"""
Visualizing computational fluid dynamics on a car
===================================================
In this example we visualize a mesh drawn from the :class:`~neuralop.data.datasets.car_cfd_dataset.CarCFDDataset`.
This tutorial demonstrates how to work with unstructured mesh data from computational fluid dynamics (CFD)
simulations. We will explore the 3D geometry of a car and understand how pressure fields are distributed
over the surface, which is crucial for aerodynamic analysis and neural operator applications.
The CarCFD dataset contains:
- 3D triangular mesh data representing the car surface
- Pressure fields computed from CFD simulations
- Query points for neural operator training
"""
# %%
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#
#
#
# Import dependencies
# --------------------
# We first import our `neuralop` library and required dependencies.
import numpy as np
import torch
import matplotlib
import matplotlib.pyplot as plt
from neuralop.data.datasets import load_mini_car
font = {"size": 12}
matplotlib.rc("font", **font)
torch.manual_seed(0)
np.random.seed(0)
# %%
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#
#
#
# Understanding the data structure
# ---------------------------------
# The data in a ``MeshDataModule`` is structured as a dictionary of tensors and important scalar values encoding
# a 3D triangle mesh over the surface of a car.
# Each sample includes the coordinates of all triangle vertices and the centroids of each triangle face.
#
# In this case, the creators used OpenFOAM to simulate the surface air pressure on car geometries in a wind tunnel.
# The 3D Navier-Stokes equations were simulated for a variety of inlet velocities over each surface using the
# **OpenFOAM** computational solver to predict pressure at every vertex on the mesh.
# Each sample here also has an inlet velocity scalar and a pressure field that maps 1-to-1 with the vertices on the mesh.
# The :class:`CarCFDDataset ` (full dataset) is stored in triangle mesh files for downstream processing.
# For the sake of simplicity, we've packaged a few examples of the data after processing in tensor form to visualize here:
data_list = load_mini_car()
sample = data_list[0]
print(f"Available data keys: {sample.keys()}")
# %%
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#
#
#
# Visualizing the car surface with pressure distribution
# ------------------------------------------------------
# Let's take a look at the vertices and pressure values to understand the 3D structure
# and how pressure varies across the car surface.
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(projection="3d")
# By default the data is normalized into the unit cube. To get a
# better look at it, we scale the z-direction up.
scatter = ax.scatter(sample["vertices"][:, 0], sample["vertices"][:, 1],
sample["vertices"][:, 2] * 2, s=2, c=sample["press"].numpy(), cmap="viridis")
ax.set_xlim(0,2)
ax.set_ylim(0,2)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
ax.view_init(elev=20, azim=150, roll=0, vertical_axis="y")
ax.set_title("Pressure distribution over car mesh vertices")
fig.colorbar(scatter, pad=0.2, label="normalized pressure", ax=ax)
plt.draw()
# %%
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#
#
#
# Understanding query points for neural operator training
# --------------------------------------------------------
# Each sample in the ``CarCFDDataset`` also includes a set of latent query points on which we learn a function
# to enable learning with an FNO in the middle of our geometry-informed models. Let's visualize the queries
# on top of the car from before:
fig = plt.figure(figsize=(8,10))
ax = fig.add_subplot(projection="3d")
scatter = ax.scatter(sample["vertices"][:, 0], sample["vertices"][:, 1], sample["vertices"][:, 2] * 2, s=4, label="Car surface")
queries = sample["query_points"].view(-1, 3) # unroll our cube tensor into a point cloud
ax.scatter(queries[:, 0], queries[:, 1], queries[:, 2] * 2, s=1, alpha=0.5, label="Latent queries")
ax.set_xlim(0, 2)
ax.set_ylim(0, 2)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
ax.legend()
ax.view_init(elev=20, azim=150, roll=0, vertical_axis="y")
ax.set_title("Query points and car surface vertices")
# %%
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#
#
#
# Neighbor search between 3D point clouds
# ----------------------------------------
# In :doc:`../layers/plot_neighbor_search` we demonstrate our neighbor search
# on a simple 2D point cloud. Let's try that again with our 3D car surface points here.
from neuralop.layers.neighbor_search import native_neighbor_search
verts = sample["vertices"]
query_point = queries[3300]
nbr_data = native_neighbor_search(data=verts, queries=query_point.unsqueeze(0), radius=0.5)
