Calculations

Calculations

• Convert between two units

  A value in one unit as a value in another unit of the same kind.

  result = v × (n₁ × d₂) ÷ (d₁ × n₂)

  Unit conversion unit-table.js Every app
  Exact

• Typed text to a unit

  What was typed, with its unit, as a value in the unit the field wants.

  3 yd typed into a feet field = convert(3, yd, ft) = 9

  Unit conversion unit-table.js Every app
  Exact

• A value to the base unit

  A number in any unit as meters, square meters, cubic meters, radians or rise over run.

  base = v × n ÷ d (v × π × n ÷ d for degrees and gons)

  Unit conversion unit-table.js Every app
  64-bit

• A base value to a unit

  A stored base value as a number in the unit shown.

  value = base × d ÷ n (base ÷ π × d ÷ n for degrees and gons)

  Unit conversion unit-table.js Every app
  64-bit

• Add, subtract, multiply, divide

  The four operations on values that carry units.

  a + b and a − b need the same dimensions; a × b and a ÷ b combine them

  Calc sheets calc.js Every app
  64-bit

• Comparisons

  Pass or fail checks such as M <= 40 kN m.

  a ≤ b is true when a ≤ b + 1e-12 × max(1, |a|, |b|)

  Calc sheets calc.js Every app
  64-bit

• Number shown

  A result as text in the sheet.

  6 significant digits; exponent form from 1e9 up and below 1e-4

  Calc sheets calc.js Every app
  64-bit

• Size in millimeters

  The width and height of the copied area, on paper or at the drawing's real size.

  paper: mm = pixels × ptPerPx × (25.4 ÷ 72); real: mm = pixels × mmPerPx

  Size of a copied area areaclip.js

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• Render size in pixels

  The pixel width and height for an area given in points at a resolution, lowered so neither side passes the cap.

  d = dpi × min(1, maxPx ÷ (longer side × dpi ÷ 72)); w = round(wPt × d ÷ 72); h = round(hPt × d ÷ 72)

  Size of a copied area areaclip.js

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• Scale and turn from two points

  The scale, the angle and the point mapping that carry two points on the picture onto the two points where they belong.

  scale = |b₂ − b₁| ÷ |a₂ − a₁|; angle = atan2(b₂ − b₁) − atan2(a₂ − a₁); map(p) = b₁ + scale · R(angle) · (p − a₁)

  Size of a copied area areaclip.js

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  64-bit

• Box round a turned picture

  The width and height of the upright box round a picture turned by an angle.

  w′ = w·|cos θ| + h·|sin θ|; h′ = w·|sin θ| + h·|cos θ|

  Size of a copied area areaclip.js

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  64-bit

• Outline of an elliptical area

  The points of the ellipse that fits a box, used as the outline of a round copied area.

  pᵢ = (cx + rx·cos(2π·i ÷ n), cy + ry·sin(2π·i ÷ n)), n = 96

  Size of a copied area areaclip.js

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• abs, round, ceil and floor

  The four functions an expression may call.

  round(x) = floor(x + 0.5) for x ≥ 0, −floor(−x + 0.5) for x < 0; ceil(x) = ⌈x − 1e-9·max(1, |x|)⌉; floor(x) = ⌊x + 1e-9·max(1, |x|)⌋

  Arithmetic on typed lengths lencalc.js

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  64-bit

• Adding and subtracting

  Sums and differences of lengths, left to right.

  Arithmetic on typed lengths lencalc.js

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  64-bit

• Multiplying and dividing

  Products and quotients of a length and plain numbers, left to right.

  Arithmetic on typed lengths lencalc.js

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  64-bit

• The answer

  The final value and whether it is a length or a plain number.

  Arithmetic on typed lengths lencalc.js

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• Unit sizes

  Builds each unit's row: its fraction of the base unit and the factor used for quick conversion.

  factor = n ÷ d (× π for degrees and gons)

  Unit table: reading and writing values unit-table.js Every app
  Exact

• Numbers and fractions

  Reads 6, 6.5, 6 1/2, 6-1/2 or 1/2 as a number.

  whole + numerator ÷ denominator

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Feet and inches

  Reads 12'6", 12'-6 1/2" or 6" as inches.

  inches = feet × 12 + inches

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Degrees, minutes and seconds

  Reads 45°30'15" or 45d30m15s as degrees.

  degrees + minutes ÷ 60 + seconds ÷ 3600

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Slopes

  Reads 2%, 3H:1V, 1:3 or 6/12 as a grade (rise over run).

  percent ÷ 100; H:V → V ÷ H; rise:run → rise ÷ run

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Writing feet and inches

  Writes a length as feet, inches and a fraction of an inch.

  n = round(|inches| × den); feet = ⌊n ÷ 12den⌋; inches = ⌊rest ÷ den⌋; fraction = rest ÷ den, reduced

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Writing degrees, minutes and seconds

  Writes an angle as degrees, minutes and seconds.

  t = round(|degrees| × 3600 × 10^dec); split by 3600 and 60

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Writing decimals

  Writes a number with a fixed count of decimals.

  text = v.toFixed(dec)

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Circle through a stroke

  The circle that best fits the stroke's points, with its root-mean-square error.

  u = x − x̄, v = y − ȳ; solve [Σu² Σuv; Σuv Σv²]·(u_c, v_c) = ½(Σu³ + Σuv², Σv³ + Σvu²); r² = u_c² + v_c² + (Σu² + Σv²) ÷ n

  Pen sketch cleanup sketch.js

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• Turn of a stroke about a center

  How far the stroke goes round the fitted center, signed.

