skymask-py 0.1.0

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skymask-py

Compute piecewise analytical solutions of skymask for given polyhedra.
Provides efficient algorithms, parallel computing, and sampling methods.

Python binding of rust crate skymask-rs.

Benchmark

Runs on 11th Gen Intel(R) Core(TM) i7-11800H @ 2.30GHz (8 Physical Cores / 16 Logical Threads) and NVIDIA GeForce RTX 3070 Laptop GPU. The benchmark code is available at benchmark.py.

Method	Fps	Time Complexity
Parallel sampling: World.par_samples	1648.87	$O((k \cdot n \log n + m) \cdot \log r)$
Sequential sampling: SkymaskMap.samples	176.05	$O((k \cdot n \log n + m) \cdot \log r)$
Naive approach with Cupy	63.40	$O(m \cdot n)$
Naive approach with Numpy	5.44	$O(m \cdot n)$

Where $n$ represents the number of line segments, and $k$ denotes the average number of segments each line overlaps with in the analytical result. $r$ denotes the number of segments in the analytical result, and $m$ refers to the number of discrete sample points taken from the skymask.

Install

Precompiled wheels at https://github.com/HellOwhatAs/skymask-py/releases.

Example

import skymask_py
import numpy as np
import matplotlib.pyplot as plt

lines = np.array([
    #  xa,   ya,   za,   xb,   yb,   zb
    [ 1.0,  1.0,  1.0, -1.0,  1.0,  1.0],
    [-1.0,  1.0,  1.0, -1.0, -1.0,  1.0],
    [-1.0, -1.0,  1.0,  1.0, -1.0,  1.0],
    [ 1.0, -1.0,  1.0,  1.0,  1.0,  1.0],
])
world = skymask_py.World.from_lines(lines, np.inf)
for pos in [(0, 0), (0.5, 0)]:
    skymask = world.skymask(pos)
    print(f"\nskymask at {pos}")
    print("\n".join(
        f"pi/2-atan({a}*cos(t) + {b}*sin(t)) if t in [{s}, {e})"
        for (s, e), (a, b) in skymask.segments()
    ))

    fig, ax = plt.subplots(subplot_kw={"projection": "polar"})
    ax.set_title(f"skymask at {pos}")
    ax.yaxis.set_major_formatter("")
    x = np.linspace(-np.pi, np.pi, num=500, endpoint=True)
    x[-1] = x[0]
    y = np.pi / 2 - skymask.samples(x)
    ax.plot(x, y)
    ax.fill_between(x, y, np.pi / 2, alpha=0.2)
    ax.set_ylim(0, np.pi / 2)
plt.show()

Outputs

skymask at (0, 0)
pi/2-atan(-1.0*cos(t) + -0.0*sin(t)) if t in [-3.141592653589793, -2.356194490192345)
pi/2-atan(-0.0*cos(t) + -1.0*sin(t)) if t in [-2.356194490192345, -0.7853981633974483)
pi/2-atan(1.0*cos(t) + -0.0*sin(t)) if t in [-0.7853981633974483, 0.7853981633974483)
pi/2-atan(-0.0*cos(t) + 1.0*sin(t)) if t in [0.7853981633974483, 2.356194490192345)
pi/2-atan(-1.0*cos(t) + -0.0*sin(t)) if t in [2.356194490192345, 3.141592653589793)

skymask at (0.5, 0)
pi/2-atan(-0.6666666666666666*cos(t) + -0.0*sin(t)) if t in [-3.141592653589793, -2.5535900500422257)
pi/2-atan(-0.0*cos(t) + -1.0*sin(t)) if t in [-2.5535900500422257, -1.1071487177940904)
pi/2-atan(2.0*cos(t) + -0.0*sin(t)) if t in [-1.1071487177940904, 1.1071487177940904)
pi/2-atan(-0.0*cos(t) + 1.0*sin(t)) if t in [1.1071487177940904, 2.5535900500422257)
pi/2-atan(-0.6666666666666666*cos(t) + -0.0*sin(t)) if t in [2.5535900500422257, 3.141592653589793)