Calculations

Calculations

• Align the old sheet in a comparison

  The fit of the old sheet onto the new one from two points picked on each, and the scale and turn reported for it.

  scale = hypot(M₀, M₁); turn = atan2(M₁, M₀) × 180 ÷ π

  Markup geometry while drawing and editing markupcraft.js

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• Line up a picture by two points

  The new box of a picture markup so two points on it land on two points on the sheet.

  k = √(rw·rh ÷ (W·H)) × fit scale; box = center ± (w·k ÷ 2, h·k ÷ 2)

  Markup geometry while drawing and editing markupcraft.js

  • MarkupCraft
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• Length measurement label

  The dimension line, its end ticks and the length text of a measure markup.

  len = hypot(bₓ − aₓ, b_y − a_y); label = len × mmPerPt, formatted

  Markup outlines and measurement labels shapes.js

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• Area measurement label

  The area and perimeter text of an area markup, placed at the outline's centroid.

  Markup outlines and measurement labels shapes.js

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• Angle measurement label

  The angle text of an angle markup and where it sits.

  label = angle at the vertex, 1 decimal; position = vertex + (r + 1.2 × font size) along the bisector

  Markup outlines and measurement labels shapes.js

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• Count total

  The running total shown beside the first mark of a count group.

  n = number of marks

  Markup outlines and measurement labels shapes.js

  • MarkupCraft
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• Centroid of an outline

  The area centroid of a closed outline, used to place the label of an area or a named zone.

  k = xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ; cₓ = Σ (xᵢ + xᵢ₊₁)·k ÷ (3·Σ k)

  Markup outlines and measurement labels shapes.js

  • MarkupCraft
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• Circle-to-Bézier constant

  The control-point factor for drawing a quarter circle as one cubic Bézier.

  K = 4·(√2 − 1) ÷ 3 ≈ 0.5522847498

  Markup outlines and measurement labels shapes.js

  • MarkupCraft
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• Ellipse outline

  An ellipse markup's outline as four cubic Bézier curves inside its box.

  c = (p₀ + p₁) ÷ 2; r = (p₁ − p₀) ÷ 2; control offset = r × K

  Markup outlines and measurement labels shapes.js

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• Revision cloud outline

  The scalloped outline of a cloud markup round its corner points.

  n = max(1, round(edge ÷ arc)); step = edge ÷ n; bulge height = 0.6667 × step

  Markup outlines and measurement labels shapes.js

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• Signed area of an outline

  The signed shoelace area used to tell which way an outline runs.

  A = Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ) ÷ 2

  Markup outlines and measurement labels shapes.js

  • MarkupCraft
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• A number in an appearance stream

  Turns a number into the text written in a PDF appearance stream.

  text = v rounded to 3 decimals, trailing zeros removed; |v| < 1e-6 → 0

  Numbers written to the saved PDF pdf-write.js

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• Appearance stream of a markup

  The drawing operators that show a markup in any PDF viewer.

  Numbers written to the saved PDF pdf-write.js

  • MarkupCraft
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• Private copy of a markup

  The JSON kept with each annotation so it reopens exactly: points, box, cut-outs, style and the rest.

  ar = round(rect × 1000) ÷ 1000

  Numbers written to the saved PDF pdf-write.js

  • MarkupCraft
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• Annotation rectangle

  The /Rect of a markup's annotation, which is also the bounding box of its appearance.

  rect = bounds ± 1 pt; each side ≥ 2 × line width + 2 pt

  Numbers written to the saved PDF pdf-write.js

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• Bounds of a display list

  The box round everything a markup draws, used for its annotation rectangle.

  Numbers written to the saved PDF pdf-write.js

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• Rectangle differences of a box or ellipse

  The /RD entry: how far the shape's outer edge sits inside the annotation rectangle on each side.

  RD = [left, top, right, bottom] gaps between rect and box ± half line width, each ≥ 0

  Numbers written to the saved PDF pdf-write.js

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• Count marks as ink rings

  Writes a count group as one Ink annotation with a small ring round each mark.

  ring: 13 points at 30° steps, radius max(3, 0.8 × font size)

  Numbers written to the saved PDF pdf-write.js

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• Arc exported as a PolyLine

  Writes an arc markup's /Vertices as points along the arc, because PDF has no arc annotation.

  n = max(8, ⌈|sweep| ÷ (π ÷ 32)⌉); vertex k = c + r × (cos, sin)(a₀ + sweep × k ÷ n)

  Numbers written to the saved PDF pdf-write.js

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• Picture placement matrix

  The matrix that paints a picture markup into its box, upright for the page's rotation.

  cm = [u·W, −v·H, origin + v·H], each number to 4 decimals

  Numbers written to the saved PDF pdf-write.js

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• Scale as a /Measure dictionary

  The sheet's scale in the form other PDF programs read: the factor from points to the unit and the display precision.

  X.C = mmPerPt ÷ 304.8 (ft), ÷ 25.4 (in), ÷ 1000 (m), or mmPerPt (mm)

  Numbers written to the saved PDF pdf-write.js

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• Scale written on the page

  Stores a sheet's calibration on its page in the saved PDF.

  Numbers written to the saved PDF pdf-write.js

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• Measured text in /Contents

  The text other PDF programs show for a measurement: the length, the area and perimeter, the angle or the count.

  Numbers written to the saved PDF pdf-write.js

  • MarkupCraft
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• Flattened markup

  Paints a markup into the page itself instead of saving it as an annotation.

  Numbers written to the saved PDF pdf-write.js

  • MarkupCraft
  64-bit

• Outline points of a PolyLine or Polygon

  The points of a polyline, polygon, cloud or area markup read from an annotation.

