Reuse one geometry across registered tracers

    ## Author

    [Rafael S. de Souza](https://rafaelsdesouza.com.br/)

    ## Learning goals

    - separate geometry from measurement

• compare profiles without redefining radial position

    ## Keywords
  
    registered tracers, geometry reuse, radial profiles
  
    ## Summary
  
    Measure brightness, colour, and velocity-like fields on one immutable geometry.
  
    ## Resources
  
    - [Open in Colab](https://colab.research.google.com/github/RafaelSdeSouza/radialpaths/blob/v0.1.0/examples/04_registered_tracers.ipynb)
    - [Documentation](https://rafaelsdesouza.com.br/radialpaths/docs/)
    - [Source](https://github.com/RafaelSdeSouza/radialpaths)
    - Paper/preprint: bibliographic link pending
    - [Citation metadata](https://github.com/RafaelSdeSouza/radialpaths/blob/v0.1.0/CITATION.cff)
  
    In Colab, the setup cell installs the immutable RadialPaths 0.1.0 tag.
    In a local checkout, it imports the source tree directly.

from pathlib import Path
import subprocess
import sys

if "google.colab" in sys.modules:
    subprocess.check_call([
        sys.executable, "-m", "pip", "install", "-q",
        "radialpaths[plot] @ git+https://github.com/RafaelSdeSouza/radialpaths.git@v0.1.0",
    ])
else:
    source = Path("src") if Path("src/radialpaths").exists() else Path("../src")
    if str(source.resolve()) not in sys.path:
        sys.path.insert(0, str(source.resolve()))

import matplotlib.pyplot as plt
import numpy as np
from radialpaths import build_geometry, radial_profile

plt.rcParams.update({"font.size": 10, "axes.titlesize": 11, "axes.linewidth": 0.8})

yy, xx = np.indices((91, 121), dtype=float)
support = ((xx - 55) / 47) ** 2 + ((yy - 45) / 31) ** 2 <= 1
support |= ((xx >= 48) & (xx <= 106) & (np.abs(yy - (45 + 0.25 * (xx - 48))) <= 7))
centres = [(43, 28), (54, 81)]
geometry = build_geometry(support, centres)

brightness = np.full(support.shape, np.nan)
colour = np.full(support.shape, np.nan)
velocity = np.full(support.shape, np.nan)
brightness[support] = np.exp(-geometry.centre_distance[support] / 13)
colour[support] = 0.2 + 0.65 * xx[support] / support.shape[1]
velocity[support] = -90 + 180 * xx[support] / support.shape[1]

measurements = {
    "brightness": radial_profile(brightness, geometry, coordinate="rho_X"),
    "colour": radial_profile(colour, geometry, coordinate="rho_X"),
    "velocity": radial_profile(velocity, geometry, coordinate="rho_X"),
}

fig, axes = plt.subplots(1, 3, figsize=(10.7, 3.2), constrained_layout=True)
for ax, (name, profile) in zip(axes, measurements.items()):
    for centre_index, values in enumerate(profile.median):
        ax.plot(profile.radius, values, lw=2, label=f"Centre {centre_index + 1}")
    ax.set(xlabel=r"Normalized progression $\rho_X$", title=name.capitalize())
    ax.spines[["top", "right"]].set_visible(False)
axes[0].legend(frameon=False, fontsize=8)
plt.show()

All three profile calls use the same support, centre assignment, graph distances, and coordinate arrays. Only the registered pixel values passed to the estimator differ.