Calculations

Calculations

• Where a wall's framing starts and stops

  Finds the framed start and end of a wall at corners and T junctions with other walls.

  t = cross(q − p, e) ÷ cross(d, e)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Length of a wall piece

  Records a wall piece as a box and takes its length as the longer of its extent along the wall and its height.

  length = max(x₁ − x₀, z₁ − z₀)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Framing around a wall opening

  Places the jack and king studs, the header, the cripples and the rough sill around each door and window.

  header top = min(head + header depth, underside of top plate); cripples at x₀ + k × spacing

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Studs on layout

  Places the common studs on center from the wall's framed start.

  x = x₀ + k × spacing, k = 1, 2, … while x < x₁ − T

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Line clipped to a polygon

  Finds the stretches of a joist, rafter or truss line that lie inside a floor outline or a roof face.

  t = cross(a − p, e) ÷ cross(d, e); s = cross(a − p, d) ÷ cross(d, e)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Outline moved in by a distance

  Moves every edge of a floor outline inward by a fixed distance and finds the new corners.

  corner = p₀ + u_prev × cross(p₁ − p₀, u) ÷ cross(u_prev, u)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Joist lines and the governing span

  Sets the joist lines across a floor and takes the longest clipped joist as the span that sizes them.

  c = c₀ + spacing, then + spacing while c < c₁ − 1; span = max(t₁ − t₀)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Joists cut round floor openings

  Makes each joist piece, cutting it 3 inches short of an opening it crosses, and records its length.

  length = s₁ − s₀

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Trusses across a roof

  Places a truss at each spacing along the roof and takes its top profile from the roof's underside.

  top profile sampled at t₀ + (t₁ − t₀) × k ÷ 40, k = 0 … 40

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Rafters and their size

  Sizes the rafters from the longest horizontal run, places them along each roof face and records each one's sloped length.

  run = max((p − o) · n); length = √((t₁ − t₀)² + (z_b − z_a)²)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Collar ties

  Places a collar tie every 4 feet under each ridge, two thirds of the way from the plate to the ridge, and finds how far it reaches each way.

  z_c = plate + (z_ridge − plate) × 2 ÷ 3; reach by 40 halvings of [0, 20000 mm]

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Ceiling joists

  Lays ceiling joists out like floor joists at the plate and sizes them from the ceiling span table.

  span = max(joist length); z = plate + depth ÷ 2

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Solid of a sloped member

  Builds the solid of a joist, rafter, hip, valley or ridge as a rectangle swept along its 3D line with plumb ends.

  slope = |Δz| ÷ √(Δx² + Δy²); plumb depth = depth × √(1 + slope²)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Length and board feet written on a piece

  Writes each piece's role, size, length and board feet into the model, and adds up the board feet of the framing.

  Length = round(L ÷ unit, 3); BoardFeet = round(bf × plies, 3)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Board feet of a framing

  Writes the piece count and the total board feet of one framed wall, floor or roof.

  BoardFeet = round(Σ bf, 2)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Cut list by stock length

  Groups every framing piece by size and stock length, and totals the counts and board feet.

  stock = max(8 ft, ⌈L ÷ 2 ft⌉ × 2 ft); metric: max(2400, ⌈L ÷ 600⌉ × 600)

  Wall, floor and roof framing layout res-framing.js

  • BimCraft
  64-bit

• Wall under each roof edge

  Finds the drawn wall whose outer face lies along each edge of the building's outline.

  d = |cross(û_wall, m − a)|; match when |d − t ÷ 2| ≤ 2 mm

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Per-wall pitch and overhang as stored

  Writes each wall's roof setting (pitched, gable or none, with its pitch and overhang) as the text kept in the model.

  pitch → round(pitch, 4) degrees; overhang → round(overhang, 2) mm

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Sloped roof slabs

  Builds one slab per roof face in the face's own sloped plane.

  profile y = ((p − o) · n) ÷ cos θ; depth = thickness ÷ cos θ; sweep direction (0, sin θ, cos θ)

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Gable wall profile

  Builds each gable wall from the top of the wall below up to the underside of the roof.

  z sampled at a + (b − a) × k ÷ 64, k = 0 … 64, 1 mm inside the edge

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Fascia boards

  Builds a fascia board along each eave and rake run and totals their length.

  length = Σ board lengths; board profile rises by z_b − z_a over its run

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Soffit area

  Adds up the area of the level soffit panels under the eaves.

  area = Σ |polygon area|

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Roof areas and line lengths written to the model

  Writes the roof's sloped area, projected area and the lengths of its ridges, hips, valleys, eaves and rakes.