  Σ (aᵢ − aᵢ₋₁) with each step brought into (−π, π]

  Pen sketch cleanup sketch.js

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• Squaring a direction

  Makes a direction level or plumb when it is within a few degrees of it.

  q = round(a ÷ (π ÷ 2)) × (π ÷ 2); used when |a − q| ≤ deg × π ÷ 180

  Pen sketch cleanup sketch.js

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• Where two sides meet

  The corner where two straight sides cross.

  det = l × m; t = ((m₀ − l₀) × m) ÷ det; point = l₀ + l·t

  Pen sketch cleanup sketch.js

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• Distance from a point to a segment

  How far a pen point is from the straight line between two others.

  t = ((p − a)·(b − a)) ÷ |b − a|², held to [0, 1]; distance = |p − (a + t(b − a))|

  Pen sketch cleanup sketch.js

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• Straight sides and rectangles

  Cuts a stroke at its corners, squares each side, and rebuilds the corners where the sides cross.

  Pen sketch cleanup sketch.js

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• A stroke as a line

  Makes a nearly straight stroke a line, exactly level or plumb when it is close to it.

  straight when max distance ≤ max(eps, 3.5 % of the gap) and gap > 90 % of the length

  Pen sketch cleanup sketch.js

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• A stroke as a circle or an arc

  Makes a round stroke a circle, or an arc from the stroke's first point to its last.

  accepted when rms ÷ r < 0.07 and r < 3 × box diagonal; circle when |turn| > 0.85 × 2π

  Pen sketch cleanup sketch.js

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• Joining loose ends

  Pulls each loose end onto the nearest corner of another stroke or of the drawing.

  nearest corner with distance ≤ tol; tol = 6 % of the sketch's box diagonal unless given

  Pen sketch cleanup sketch.js

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• Markups carried onto a revised sheet

  The points and rectangle of each markup on the new sheet, scaled when the new page has another size.

  k = min(w₂ ÷ w₁, h₂ ÷ h₁); p′ = origin₂ + (p − origin₁) × k

  Carried, stamped and pasted markup geometry slip.js

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• Superseded stamp position

  The rectangle of the Superseded stamp across the top middle of the old sheet.

  w = min(0.4 × page width as read, 432); h = max(36, 0.18 × w); rect = center ± half size

  Carried, stamped and pasted markup geometry slip.js

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• Picture size fitted to a box

  A picture's width and height scaled to fit a maximum size, keeping its proportions.

  k = min(maxW ÷ w, maxH ÷ h, 1e9); size = (w × k, h × k)

  Carried, stamped and pasted markup geometry imagestamp.js

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• Rectangle of a placed picture

  The rectangle of a picture of a given size centered on a point, turned with the page.

  rect = (cx − w ÷ 2, cy − h ÷ 2, cx + w ÷ 2, cy + h ÷ 2), with w and h swapped on a page turned 90° or 270°

  Carried, stamped and pasted markup geometry imagestamp.js

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• Box of copied page content

  The box around the selected objects that becomes the copied page's size.

  box = union of the objects' boxes, grown by max(line width ÷ 2 + 0.5) on every side

  Carried, stamped and pasted markup geometry content-clip.js

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• Transform of pasted content

  The matrix that moves copied content to where it is pasted and turns it to read the same way on the target page.

  T = translate(−cx, −cy) · R(turn) · translate(target); turn = (target rotation − source rotation) mod 360

  Carried, stamped and pasted markup geometry content-clip.js

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• Camera point and view scale

  The camera's X and Y over the markup and the size of the view, in meters.

  k = 0.0254 ÷ 72; cx = (x₀ + x₁) ÷ 2 × k; scale = 1.4 × max(Δx, Δy, 36) × k

  BCF viewpoint of a markup bcf.js

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• Paper sizes in points

  The width and height of each paper size in PDF points.

  inch = 72 points; mm = 72 ÷ 25.4 points; A4 = 210 mm × 297 mm

  Blank pages: paper sizes and grid blank.js

  • MarkupCraft
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• Grid lines and dots

  How many grid steps fit inside the margins and where each line or dot is drawn.

  n = floor((size − 2 × margin) ÷ pitch + 1e-6); start = (size − n × pitch) ÷ 2; line i = start + i × pitch

  Blank pages: paper sizes and grid blank.js

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• Old and new sheet mixed per pixel

  The color of each pixel of the compare picture, and counts of removed, added and unchanged pixels.

  Sheet compare picture compare.js

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  32-bit, display only

• Value of a number row

  The number handed to the app when a person changes a number box.

  v = min(max, max(min, typed value))

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit

• Rounding of a slider value

  Removes binary noise such as 0.30000000000000004 from a slider's value.

  v = round to (decimals of the step + 2) decimals, at most 8

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit

• Value of a slider row

  The number handed to the app while a slider is dragged or its box is changed.

  v = fix(clamp(value, min, max), step)

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit

• Integer or float

  Decides how a number is written.

  Numbers sent between people editing together live-client.js Every app
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• Writing a float

  Writes a number as 8 bytes.

  Numbers sent between people editing together live-client.js Every app
  64-bit

• Writing an integer

  Writes a whole number in the shortest integer form that holds it.

  Numbers sent between people editing together live-client.js Every app
  Exact

• Reading a float

  Reads a 4-byte or an 8-byte float from a message.

  Numbers sent between people editing together live-client.js Every app
  64-bit