How every sheet is computed

A uniform square lattice with an optional heavier major line every N cells and optional centre axes. Columns and rows are the floor of the usable dimension divided by the requested spacing; leftover space is reported, never absorbed.

• usable = page − left margin − right margin (and top/bottom)
• columns = floor(usable width / spacing)
• rows = floor(usable height / spacing)
• line xᵢ = left + i · spacing, i = 0 … columns

Horizontal rules at a fixed line spacing, with an optional tinted margin rule and an optional header block of wider-spaced rules. Line count is the floor of the available height over the spacing.

• available height = usable height − header offset
• lines = floor(available height / line spacing)
• rule yⱼ = top + offset + j · spacing

A lattice of dots at the intersections of a square grid, with adjustable radius and opacity and optional larger major markers every N dots. Dots are placed at computed coordinates; the count is (columns+1) × (rows+1).

• columns = floor(usable width / spacing), rows = floor(usable height / spacing)
• dot (i,j) at (left + i·spacing, top + j·spacing)
• total dots = (columns + 1) · (rows + 1)

A square grid with emphasised x and y axes whose origin is placed at a configurable fraction of the page, optional tick numbering, and quadrant-aware axis drawing. Lives inside the Studio editor.

• origin = (left + originXFrac · usable width, top + originYFrac · usable height)
• grid lines as square grid; axes drawn through the origin

A lattice of equilateral triangles whose lines run at 0°, 60° and 120°. The vertical row height is derived from the triangle side, not set independently, which is what keeps circles circular and cubes undistorted.

• row height = side · √3 / 2
• rows = floor(usable height / row height)
• three line families at 0°, +60°, −60° (orientation flips the handedness)

A tessellation of regular hexagons, flat-top or pointy-top. Every other dimension follows from the side length; the centre-to-centre distance between adjacent hexes is side · √3, which is what makes the tiling close without gaps.

• centre-to-centre (adjacent) = side · √3
• column and row pitch derived from side and orientation
• vertices placed at 60° increments around each centre

Concentric rings at a fixed radial spacing and an even division of 360° into radial spokes, with degree or radian labels. Rings are exactly concentric and spokes exactly equally spaced.

• rings = floor(max radius / ring spacing)
• spoke angle k = k · 360° / radials (or k · 2π / radials)
• centre placed at the middle of the usable area

A two-level hierarchy: fine minor lines with a heavier major line every N minors, plus an optional drawing border. Major spacing is N times the minor spacing; both column/row counts are reported.

• major spacing = majorEvery · minor spacing
• minor columns = floor(usable width / minor spacing)
• major columns = floor(minor columns / majorEvery)

Subdivisions generated mathematically, not evenly spaced. Within each decade the line for value m sits at log(m)/log(base) of the way across the cycle; decade boundaries carry a heavier weight and optional labels. Semi-log makes one axis logarithmic, log-log both.

• cycle width = usable width / cycles
• subdivision position = (log(m) / log(base)) · cycle width, m = 1 … base−1
• decade lines at whole multiples of the cycle width

A three-line system per row — solid baseline, dashed midline, descender line — defined by one baseline spacing and two ratios, so the whole row scales proportionally. Optional slant guides at a chosen angle and an optional picture area.

• midline offset = midlineRatio · baseline spacing (above baseline)
• descender depth = descenderRatio · baseline spacing (below baseline)
• rows = floor(usable height / baseline spacing)