Ruled paper laid out to the millimetre

What this works out

Ruled paper is a physical layout, not a repeating screen background. This tells you exactly where the first and last baselines sit on the trimmed sheet, how many fit, and how much horizontal rule is drawn. The downloaded vector is made from that same geometry, so the result panel and the page cannot disagree.

The method

The blank border is taken off both sides of the page. Vertically, the first baseline is placed after both the top border and the extra heading space. The remaining distance down to the bottom border is divided by the requested line spacing and rounded down; one is then added because two endpoints contain one interval, three endpoints contain two, and so on.

All of that happens in whole micrometres. A quarter inch is exactly 6.35 mm, or 6,350 micrometres, so each addition remains exact. The output converts back to millimetres only after every line has its final position.

Before you read on

There are exactly 36 quarter-inch gaps from the first permitted baseline to the last. How many horizontal rules are drawn?

• A36, one rule for each gap.

  A gap sits between two rules, so this loses one endpoint.

• B37, because 36 intervals have 37 endpoints.

  Exactly. The final rule is allowed because it lands on the boundary.

• C35, because both edge rules are omitted.

  The edge margin is already in the geometry; permitted boundary rules are included.

37. A sequence with 36 intervals has 37 baselines: the first endpoint, one after each interval, and the final endpoint. The calculation therefore uses floor(available ÷ spacing) + 1 whenever the first rule fits.

A worked example

A4 portrait, 8 mm spacing, 12 mm blank edge, 20 mm heading space and a 0.2 mm solid rule:

page                   210 x 297 mm
first baseline         12 + 20 = 32 mm from the top
bottom boundary        297 - 12 = 285 mm
complete intervals     floor((285 - 32) / 8) = 31
writing lines          31 + 1 = 32
last baseline          32 + 31 x 8 = 280 mm
rule width             210 - 24 = 186 mm
total horizontal ink   32 x 186 = 5.952 m of rule

The final 5 mm between the last baseline and the bottom boundary is a remainder, not enough for another 8 mm interval. Those figures are asserted in the formula tests and reproduced in the first intent page.

US Letter with a half-inch margin, one inch of heading space and quarter-inch ruling is the exact imperial example. The first baseline is 1.5 inches from the top, 36 complete quarter-inch intervals reach the 10.5-inch bottom boundary, and therefore 37 rules are drawn.

Printing the sheet

The SVG uses real millimetres and vector paths, but a print dialogue is allowed to ignore that intent. Choose 100% or Actual size and turn off Fit to page. A ruler across ten intervals gives the quickest check: 8 mm ruling should measure 80 mm from the first baseline to the eleventh, and quarter-inch ruling should measure exactly 2.5 inches over the same ten intervals.

firstLine = edgeMargin + headingSpace
bottom    = pageHeight - edgeMargin

if firstLine <= bottom:
  writingLines = floor((bottom - firstLine) / spacing) + 1
  lineY[n]      = firstLine + n x spacing
otherwise:
  writingLines = 0

ruledWidth     = pageWidth - 2 x edgeMargin
totalRuleLength = writingLines x ruledWidth

Every length is held as an integer number of micrometres, then written to
an SVG whose width and height are declared in millimetres.