Calculations

Calculations

• 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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• Product of two transforms

  Combines two affine transforms into one.

  p′ = p × M (row vectors); (m × n) applies m first

  Edits to a page's own content base-content.js

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• Inverse of a transform

  The inverse of the matrix an object is painted with.

  det = a·d − b·c; inverse = adjugate ÷ det

  Edits to a page's own content base-content.js

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• Path coordinates rewritten

  The new numbers of one path-building operator after a move, scale or turn.

  U = C × T × C⁻¹; (x′, y′) = (x, y) × U, written with at most 4 decimals

  Edits to a page's own content base-content.js

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• Matrix round a moved picture or form

  The cm matrix written before a picture or form XObject that was moved, scaled or turned.

  U = C × T × C⁻¹, six entries with at most 4 decimals

  Edits to a page's own content base-content.js

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• Is this a move at all

  Decides whether an edit's matrix changes anything.

  |M − identity| < 1e-9 on all six entries

  Edits to a page's own content base-content.js

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• Line width in the path's own units

  Converts a line width given in page units to the units of the path's own space.

  w = page width ÷ √|a·d − b·c|

  Edits to a page's own content base-content.js

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• Replacement picture fitted into the old one's box

  Scales a replacement picture to fit, centered, inside the box of the picture it replaces, keeping its own proportions.

  ia = W ÷ H; ba = box w ÷ box h; (sx, sy) = ia > ba ? (1, ba ÷ ia) : (ia ÷ ba, 1)

  Edits to a page's own content base-content.js

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• Advance of a text run as read

  How far each text-showing operator moves the text position when a page's content is read, kept so a later edit can leave the rest of the line in place.

  string: Σ (width ÷ 1000 × size + char spacing + word spacing on a single-byte space) × horizontal scale; number in TJ: −v ÷ 1000 × size × horizontal scale

  Edits to a page's own content base-content.js

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• Advance of a text run

  How far a string moves the text position, in unscaled text space.

  Σ (glyph width ÷ 1000 × size + char spacing + word spacing on a space) × horizontal scale

  Edits to a page's own content base-content.js

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• Padding after reworded text

  The adjustment written after a reworded run so the text that follows on the line does not move.

  k = −(old advance − new advance) × 1000 ÷ (size × horizontal scale)

  Edits to a page's own content base-content.js

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• Matrix of a moved text run

  The text matrix written before a text run that was moved.

  Tm′ = (Tm × C) × T × C⁻¹

  Edits to a page's own content base-content.js

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• Line position put back after a moved run

  Restores where the text line continues after a run on it was moved.

  Tm = line matrix; then advance by −(start + advance) × 1000 ÷ (size × horizontal scale)

  Edits to a page's own content base-content.js

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• A move added to an object's edits

  Adds a move, scale or turn to what an object already had.

  T′ = T_old × T_new

  Edits to a page's own content base-edit.js

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• A moved path point

  The new numbers of a path when one of its points or handles is dragged to a place on the page.

  u = p_page × (C × T)⁻¹; attached handles shift by u − u_old

  Edits to a page's own content base-edit.js

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• Drawn-in paths written to the page

  Writes paths that were drawn into the page, and the matrix of pasted content, as content stream text.

  Edits to a page's own content base-edit.js

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• A stored matrix accepted

  Checks a move matrix read from a file or autosave before it is used.

  |a·d − b·c| > 1e-9 and every |number| < 1e7

  Edits to a page's own content base-edit.js

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• Box of part of a text item

  The box on the sheet round some characters of one piece of the drawing's text.

  s = width × i ÷ n; box corners = origin + u·s + v·t, t from −0.22 to 0.9 of the size

  Text positions: search hits and the OCR text layer textsearch.js

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• Cloud round a search hit

  The box of the cloud markup placed round a found word.

  box = hit box grown by pad on each side

  Text positions: search hits and the OCR text layer textsearch.js

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• Picture scale for reading text

  The scale at which a scanned page is drawn before its text is read.

  s = min(dpi ÷ 72, maxSide ÷ max(w, h), √(maxPixels ÷ (w·h))), at least 0.05

  Text positions: search hits and the OCR text layer ocr.js

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• Matrix that places the text layer

  The matrix that puts the recognizer's text-only page onto the sheet, written into the saved PDF.

  M = viewport⁻¹ ∘ [W_px ÷ W_pt, 0, 0, −H_px ÷ H_pt, 0, H_px]

  Text positions: search hits and the OCR text layer ocr.js

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• Words placed on the sheet

  The position, direction and size of each word read from a scan, for Find and Select text.

  baseline y at x by linear interpolation along the line's baseline; size = height above the baseline ÷ 0.9

  Text positions: search hits and the OCR text layer ocr.js

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• Word count and mean confidence

  The number of words read on a page and their mean confidence, for the status line.

  conf = round(Σ confidence ÷ n)

  Text positions: search hits and the OCR text layer ocr.js

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• Significand width of a number

  How many bits of a number this device keeps.

  bits = the first n where 1 + 2⁻ⁿ = 1

  Device number check accuracy.js Every app
  Exact

• Digits of a graphics float

  The number of significant digits stated for the graphics processor's float type.

  bits < 23: digits = max(1, ⌊(bits + 1) × log₁₀ 2⌋); bits ≥ 23: the fixed text "about 7"

  Device number check accuracy.js Every app
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• Size and position text

  A dimension, port size or port position as text in millimeters.

  text = round(x × 10⁴) ÷ 10⁴

  Library configurator sizes library-configurator.js Every app
  64-bit

• Option value used for matching

  The text an option value is compared by when the page picks the variant that matches the selected options.

  numbers: round(v × 10⁴) ÷ 10⁴ as text; other values: trimmed text

  Library configurator sizes library-configurator.js Every app
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• Mesh buffers

  The item's box or mesh as geometry for drawing, turned from z up to y up.

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Camera position

  Where the camera sits as the view is turned and zoomed.

  position = target + dist × (sin φ sin θ, cos φ, sin φ cos θ)

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Variant body buffers

  The chosen variant's box or mesh as geometry for drawing.

  Library 3D preview library-configurator.js Every app
  32-bit, display only

• Required and found values as text

  A limit or a measured value in words, such as ≤ 196.85 mm or 863.6–965.2 mm.

  text = round(x × 100) ÷ 100, then the unit

  Check report values problems.js Every app
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• Built-in unit factors

  The factor from each built-in unit of mass, time, force, pressure, energy, power, current, voltage and volume to SI.

  lb = 0.45359237 kg; lbf = 4.4482216152605 N; psi = 6894.757293168 Pa; psf = 47.88025898 Pa

  Calc sheet units, functions and driven parameters calc.js Every app
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• Constants and fallback lengths

  pi, e, standard gravity g0, and the length units used when no unit table is given.

  g0 = 9.80665 m/s²; in = 0.0254 m; ft = 0.3048 m; yd = 0.9144 m

  Calc sheet units, functions and driven parameters calc.js Every app
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• Unit lookup

  The SI factor and dimension of a unit name.

  deg = π ÷ 180; rad = 1

  Calc sheet units, functions and driven parameters calc.js Every app
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• Dimension comparison

  Whether two values have the same dimensions, so they can be added, compared or converted.

  |aᵢ − bᵢ| < 1e-9 for each of the five exponents

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Power

  a ^ b for a value with units.

  value = aᵇ; dimensions × b

  Calc sheet units, functions and driven parameters calc.js Every app
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