Calculations

Calculations

• Height above the level

  The lines of a readout: the level and the height above its floor, X and Y from the project origin, Z, and the map position.

  height above the level = z − level elevation

  Coordinate readouts and survey point coords.js

  • BimCraft
  64-bit

• Plan point to file coordinates

  A point in a storey's plan, in the file's coordinates.

  q = M (x, y, 0)

  Coordinate readouts and survey point coords.js

  • BimCraft
  64-bit

• File coordinates to plan point

  A point in the file's coordinates, in a storey's plan.

  p = M⁻¹ q

  Coordinate readouts and survey point coords.js

  • BimCraft
  64-bit

• File coordinates to the 3D view

  Where a point of the file sits in the 3D view, to draw the origin and survey markers.

  (x, y, z) × unit → (x, z, −y) → C → placement

  Coordinate readouts and survey point coords.js

  • BimCraft
  64-bit

• A length as text

  Millimeters as feet and inches to 1/16 inch, or as a decimal number in mm, cm, m, inches or feet.

  sixteenths = round(|mm| ÷ 25.4 × 16); feet = ⌊sixteenths ÷ 192⌋; inches = ⌊rest ÷ 16⌋

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• Unit factors

  How many millimeters, square millimeters and cubic millimeters one display unit is.

  in = 25.4 mm; ft = 12 × 25.4 mm; cm = 10 mm; m = 1000 mm

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• A coordinate as a number

  A coordinate in millimeters as a number in the display unit, with a fixed count of decimals.

  value = mm ÷ factor, to 1 (mm), 2 (cm, in) or 3 (m, ft) decimals

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• A small length to three figures

  A tolerance or a scale per pixel as text with three significant figures.

  value = mm ÷ factor, toPrecision(3)

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• An area or a volume as text

  Square or cubic millimeters as text in the matching square or cubic display unit.

  value = v ÷ factor, to the unit's decimals; in² = 25.4² mm²; ft² = (12 × 25.4)² mm²; ft³ = (12 × 25.4)³ mm³

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• From meters, square meters and cubic meters

  What calculations give in SI, handed to the same formatters.

  mm = m × 1000; mm² = m² × 10⁶; mm³ = m³ × 10⁹

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• Lengths inside a message

  Rewrites plain "N mm" and "N m" inside a message into the display unit.

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• Quantities inside a sentence

  Rewrites lengths, areas and volumes inside a calculation's sentence into the display unit.

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• A paper size as text

  A sheet's width and height in the display unit.

  value = mm ÷ factor, to 1 (mm, cm), 2 (in) or 3 (m, ft) decimals

  Lengths, areas and volumes as text display-units.js

  • BimCraft
  64-bit

• Area of a region

  The signed area of a closed outline, used to refuse a hatch with no area.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Points taken from a drawing gesture

  The points of a new line or region, without repeats.

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Points read from the file

  A drafting item's points in millimeters, from the IFC polyline that stores them.

  mm = stored coordinate × file length unit in mm

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Hatch spacing and angle written to the file

  The IFC fill style of a pattern: one hatching per line family with its spacing and angle.

  spacing = gap × scale in file units; angle = degrees × π ÷ 180 (× 180 ÷ π when the file's angles are degrees)

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Is the item big enough

  Refuses a hatch with fewer than 3 corners or under 100 mm², and a line under 10 mm.

  L = Σ √(Δx² + Δy²); refuse when L < 10 mm or |area| < 100 mm²

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Move drafting items

  Every point of the picked items moved by one offset.

  (x, y) → (x + dx, y + dy)

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Is a point inside the region

  Whether a point lies inside the outline and outside its holes.

  even-odd count of edges crossed by a ray toward +x

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Clip a stroke to the region

  The pieces of a straight stroke that lie inside the region.

  t = ((c − a) × e) ÷ (d × e), u = ((c − a) × d) ÷ (d × e); keep 0 < t < 1, 0 ≤ u ≤ 1

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Strokes of a hatch pattern

  The lines, dots or zigzags of a pattern inside a region, at its scale.

  line k of a family: n · p = ⌊(n_min − offset) ÷ gap⌋ × gap + k × gap, gap = pattern gap × scale

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• Pattern scale

  The scale of a hatch pattern as it is kept.

  scale = min(50, max(0.1, v)), or 1 when v is not a positive number

  Drafting lines and hatch regions drafting.js

  • BimCraft
  64-bit

• A typed point

  The next point of a drafting line from typed coordinates, a typed offset, a typed length and angle, or a typed length along the pointer's direction.

  polar: (x + L·cos(a·π ÷ 180), y + L·sin(a·π ÷ 180)); length only: last + L × (to − last) ÷ |to − last|

  Drafting lines and hatch regions drafting-ui.js

  • BimCraft
  64-bit

• Viewport windows on the model

  For each sheet viewport, the half width and half height of the model area it shows.

