Calculations

Calculations

• Calculated composition for the lab system

  A stream's composition as mass or mole fractions, percent or ppm, to send back as calculated values.

  wᵢ = zᵢ × MWᵢ ÷ Σ(z × MW); mass % = w × 100; ppm = w × 1e6

  Lab results to stream composition process/env/lims.js

  • CadCraft
  • BimCraft
  64-bit

• Rational tag value

  A TIFF RATIONAL (two 32-bit integers) as one number.

  value = numerator ÷ denominator

  TIFF scan resolution raster/tiff.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Resolution in dots per inch

  The horizontal and vertical resolution of a page, in dots per inch.

  dpi = resolution × 2.54 (centimeter files); dpi = resolution (inch files)

  TIFF scan resolution raster/tiff.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Triangulate a polygon with holes

  The triangles of a polygon, as indexes into its point list.

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Winding of a ring

  Whether a ring runs clockwise or counterclockwise.

  sum = Σ (xⱼ − xᵢ) × (yᵢ + yⱼ)

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Orientation of three points

  On which side of the line through two points a third point lies.

  area = (q.y − p.y) × (r.x − q.x) − (q.x − p.x) × (r.y − q.y)

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Removing duplicate and collinear points

  Drops points that repeat their neighbor or lie on the line between their neighbors.

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Ear test

  Whether a corner can be cut off as a triangle: it is convex and no other point of the ring lies inside it.

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Point in triangle

  Whether a point lies inside or on a triangle.

  three cross products of (corner − point) pairs, each ≥ 0

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Bridge from a hole to the outer ring

  The point of the outer ring a hole is connected to.

  x = p.x + (h.y − p.y) × (p′.x − p.x) ÷ (p′.y − p.y); tan = |h.y − p.y| ÷ (h.x − p.x)

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Do two segments cross

  Whether two edges intersect, including touching and collinear overlap.

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
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  64-bit

• Is the middle of a diagonal inside the polygon

  Whether a diagonal between two corners runs through the inside of the polygon.

  midpoint = ((a.x + b.x) ÷ 2, (a.y + b.y) ÷ 2); even-odd count of edges crossed by a ray

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
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  • ModelCraft
  • TakeoffCraft
  • CivilCraft
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  64-bit

• Fire rating text as minutes

  A rating written as '2HR', '120 min', 'REI 120' or a bare number, as minutes.

  minutes = round(hours × 60)

  Assistant answers: fire ratings and room areas ask-tools.js

  • BimCraft
  64-bit

• Matching walls to the rating asked for

  Which walls are rated exactly, or at least, the time asked for.

  want = minutes, or hours × 60; match: minutes ≥ want, or minutes = want

  Assistant answers: fire ratings and room areas ask-tools.js

  • BimCraft
  64-bit

• Rooms under or over an area

  The rooms smaller or larger than a limit, with each area in square meters and square feet.

  limit in m² = limit in sq ft × 0.09290304; area in sq ft = area ÷ 0.09290304

  Assistant answers: fire ratings and room areas ask-tools.js

  • BimCraft
  64-bit

• Elements above, and the gap to each

  What sits over an element's footprint and how far above its top each one starts.

  gap = max(0, lowest Y of the other element − top Y of this element)

  Assistant answers: what is above an element ask-tools.js

  • BimCraft
  32-bit in part

• Rounding to a number of decimals

  A value rounded to three decimals (or another count) for the workbook.

  round(x, d) = Math.round(x × 10ᵈ) ÷ 10ᵈ

  COBie export: sizes, areas and durations assets-bim-cobie.js

  • BimCraft
  64-bit

• Lengths and areas written to the sheet

  Floor elevation and height, room height and room areas as the workbook holds them.

  length = round(x × k, 3); area = round(x × k², 3)

  COBie export: sizes, areas and durations assets-bim-cobie.js

  • BimCraft
  64-bit

• Floor height

  The height of each floor, from its elevation to the next floor's.

  height = elevationₙ₊₁ − elevationₙ

  COBie export: sizes, areas and durations assets-bim-cobie.js

  • BimCraft
  64-bit

• Warranty duration in years

  The length of a warranty from its start and end dates.

  years = (end − start) ÷ (365.25 × 86400000 ms), rounded to 0.1

  COBie export: sizes, areas and durations assets-bim-cobie.js

  • BimCraft
  64-bit

• Expected life read from a workbook

  A type's expected life in years, from a value in years, months, weeks or days.

  years = months ÷ 12, weeks ÷ 52.1775, days ÷ 365.25; rounded to 0.1

  COBie export: sizes, areas and durations assets-bim-cobie.js

  • BimCraft
  64-bit

• Warranty end date from its duration

  The day a warranty ends, when the workbook gives only its start and its length in years.

  end = start + round(years × 12) months

  COBie export: sizes, areas and durations assets-bim-cobie.js

  • BimCraft
  64-bit

• Service life read from the file

  The service life shown in the asset form, in years.

  years = seconds ÷ 31557600, or Y + M ÷ 12; rounded to 0.1

  Asset service life and maintenance due dates assets-bim.js

  • BimCraft
  64-bit

• Service life written to the file

  The service life as the IFC property holds it.

  IFC2x3: seconds = round(years × 31557600); IFC4: 'P' + years + 'Y'

  Asset service life and maintenance due dates assets-bim.js

  • BimCraft
  64-bit

• Day number of a date

  A calendar date as a count of days since 1970-01-01.

  day = round(ms at 00:00 UTC ÷ 86400000)

  Asset service life and maintenance due dates assets-bim.js

  • BimCraft
  Exact

• Overdue or due soon

  Whether an asset's next maintenance date has passed or falls within 30 days.

  d = day(next due) − day(today); overdue if d < 0; soon if d ≤ 30

  Asset service life and maintenance due dates assets-bim.js

  • BimCraft
  Exact

• Reading text as a number

  A cell of a sensor file as a value.