  Annotations and scales read from a PDF pdf-read.js

  • MarkupCraft
  32-bit in part

• Stroke points of an Ink annotation

  The points of pen and highlighter strokes, and of count rings, read from an annotation.

  Annotations and scales read from a PDF pdf-read.js

  • MarkupCraft
  32-bit in part

• End points of a Line annotation

  The two end points of a line, arrow or length measurement read from an annotation.

  Annotations and scales read from a PDF pdf-read.js

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• Box of a Square or Circle annotation

  The box of a rectangle, ellipse or cloud rectangle markup from the annotation's /Rect.

  box = rect inset by RD and by half the border width on each side

  Annotations and scales read from a PDF pdf-read.js

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• Count mark from its ring

  The position of each count mark, from the ring written for it in the ink list.

  center = mean of the ring's points (the closing point dropped)

  Annotations and scales read from a PDF pdf-read.js

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• Moved by another program

  Decides whether a markup's private JSON still matches the annotation, or another program moved or resized it since.

  |ar − rect| > 0.75 pt on any of the four numbers → use the annotation's own geometry

  Annotations and scales read from a PDF pdf-read.js

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• Scale from another program's /Measure

  A sheet calibration from the measurement dictionary another PDF program wrote.

  mmPerPt = C × mm per unit (ft 304.8, in 25.4, m 1000, cm 10, mm 1)

  Annotations and scales read from a PDF pdf-read.js

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• Which scale a sheet opens with

  Picks the calibration of a page: MarkupCraft's own saved copy, else the page's measure viewport.

  Annotations and scales read from a PDF pdf-read.js

  • MarkupCraft
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• Text size from an appearance stream

  The size of the first visible text that another program's text box draws.

  size = |Tf size × text matrix scale × cm scale|, rounded to 0.01

  Annotations and scales read from a PDF freetext.js

  • MarkupCraft
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• Text size from a style string

  Reads 12pt, 16px or 1.2em from a text box's style as points.

  px × 0.75; em × 12; pt as written

  Annotations and scales read from a PDF freetext.js

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• A page's paths as segments

  Every drawn path of a page as straight segments in page coordinates.

  curve point = Bézier at t = j ÷ 8, j = 1…8; p′ = CTM × p

  Drawing comparison by vector paths vecdiff.js

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• Distance from a point to a segment

  How far a sample point is from one segment of the other sheet.

  t = clamp((p − a)·d ÷ |d|², 0, 1); distance = hypot(p − (a + t·d))

  Drawing comparison by vector paths vecdiff.js

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• Grid of segments

  Files each segment under the grid cells its bounding box covers, to find nearby segments quickly.

  cells = (⌊x_max ÷ cell⌋ − ⌊x_min ÷ cell⌋ + 1) × (same in y); more than 4000 → not in the grid

  Drawing comparison by vector paths vecdiff.js

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• Parts of a sheet with no match

  The pieces of one sheet's segments that have no segment of the other sheet within the tolerance.

  n = max(1, ⌈length ÷ step⌉) samples; miss when no segment within tol

  Drawing comparison by vector paths vecdiff.js

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• Removed and added lines

  The lines of the old sheet that are not on the new one, and the other way round.

  Drawing comparison by vector paths vecdiff.js

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• Boxes round groups of changes

  Groups changed segments that are close together into boxes, for clouding and for the list of changes.

  merge boxes closer than gap; keep groups with Σ length ≥ minLen

  Drawing comparison by vector paths vecdiff.js

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• Size of a changed area in words

  The size of a changed area as text: inches on the sheet and, on a calibrated sheet, the real size.

  in = round(pt ÷ 72, 1 decimal); real = pt × mmPerPt, in m to 1 decimal from 1000 mm, else whole mm

  Drawing comparison by vector paths changes.js

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• Where on the sheet

  Names the part of the sheet a point is in, on a 3 × 3 grid (upper left, center, lower right and so on).

  column = ⌊(x − x₀) ÷ w × 3⌋; row = ⌊(y₁ − y) ÷ h × 3⌋, each clamped to 0…2

  Drawing comparison by vector paths changes.js

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• Amount of change in an area

  How many points of line were removed and added inside one changed area, and whether it counts as added, removed or modified.

  removed = Σ hypot over removed pieces in the box; modified when both ≥ 6 pt

  Drawing comparison by vector paths changes.js

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• Segments clipped to a region

  The parts of a sheet's segments that lie inside a task's region.

  Liang–Barsky: r = q ÷ p per box side; keep when t₁ − t₀ > 1e-9

  Drawing comparison by vector paths tasks.js

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• Region snapshot

  What a task's region link stores when it is made: the sheet's lines inside the region.

  keep the 300 longest clipped segments; each coordinate rounded to 0.1 pt

  Drawing comparison by vector paths tasks.js

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• Has the region changed

  Decides whether the drawing inside a task's region changed between the snapshot and the new revision.

  changed when removed + added ≥ 4 pt and (removed + added) ÷ stored length ≥ 0.02

  Drawing comparison by vector paths tasks.js

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• Has a model element changed

  Compares the stored state of a linked model element with its state now, number by number.

  same when |x − y| ≤ tol

  Drawing comparison by vector paths tasks.js

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• Removed and added line reported

  The amount of removed and added line shown after comparing two sheets by their lines.

  amount = round(Σ hypot(Δx, Δy)) in points

  Drawing comparison by vector paths markupcraft.js

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• Sheets ranked by change

  Ranks the sheet pairs of two sets by how much line changed and marks the ones that changed.

  len = round(Σ hypot over removed and added); changed when len ≥ 6

  Drawing comparison by vector paths markupcraft.js

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• Clouds round the changes

  Adds a cloud rectangle markup round each group of changes on every changed sheet.

  cloud box = cluster box grown by 8 pt on each side

  Drawing comparison by vector paths markupcraft.js

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