape (N, 2) containing latitudes and longitudes
"""
lat = torch.arcsin(xyz[:, 2] / radius)
lon = torch.arctan2(xyz[:, 1], xyz[:, 0])
if unit == "deg":
return torch.stack((rad2deg(lat), rad2deg(lon)), dim=1)
elif unit == "rad":
return torch.stack((lat, lon), dim=1)
else:
raise ValueError("Not a valid unit")
def geospatial_rotation(
invar: Tensor, theta: Tensor, axis: str, unit: str = "rad"
) -> Tensor:
"""Rotation using right hand rule
Parameters
----------
invar : Tensor
Tensor of shape (N, 3) containing x, y, z coordinates
theta : Tensor
Tensor of shape (N, ) containing the rotation angle
axis : str
Axis of rotation
unit : str, optional
Unit of the theta, by default "rad"
Returns
-------
Tensor
Tensor of shape (N, 3) containing the rotated x, y, z coordinates
"""
# get the right unit
if unit == "deg":
invar = rad2deg(invar)
elif unit == "rad":
pass
else:
raise ValueError("Not a valid unit")
invar = torch.unsqueeze(invar, -1)
rotation = torch.zeros((theta.size(0), 3, 3))
cos = torch.cos(theta)
sin = torch.sin(theta)
if axis == "x":
rotation[:, 0, 0] += 1.0
rotation[:, 1, 1] += cos
rotation[:, 1, 2] -= sin
rotation[:, 2, 1] += sin
rotation[:, 2, 2] += cos
elif axis == "y":
rotation[:, 0, 0] += cos
rotation[:, 0, 2] += sin
rotation[:, 1, 1] += 1.0
rotation[:, 2, 0] -= sin
rotation[:, 2, 2] += cos
elif axis == "z":
rotation[:, 0, 0] += cos
rotation[:, 0, 1] -= sin
rotation[:, 1, 0] += sin
rotation[:, 1, 1] += cos
rotation[:, 2, 2] += 1.0
else:
raise ValueError("Invalid axis")
outvar = torch.matmul(rotation, invar)
outvar = outvar.squeeze()
return outvar
def azimuthal_angle(lon: Tensor) -> Tensor:
"""
Gives the azimuthal angle of a point on the sphere
Parameters
----------
lon : Tensor
Tensor of shape (N, ) containing the longitude of the point
Returns
-------
Tensor
Tensor of shape (N, ) containing the azimuthal angle
"""
angle = torch.where(lon >= 0.0, 2 * np.pi - lon, -lon)
return angle
def polar_angle(lat: Tensor) -> Tensor:
"""
Gives the polar angle of a point on the sphere
Parameters
----------
lat : Tensor
Tensor of shape (N, ) containing the latitude of the point
Returns
-------
Tensor
Tensor of shape (N, ) containing the polar angle
"""
angle = torch.where(lat >= 0.0, lat, 2 * np.pi + lat)
return angle
def deg2rad(deg: Tensor) -> Tensor:
"""Converts degrees to radians
Parameters
----------
deg :
Tensor of shape (N, ) containing the degrees
Returns
-------
Tensor
Tensor of shape (N, ) containing the radians
"""
return deg * np.pi / 180
def rad2deg(rad):
"""Converts radians to degrees
Parameters
----------
rad :
Tensor of shape (N, ) containing the radians
Returns
-------
Tensor
Tensor of shape (N, ) containing the degrees
"""
return rad * 180 / np.pi
def cell_to_adj(cells: List[List[int]]):
"""creates adjancy matrix in COO format from mesh cells
Parameters
----------
cells : List[List[int]]
List of cells, each cell is a list of 3 vertices
Returns
-------
src, dst : List[int], List[int]
List of source and destination vertices
"""
num_cells = np.shape(cells)[0]
src = [cells[i][indx] for i in range(num_cells) for indx in [0, 1, 2]]
dst = [cells[i][indx] for i in range(num_cells) for indx in [1, 2, 0]]
return src, dst
def max_edge_length(
vertices: List[List[float]], source_nodes: List[int], destination_nodes: List[int]
) -> float:
"""
Compute the maximum edge length in a graph.
Parameters:
vertices (List[List[float]]): A list of tuples representing the coordinates of the vertices.
source_nodes (List[int]): A list of indices representing the source nodes of the edges.
destination_nodes (List[int]): A list of indices representing the destination nodes of the edges.
Returns:
The maximum edge length in the graph (float).
"""
vertices_np = np.array(vertices)
source_coords = vertices_np[source_nodes]
dest_coords = vertices_np[destination_nodes]
# Compute the squared distances for all edges
squared_differences = np.sum((source_coords - dest_coords) ** 2, axis=1)
# Compute the maximum edge length
max_length = np.sqrt(np.max(squared_differences))
return max_length
def get_face_centroids(
vertices: List[Tuple[float, float, float]], faces: List[List[int]]
) -> List[Tuple[float, float, float]]:
"""
Compute the centroids of triangular faces in a graph.
Parameters:
vertices (List[Tuple[float, float, float]]): A list of tuples representing the coordinates of the vertices.
faces (List[List[int]]): A list of lists, where each inner list contains three indices representing a triangular face.
Returns:
List[Tuple[float, float, float]]: A list of tuples representing the centroids of the faces.
"""
centroids = []
for face in faces:
# Extract the coordinates of the vertices for the current face
v0 = vertices[face[0]]
v1 = vertices[face[1]]
v2 = vertices[face[2]]
# Compute the centroid of the triangle
centroid = (
(v0[0] + v1[0] + v2[0]) / 3,
(v0[1] + v1[1] + v2[1]) / 3,
(v0[2] + v1[2] + v2[2]) / 3,
)
centroids.append(centroid)
return centroids
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