vortrace
Exact projections through voronoi meshes faster than you can say "I have a problem with your AGN model."
What does vortrace do?
One-dimensional integrals through voronoi meshes can be expensive. Because the mesh is unstructured, it is not obvious a priori where a line intersects the faces of which cells. Brute force methods which just sample large numbers of points struggle with systems with a large dynamic range in cell size, like cosmological simulations.
vortrace does one-dimensional integrals with the fewest number of nearest neighbor calls possible. With an optimized yet lightweight C++ backend and a user-friendly python frontend, it's easy to get started.
Installation
Installing vortrace can be done using pip:
pip install vortrace
Or see the docs for more installation options.
Getting Started
Making your first projection takes only three lines if you've already prepared your coordinates (pos), density (rho), and projection parameters (BoxSize, L, npix):
# assuming pos and rho have been defined elsewhere
# pos is a (N,3) numpy array
# rho is a (N,) numpy array
BoxSize = 100
center = np.array([BoxSize]*3)/2.
# define image grid. e.g., want to make a 20 kpc x 20 kpc image
L = 20
extent = [center[0]-L/2., center[0]+L/2., center[1]-L/2., center[1]+L/2.]
# integrate through the full box along the z-axis with resolution 256^2
bounds = [0, BoxSize]
npix = 256
# now we make the projection. proj_xy is a (npix, npix) numpy array
import vortrace as vt
pc = vt.ProjectionCloud(pos, rho)
proj_xy = pc.grid_projection(extent, npix, bounds)
Volume Rendering
vortrace also supports volume rendering. Define a transfer function in Python that maps cell quantities to (R, G, B, alpha), then pass the 4-field array to the integrator:
# apply a transfer function to get RGBA per cell
R, G, B, alpha = my_transfer_function(rho)
fields_rgba = np.column_stack([R, G, B, alpha])
pc = vt.ProjectionCloud(pos, fields_rgba)
img = pc.grid_projection(extent, npix, bounds, reduction='volume')
# img is a (npix, npix, 3) RGB array
See the volume rendering tutorial for a complete example with a sample transfer function.
How Does vortrace Work?
A one-dimensional integral through an unstructured mesh at first glance seems very complicated, as one must wrangle with the complex geometry of a Voronoi mesh. However, one can use the definition of the mesh to simplify the operation considerably.
vortrace is a recursive algorithm that works by continually splitting the integral up until you are simply integrating between two points in neighboring cells, at which point the integral is trivial. It starts by constructing a kDTree using nanoflann to allow for efficient nearest neighbor searches. Then:
-
Assume the two points you are trying to integrate between (
p_aandp_b) are in neighboring Voronoi cells. Find those cells (v_aandv_b) quickly using thekDTree. -
Using these four points, find the split point
p_s- the point on the line connectingp_atop_bwhich intersects the face between cellsv_aandv_b. -
Query the
kDTreefor the cell thatp_sis in. If it is one ofv_aorv_b, go to 3a. If not, go to 3b.a. You are done and can return the integral as the sum of
|p_a - p_s| * rho_aand|p_s - p_b| * rho_b, whererho_iis the density of celli.b. Return to 1 and start the integrals
p_a -- p_sandp_s -- p_b.
License
vortrace is released under the MIT License. It is authored by Angus Beane and Matthew C. Smith.
This project incorporates nanoflann v1.3.2, a header-only library distributed under the BSD License.
1 maintainer
Metadata
1 maintainer
Release files for vortrace 0.1.3
For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.
Source distribution (sdist)
| File | Size | Uploaded | Provenance | Actions |
|---|---|---|---|---|
| vortrace-0.1.3.tar.gz | 4.8 MB | Without provenance | Details for vortrace-0.1.3.tar.gz |
Built distributions (wheels)
Total release size: 38.0 MB
Release files / vortrace-0.1.3.tar.gz
| Download URL | vortrace-0.1.3.tar.gz |
|---|---|
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| Tags | Source |
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Release files / vortrace-0.1.3-cp311-cp311-musllinux_1_2_x86_64.whl
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Release files / vortrace-0.1.3-cp311-cp311-musllinux_1_2_aarch64.whl
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Release files / vortrace-0.1.3-cp311-cp311-manylinux_2_26_aarch64.manylinux_2_28_aarch64.whl
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Release files / vortrace-0.1.3-cp311-cp311-macosx_11_0_arm64.whl
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Release files / vortrace-0.1.3-cp311-cp311-macosx_10_9_x86_64.whl
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Release files / vortrace-0.1.3-cp310-cp310-musllinux_1_2_x86_64.whl
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Release files / vortrace-0.1.3-cp310-cp310-musllinux_1_2_aarch64.whl
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Release files / vortrace-0.1.3-cp310-cp310-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
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Release files / vortrace-0.1.3-cp310-cp310-manylinux_2_26_aarch64.manylinux_2_28_aarch64.whl
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Release files / vortrace-0.1.3-cp310-cp310-macosx_11_0_arm64.whl
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Release files / vortrace-0.1.3-cp310-cp310-macosx_10_9_x86_64.whl
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Release files / vortrace-0.1.3-cp39-cp39-musllinux_1_2_x86_64.whl
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Release files / vortrace-0.1.3-cp39-cp39-musllinux_1_2_aarch64.whl
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Release files / vortrace-0.1.3-cp39-cp39-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
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Release files / vortrace-0.1.3-cp39-cp39-manylinux_2_26_aarch64.manylinux_2_28_aarch64.whl
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Release files / vortrace-0.1.3-cp39-cp39-macosx_11_0_arm64.whl
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Release files / vortrace-0.1.3-cp39-cp39-macosx_10_9_x86_64.whl
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Release files / vortrace-0.1.3-cp38-cp38-musllinux_1_2_x86_64.whl
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Release files / vortrace-0.1.3-cp38-cp38-musllinux_1_2_aarch64.whl
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Release files / vortrace-0.1.3-cp38-cp38-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
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Release files / vortrace-0.1.3-cp38-cp38-manylinux_2_26_aarch64.manylinux_2_28_aarch64.whl
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Release files / vortrace-0.1.3-cp38-cp38-macosx_11_0_arm64.whl
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Release files / vortrace-0.1.3-cp38-cp38-macosx_10_9_x86_64.whl
| Download URL | vortrace-0.1.3-cp38-cp38-macosx_10_9_x86_64.whl |
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Security for vortrace 0.1.3
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