Hexagons

Defined in src/regular/hexagons.scad. Hexagons are sized by radius, the distance from the centre to a corner, which for a regular hexagon equals the edge length. The distance across the flats is radius * sqrt(3).

The layouts place hexagons with a corner pointing up. Theory derives the spacing.

hexagons_centers_rect

hexagons_centers_rect(radius, n, m)

Returns the centres of m rows of n hexagons, the regular 6.6.6 tiling.

Parameter	Meaning
radius	Centre-to-corner distance
n	Number of hexagons in each row
m	Number of rows

Hexagons in a row are radius * sqrt(3) apart. Rows are radius * 1.5 apart, and odd rows are shifted half a hexagon toward +X. The first centre is at the origin. The result has n * m points.

use <tessella/tess.scad>

echo(hexagons_centers_rect(10, 3, 2));
// ECHO: [[0, 0], [8.66025, 15], [17.3205, 0], [25.9808, 15], [34.641, 0],
//        [43.3013, 15]]

hexagons_centers_radial

hexagons_centers_radial(radius, levels)

Returns the centres of a hexagon surrounded by complete rings of hexagons.

Parameter	Meaning
radius	Centre-to-corner distance
levels	Number of rings, counting the central hexagon as one

The pattern is centred on the origin. The result has 3 * levels^2 - 3 * levels + 1 points: 1, 7, 19, 37, 61 for levels 1 to 5.

use <tessella/tess.scad>

echo(hexagons_centers_radial(10, 2));
// ECHO: [[-17.3205, 0], [0, 0], [17.3205, 0], [-8.66025, 15], [8.66025, 15],
//        [-8.66025, -15], [8.66025, -15]]

hexagons_vertices

hexagons_vertices(radius, centers, angular_offset = 30)

Returns the six corners of a hexagon around each centre.

Parameter	Meaning
radius	Centre-to-corner distance of the hexagons drawn
centers	List of centre points
angular_offset	Angle of the first corner from +X; 30 puts a corner pointing up

Corners are listed anticlockwise. Keep the default angular_offset with centres from the two functions above. Another angle rotates each hexagon in place, and unless the change is a multiple of 60 they no longer fit together.

Pass a radius smaller than the one the centres were laid out with to leave a gap. The gap between neighbouring hexagons is sqrt(3) times the difference.

use <tessella/tess.scad>

echo(hexagons_vertices(10, [[0, 0]]));
// ECHO: [[[8.66025, 5], [0, 10], [-8.66025, 5], [-8.66025, -5], [0, -10],
//        [8.66025, -5]]]

Render with paths = [[0, 1, 2, 3, 4, 5, 0]].