Periodic Boundary Conditions

vortrace supports periodic boundary conditions for cosmological simulation boxes. When enabled, the nearest-neighbor search checks periodic images of each query point, ensuring correct projections across box boundaries.

Note

Periodic integrals are assumed to lie entirely within a single periodic image of the box. If your ray spans multiple periodic images, you must split it into segments that each fit within one box image.

Usage

Python

import numpy as np
import vortrace as vt

pc = vt.ProjectionCloud(
    pos, rho,
    boundbox=[0, BoxSize, 0, BoxSize, 0, BoxSize],
    periodic=True,
)

image = pc.grid_projection(
    extent=[0, BoxSize],
    nres=256,
    bounds=[0, BoxSize],
    center=None,
)

fig, ax, im = vt.plot.plot_grid(
    image,
    extent=[0, BoxSize, 0, BoxSize],
    label=r"$\Sigma$",
)

C++

#include <vortrace/vortrace.hpp>

std::array<double, 6> subbox = {0, BoxSize, 0, BoxSize, 0, BoxSize};

PointCloud cloud;
cloud.loadPoints(
    pos, npart, fields, npart, 1, subbox,
    nullptr, 0,   // no cell volumes
    true          // periodic = true
);
cloud.buildTree();

// Projections work as usual -- periodicity is handled internally
Projection proj(starts, ends, ngrid);
proj.makeProjection(cloud, ReductionMode::Sum);

Behavior differences

When periodic=True:

• The bounding box defines the periodic domain. The kD-tree wraps queries across boundaries.

• No spatial filtering is applied – all particles are used regardless of the bounding box. (In non-periodic mode, particles outside the padded subbox are discarded to reduce computation.) If you need to reduce the number of particles for performance, filter them yourself before passing them to vortrace.

Note

The bounding box must match the simulation box for periodic mode to produce correct results.