  Sensor readings: values, times and limits assets-bim-sensors.js

  • BimCraft
  64-bit

• Time text as milliseconds

  The time of a reading, from Unix time or a written date and time.

  Unix seconds × 1000; with a zone: UTC ms − sign × (hh × 60 + mm) × 60000

  Sensor readings: values, times and limits assets-bim-sensors.js

  • BimCraft
  64-bit

• High or low against the limits

  Whether a reading is above the asset's high limit or below its low limit.

  high if v > high; low if v < low

  Sensor readings: values, times and limits assets-bim-sensors.js

  • BimCraft
  64-bit

• Open or closed surface

  The elements of a batch whose triangles do not close.

  key = round(x × 1e4), round(y × 1e4), round(z × 1e4); open if any edge count is odd

  Section caps: which elements are closed solids caps-closed.js

  • BimCraft
  32-bit, display only

• Elements split over several batches

  Checks again, over all its parts, an element that is drawn in more than one batch.

  Section caps: which elements are closed solids caps-closed.js

  • BimCraft
  32-bit, display only

• Number from a factor or cost cell

  A cell such as '$1,250.00' as a number.

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Carbon factor from a file row

  A material's embodied-carbon factor in the unit the carbon pane works in.

  A1-A3 factor = value × unit factor (1 for kg, m, m², m³ and items; 0.001 for tonnes)

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Monthly climate from NASA POWER

  Twelve monthly values of daily sunlight on a horizontal surface and of air temperature.

  ghi = value rounded to 0.01 kWh/m²/day; T = value rounded to 0.01 °C

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Monthly climate from PVGIS

  Twelve monthly values of daily sunlight and air temperature, averaged over the years in the answer.

  ghi = Σ H(h)_m ÷ years ÷ days in month; T = Σ T2m ÷ years; both rounded to 0.01

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Location sent to the climate provider

  The latitude and longitude put into the request address.

  latitude.toFixed(3), longitude.toFixed(3)

  Imported carbon factors, prices and climate data data-packs.js

  • BimCraft
  64-bit

• Room floors and opening sills for flooding

  Each room's floor height above the lowest level and each opening's sill height, in meters.

  floor = (elevation − lowest elevation) ÷ 1000; sill = max(0, sill) ÷ 1000

  Building data for flood, wind and earthquake checks hazard-model.js

  • BimCraft
  64-bit

• Storey height, area, width and mass

  The storey data the wind and earthquake checks use, from the model's levels and outlines.

  area = Σ |outline area| ÷ 1e6; h = (next elevation − elevation) ÷ 1000; z = (elevation − datum) ÷ 1000 + h ÷ 2; mass = area × mass per m²; T1 = 0.1 × storeys when not given

  Building data for flood, wind and earthquake checks hazard-model.js

  • BimCraft
  64-bit

• Storey data from the analysis frame

  The same storey data when the stiffness comes from the structural frame instead of a typed period.

  z = (floor z − base) ÷ 1000 − h ÷ 2; width = extent of the nodes within 150 mm of the floor

  Building data for flood, wind and earthquake checks hazard-model.js

  • BimCraft
  64-bit

• Date text as a day number

  A YYYY-MM-DD date as a count of days since 1970-01-01.

  day = Date.UTC(y, m, d) ÷ 86400000

  4D schedule dates and status ifc-4d.js

  • BimCraft
  Exact

• Built, in progress or waiting on a date

  The state of every element that belongs to a task, on a chosen day.

  built if day > finish; in progress if start ≤ day ≤ finish; waiting if day < start

  4D schedule dates and status ifc-4d.js

  • BimCraft
  Exact

• Task counts of a stage or package

  How many tasks of a group are done, running and still to do on a day.

  4D schedule dates and status ifc-4d.js

  • BimCraft
  Exact

• Millimeters per unit of one IFC unit

  The size in millimeters of an SI or conversion-based length unit.

  mm per unit = prefix table value, or conversion factor × mm of the base unit

  IFC length unit and placement matrices ifc-util.js

  • BimCraft
  64-bit

• Length unit of the file

  The millimeters per length unit of the open file, from its project units.

  IFC length unit and placement matrices ifc-util.js

  • BimCraft
  64-bit

• Product of two 4 × 4 matrices

  Two placements combined into one.

  (A·B)ᵣ꜀ = Σₖ Aᵣₖ × Bₖ꜀

  IFC length unit and placement matrices ifc-util.js

  • BimCraft
  64-bit

• A point moved by a matrix

  A point in one frame as a point in another.

  p′ = M · (x, y, z, 1)

  IFC length unit and placement matrices ifc-util.js

  • BimCraft
  64-bit

• Inverse of a 4 × 4 matrix

  The matrix that undoes a placement.

  M⁻¹ = adj(M) ÷ det(M)

  IFC length unit and placement matrices ifc-util.js

  • BimCraft
  64-bit

• Where a federated model goes

  The matrix that puts a second model in the first model's coordinates, moved by an offset.

  M = T(offset) · C_ref · C⁻¹

  IFC length unit and placement matrices ifc-util.js

  • BimCraft
  64-bit

• Placed triangles of an element

  Every triangle of an element in the file's Z-up coordinates and length unit.

  p = (x, −z, y) of (C⁻¹ · M · v) × (1000 ÷ unitMm)

  Element triangles for analysis ifc-util.js

  • BimCraft
  32-bit in part

• Placed point in millimeters

  A point of an element's own frame in the file's coordinates, in millimeters.

  p = (M · (x, y, z, 1)) × unitMm

  Field layout points from the model layout-bim.js

  • BimCraft
  64-bit