Squares

Defined in src/regular/squares.scad. Squares are sized by side, the edge length.

squares_centers_rect

squares_centers_rect(side, n, m)

Returns the centres of an n by m grid of squares, the regular 4.4.4.4 tiling.

Parameter	Meaning
side	Edge length, and the grid pitch
n	Number of squares along X
m	Number of squares along Y

The first centre is at the origin and the grid grows along +X and +Y. The result has n * m points.

use <tessella/tess.scad>

echo(squares_centers_rect(10, 3, 2));
// ECHO: [[0, 0], [0, 10], [10, 0], [10, 10], [20, 0], [20, 10]]

squares_centers_radial

squares_centers_radial(side, levels)

Returns the centres of a pattern of centred rows that narrows above and below the middle.

Parameter	Meaning
side	Edge length
levels	Number of rows from the middle row to the top, inclusive

The middle row has 2 * levels - 1 squares and is centred on the origin. Each row away from it has one square fewer. The result has 3 * levels^2 - 3 * levels + 1 points.

Because every row is centred, adjacent rows are offset by half a square. The pattern is staggered like brickwork, not an edge-to-edge grid.

use <tessella/tess.scad>

echo(squares_centers_radial(10, 2));
// ECHO: [[-5, -10], [5, -10], [-10, 0], [0, 0], [10, 0], [-5, 10], [5, 10]]

squares_vertices

squares_vertices(side, centers, angular_offset = 45)

Returns the four corners of a square around each centre.

Parameter	Meaning
side	Edge length of the squares drawn
centers	List of centre points
angular_offset	Angle of the first corner from +X; 45 gives axis-aligned squares

Corners are listed anticlockwise. Pass a side smaller than the one the centres were laid out with to leave a gap between squares; the gap equals the difference.

angular_offset = 0 gives squares standing on a corner, which is what the 4.8.8 tiling needs.

use <tessella/tess.scad>

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

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