# %% Visualizing neighborhoods
# Let's plot the new neighbors we just found on top of the car surface point cloud.
fig = plt.figure(figsize=(8, 10))
ax1 = fig.add_subplot(2, 1, 1, projection="3d")
ax2 = fig.add_subplot(2, 1, 2, projection="3d")
neighbors = verts[nbr_data["neighbors_index"]]
# Plotting just one query point vs. the car
ax1.scatter(verts[:, 0], verts[:, 1], verts[:, 2]*2, s=1, alpha=0.1)
ax1.scatter(query_point[0], query_point[1], query_point[2]*2, s=10, c="red", label="Single query")
ax1.view_init(elev=20, azim=-20, roll=0, vertical_axis="y")
ax1.legend()
ax1.set_xlim(0, 2)
ax1.set_ylim(0, 2)
ax1.set_xlabel("x")
ax1.set_ylabel("y")
ax1.set_zlabel("z")
ax1.view_init(elev=20, azim=-20, roll=0, vertical_axis="y")
ax1.grid(False)
ax1.set_title("One query point")
# Plotting all query points and neighbors
ax2.scatter(verts[:, 0], verts[:, 1], verts[:, 2]*2, s=0.5, alpha=0.4, label="Car surface")
ax2.scatter(queries[:, 0], queries[:, 1], queries[:, 2]*2, s=0.5, alpha=0.2, label="Latent queries")
ax2.scatter(neighbors[:, 0], neighbors[:, 1], neighbors[:, 2]*2, s=10, label="Neighbors on\ncar surface",)
ax2.legend()
ax2.set_xlim(0, 2)
ax2.set_ylim(0, 2)
ax2.set_xlabel("x")
ax2.set_ylabel("y")
ax2.set_zlabel("z")
ax2.view_init(elev=20, azim=-20, roll=0, vertical_axis="y")
ax2.set_title("Neighbor points from car for one query point")
ax2.grid(False)
for ax in ax1, ax2:
ax.set_xticks([])
ax.set_yticks([])
ax.set_zticks([])
plt.draw()
# %%
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#
#
#
# Connecting neighbors to query
# ------------------------------
# First, let's make a simple utiltiy to add arrows to our 3D plot:
import numpy as np
from matplotlib import pyplot as plt
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d
class Arrow3D(FancyArrowPatch):
def __init__(self, xs, ys, zs, *args, **kwargs):
super().__init__((0, 0), (0, 0), *args, **kwargs)
self._verts3d = xs, ys, zs
def do_3d_projection(self, renderer=None):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, self.axes.M)
self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
return np.min(zs)
# Creating plots
fig = plt.figure(figsize=(8, 10))
ax1 = fig.add_subplot(projection="3d")
neighbors = verts[nbr_data["neighbors_index"]]
# Plotting just one query point vs. the car
ax1.scatter(verts[:, 0], verts[:, 1], verts[:, 2]*2, s=1, alpha=0.1)
ax1.scatter(query_point[0], query_point[1], query_point[2]*2, s=10, c="red", label="Single query")
ax1.scatter(neighbors[:, 0], neighbors[:, 1], neighbors[:, 2]*2, s=10, label="Neighbors on\ncar surface",)
ax1.view_init(elev=20, azim=-20, roll=0, vertical_axis="y")
ax1.legend()
ax1.set_xlim(0, 2)
ax1.set_ylim(0, 2)
ax1.set_xlabel("x")
ax1.set_ylabel("y")
ax1.set_zlabel("z")
ax1.view_init(elev=20, azim=-20, roll=0, vertical_axis="y")
ax1.grid(False)
ax1.set_title("One query point")
for ax in [ax1]:
ax.set_xticks([])
ax.set_yticks([])
ax.set_zticks([])
# Add arrows between neighbors and query
arrow_prop_dict = dict(mutation_scale=1, arrowstyle="-|>", color="red", shrinkA=1, shrinkB=1, alpha=0.1)
for nbr in neighbors:
a = Arrow3D(
[query_point[0], nbr[0]],
[query_point[1], nbr[1]],
[query_point[2] * 2, nbr[2] * 2],
**arrow_prop_dict,
)
ax1.add_artist(a)
fig.tight_layout()
plt.draw()