  k = h ÷ viewHeight; half width = w ÷ 2 ÷ k; half height = h ÷ 2 ÷ k

  Equipment list from drawing tags dwg-equipment.js

  • BimCraft
  64-bit

• Sheets that show a point

  Which sheets show a given model point.

  u = dx·cos − dy·sin, v = dx·sin + dy·cos; inside when |u| ≤ half width and |v| ≤ half height

  Equipment list from drawing tags dwg-equipment.js

  • BimCraft
  64-bit

• Quantity of a row

  The scheduled quantity of an item tagged in several places.

  qty = Σ tag quantities

  Equipment list from drawing tags dwg-equipment.js

  • BimCraft
  64-bit

• A piece as stored

  One stud, plate, header, joist or rafter with its length and its place in the panel.

  stored value = round(v × 10) ÷ 10

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Stud length of a wall

  The length of a full-height stud: the wall height less the plates.

  stud length = H − (top plates + 1) × plate thickness

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Studs on the spacing grid

  Where the regular studs stand, left out where an opening is.

  center c = spacing, 2 × spacing, …; stud from c − face ÷ 2 to c + face ÷ 2

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Framing round an opening

  The jack studs, header, cripples and sill of one opening.

  jack = sill + opening height − bottom plate; header = opening width + 2 × stud face; cripple above = H − top plates − header top

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Floor panel

  The joists, rim joists and blocking of a floor panel.

  joist length = span − 2 × rim thickness; blocking = clear gap between neighboring joists

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Roof panel

  The rafters and ridge board of a gable roof panel, and its pitch.

  slope = √(run² + rise²); rafter = slope + overhang × slope ÷ run; pitch = atan2(rise, run) × 180 ÷ π

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Piece count and total length

  How many pieces a panel has and their total length in meters.

  meters = Σ piece lengths ÷ 1000, rounded to 0.01

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Cut list

  One row per mark: size, length, count and total length.

  total (m) = round(length × count) ÷ 1000

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Panel placed in the model

  A point of the panel turned by the panel's angle and moved to its place in the model.

  P = O + u·(cos a, sin a) + n·(−sin a, cos a) + (0, 0, z), each coordinate rounded to 0.1 mm

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Timber profile and weight

  The profile a placed timber piece gets: its dressed size and a density for its weight.

  b × t = dressed size, rounded to 0.1 mm; density = 500 kg/m³

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Scale of the shop sheet

  The scale the panel is drawn at on its sheet, and the scale printed in the title block.

  k = min(drawing width ÷ panel width, drawing height ÷ panel height); printed scale = 1 : round(1 ÷ k)

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Scale text in the title block

  The line of the title block that states the scale and the piece count.

  text = "1:" + max(1, round(1 ÷ k))

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Map conversion as a matrix

  The transform from model units to map units, from the conversion's numbers.

  (ax, ay) = (XAxisAbscissa, XAxisOrdinate) ÷ |…|; E = Eastings + s·(ax·x − ay·y); N = Northings + s·(ay·x + ax·y); H = Height + s·z

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Meters per map unit

  The size of the map's length unit in meters, from its name.

  US survey foot = 1200 ÷ 3937 m; foot = 0.3048 m; otherwise 1

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Length unit of the map system

  Finds or makes the IFC unit for the map's coordinates.

  wanted mm per unit: m 1000, ft 304.8, US survey ft 1200 ÷ 3937 × 1000; match when |unit − wanted| < 10⁻⁹ × wanted

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Latitude and longitude as degrees, minutes, seconds

  An angle in decimal degrees split into the four whole numbers the IFC site stores.

  d = ⌊|deg|⌋; m = ⌊(|deg| − d) × 60⌋; s = ⌊rest × 60⌋; millionths = round((rest − s) × 10⁶)

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Map conversion written to the file

  The six conversion numbers written into IfcMapConversion, new or in place.

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Height of a column

  The height a column is built with: up to its top level plus an offset, else its fixed height.

  h = top elevation − own elevation + offset

  Columns: height and quantities model-columns.js

  • BimCraft
  64-bit

• Cross-section area and volume

  The quantities written on a column.

  area = π (w ÷ 2)² or w × d; volume = area × h

  Columns: height and quantities model-columns.js

  • BimCraft
  64-bit

• Sizes saved with a column

  The width, depth, angle and heights kept in the column's property set, which is what is read back.

  Columns: height and quantities model-columns.js

  • BimCraft
  64-bit

• Columns following a level

  Rebuilds columns whose height no longer matches their levels.

  rebuild when |stored − wanted| > 0.5 mm

  Columns: height and quantities model-columns.js

  • BimCraft
  64-bit

• Grid lines by spacing

  The ends of numbered and lettered grid lines from a count, a spacing or list of spacings, an origin and an angle.

  xᵢ = xᵢ₋₁ + spacing; P = origin + R(angle) × (x, y)

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Where grid lines cross

  The crossing points of every pair of grid lines, for snapping.

  den = r × s; t = (q − p) × s ÷ den; point = p + t r

  Grid lines model-grids.js

  • BimCraft
  64-bit