  GrossArea = plan.area; ProjectedArea = plan.projected; lengths = round(L ÷ unit, 6)

  Roof faces, gable ends, fascia and soffit res-roof.js

  • BimCraft
  64-bit

• Sheet scale as feet per point

  The number of feet in the building that one PDF point stands for on a sheet drawn at 1:ratio.

  ft per point = ratio × (25.4 ÷ 72) ÷ 304.8 = ratio ÷ 864

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  Exact

• Mark coordinates on the sheet

  Maps a plan point to the sheet and writes it as the PDF-point coordinates of a takeoff mark.

  mark = round(sheet mm × 72 ÷ 25.4 × 100) ÷ 100

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Roof pitch as rise per 12

  Converts a pitch in degrees to the rise per 12 that TakeoffCraft uses for sloped areas and lengths.

  rise per 12 = round(12 × tan θ × 10000) ÷ 10000

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Walls as runs with a height

  Sends each wall as a run along its center line, grouped by wall type and height.

  height (ft) = round(height ÷ 304.8 × 100) ÷ 100

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Door and window positions

  Places a count mark at the middle of each door and window along its wall.

  at = a + (b − a) ÷ L × (offset + width ÷ 2)

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Roof faces and roof lines

  Sends each roof face as a plan area with its pitch, and the ridges, hips, valleys, eaves and rakes as runs.

  face pitch = round(pitch × 100) ÷ 100; line pitch = max over the faces

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Footings, stem walls and slabs

  Sends slabs as areas with their thickness, and footings and stem walls as runs along the middle of their outline with a width and height.

  mid = (outer + inner) ÷ 2; width (in) = |gap| ÷ 25.4; height (ft) = (z₁ − z₀) ÷ 304.8

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Width of a footing ring

  The distance between a foundation's outer and inner outlines.

  width = cross(b − a, q − a) ÷ |b − a|

  Quantities handed to TakeoffCraft res-takeoff.js

  • BimCraft
  64-bit

• Survey points into model millimeters

  Converts survey points from their own unit to millimeters, moves them by the offset and measures heights from the datum.

  x = x_s × unit − offset_x; z = (z_s − datum) × unit

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Offset for far-off survey coordinates

  Finds the move that brings survey coordinates far from the origin onto the building.

  c = (min + max) ÷ 2 × unit; offset = c − target when |c| > 2e6 mm

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Thinning a large point set

  Keeps the lowest point in each square cell of a grid.

  cell index = (⌊x ÷ cell⌋, ⌊y ÷ cell⌋); keep min z

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Cell size when a ground has too many points

  Chooses the thinning cell so that about 20000 points remain.

  cell = √(bounding box area ÷ 20000) × 1.2

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• LandXML units and point order

  Reads a LandXML surface's length unit and its points, which are written northing, easting, elevation.

  x = E × k, y = N × k, z = Z × k; k = 0.01 for centimeters, 1000 for kilometers, 1 ÷ 12 for inches

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Pad outline moved out by the margin

  Moves every edge of the building's outline outward by the pad margin and finds the new corners.

  corner = p₀ + u_prev × cross(p₁ − p₀, u) ÷ cross(u_prev, u)

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Finished grade at a point

  The finished ground height at a point: flat on each pad and sloping away from it to meet the existing ground.

  z = max(z_pad − d ÷ slope, min(z_pad + d ÷ slope, z))

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Sample rings round a pad

  Adds rings of graded points round each pad, out to where its slopes can meet the ground.

  reach = max(|z_max − z_pad|, |z_pad − z_min|) × slope + 500; rings every 500 mm, points every 500 mm

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Cut and fill volumes

  The volume of earth to cut and to fill between the existing and the finished ground, in cubic meters.

  V = Σ (z_finished − z_existing) × cell² ÷ 1e9, cell = 250 mm, sampled at cell centers

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Cut and fill written to the model

  Writes the terrain's cut and fill volumes and its lowest and highest elevation.

  Cut, Fill = round(V, 3) m³

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Cut and fill of each pad

  Writes each pad's level and its cut and fill.

  pad cut = total cut ÷ number of pads

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Pad outline and level

  A pad's outline in site coordinates and its level: the walls' outline moved out by the margin, at the floor's height less the pad depth.

  z_pad = level elevation − depth

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Existing ground points as stored

  Writes the existing ground's points into the model as text.

  x, y, z = Math.round(value) mm

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Terrain body coordinates

  Writes the finished ground as a closed triangulated body in the site's axes.

  coordinate = round(value ÷ unit, 3)

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Datum after raising the ground

  Moves the existing ground up or down and corrects the stored survey datum.

  z′ = z + raise; datum′ = datum − raise ÷ (mm per source unit)

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Paving draped on the ground

  Builds a driveway, walk or patio as a surface on the finished grade and writes its area and volume.

  grid step = max(500, √(box area ÷ 2000)); GrossArea = plan area; GrossVolume = sloped area × thickness

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• LandXML export

  Writes the existing and finished ground as LandXML surfaces.

  value = (mm × k).toFixed(4), k = 0.001 for meters, 1 ÷ 304.8 for feet

  Site ground, building pads and cut and fill res-terrain.js

  • BimCraft
  64-bit

• Longitude and latitude to local meters

  The position of a point in meters east and north of the address point.

  x = (lon − lon₀) × 111320 × cos(lat₀); y = (lat − lat₀) × 111320

  Site surroundings in local meters site-context.js

  • BimCraft
  • ModelCraft
  • CivilCraft
  64-bit

• Local meters back to longitude and latitude

  The longitude and latitude of a local point.

  lon = lon₀ + x ÷ (111320 × cos(lat₀)); lat = lat₀ + y ÷ 111320

  Site surroundings in local meters site-context.js

  • BimCraft
  • ModelCraft
  • CivilCraft
  64-bit