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b0e88cf | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | """
Hexagonal grid initialization for circle packing.
A hexagonal (offset) grid provides a good starting arrangement
because it's the densest regular packing pattern. Even rows are
offset by half the spacing, which reduces wasted space.
"""
import numpy as np
def hexagonal_grid(n, margin=0.1):
"""
Generate n points on a hexagonal grid inside [margin, 1-margin]^2.
Args:
n: number of points to generate
margin: distance from edges to keep clear
Returns:
np.array of shape (n, 2) with (x, y) coordinates
"""
usable = 1.0 - 2 * margin
cols = int(np.ceil(np.sqrt(n * 2 / np.sqrt(3))))
rows = int(np.ceil(n / cols))
dx = usable / max(cols - 1, 1)
dy = usable / max(rows - 1, 1)
points = []
for row in range(rows):
for col in range(cols):
if len(points) >= n:
break
x = margin + col * dx
if row % 2 == 1:
x += dx / 2 # offset for hex pattern
y = margin + row * dy
x = np.clip(x, margin, 1 - margin)
y = np.clip(y, margin, 1 - margin)
points.append([x, y])
return np.array(points[:n])
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