Calculations

Calculations

• Sheet items to PDF operators

  Converts every line, fill, clip and text of a sheet from millimeters to PDF points and writes the page's drawing operators.

  points = mm × 72 ÷ 25.4

  Drawing sheets to scale and the PDF res-sheets.js

  • BimCraft
  64-bit

• Direction a section line looks

  The unit direction along a section line and the horizontal direction it looks.

  u = (b − a) ÷ |b − a|; look = (−u_y, u_x) or (u_y, −u_x)

  Drawing sheets to scale and the PDF res-sheets.js

  • BimCraft
  64-bit

• Section line written to the model

  Writes a section line's two ends, its look side and its depth into the model.

  AX, AY, BX, BY, Depth = round(value ÷ unit, 6)

  Drawing sheets to scale and the PDF res-sheets.js

  • BimCraft
  64-bit

• Ceiling tile grid

  Lays a ceiling pattern's grid lines inside a ceiling's outline, with a tile centered on the outline's box.

  lines at c + m ÷ 2 + j × m; crossing = q_a + (q_b − q_a) × (k − p_a) ÷ (p_b − p_a)

  Drawing sheets to scale and the PDF views-model.js

  • BimCraft
  64-bit

• Crop region of a view

  Orders the four numbers of a crop rectangle and rejects one that is not a real rectangle.

  valid when x₁ − x₀ ≥ 100 and y₁ − y₀ ≥ 100

  Drawing sheets to scale and the PDF views-model.js

  • BimCraft
  64-bit

• View positions stored on a sheet

  Stores where each view sits on a hand-arranged sheet and at which scale.

  x, y = round(value, 2) mm; ratio = whole number

  Drawing sheets to scale and the PDF views-model.js

  • BimCraft
  64-bit

• Another level drawn under a plan

  Moves another level's plan linework into this level's plan as plain segments.

  p′ = (T₀ x + T₄ y + T₁₂, T₁ x + T₅ y + T₁₃); arcs as 12 chords

  Drawing sheets to scale and the PDF views-model.js

  • BimCraft
  64-bit

• Number of risers and riser height

  The number of risers a floor-to-floor height needs, each riser's height, and whether the riser, tread, width and handrail meet the limits.

  n = max(2, ⌈H ÷ riser_max − 1e-9⌉); r = H ÷ n; treads = n − 1

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Treads of a straight flight

  The plan rectangle and the height of each tread of a straight stair.

  tread i spans i × d to (i + 1) × d; z = (i + 1) × r

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Treads before and after a turn

  Divides the treads of an L, U or winder stair between the flight before the turn and the one after.

  before = max(1, min(T − turn − 1, round((T − turn) × split))); after = T − before − turn

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Landing and second flight of a U stair

  The half landing of a U stair and the treads of the flight that comes back beside the first.

  landing width = 2 w + gap; flight 2 center at ±(w + gap); z = z_landing + (j + 1) × r

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Winder treads

  Fans three winder treads from the inside corner of a quarter turn.

  outer path of length 2 w cut at 2 w k ÷ 3, k = 0 … 3

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Spiral stair

  The wedge treads of a spiral stair round its post, the handrail, the walk line and the outline.

  Δθ = tread ÷ (r_post + 12 in); tread i from θ₀ ± i Δθ; arcs chorded at ≤ 6°

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Floor-to-floor height of a stair

  The height a stair climbs: from its level to the level above, else its own fixed height.

  H = elevation_top − elevation_bottom when that is more than 100 mm

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Stairwell opening

  Finds the treads and landings that have less than the required headroom under the floor above; their outline is cut out of that floor.

  cut where z_tread + headroom > H + offset − thickness

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Center post of a spiral stair

  Builds the spiral stair's round post as a 24-sided column.

  vertices at r × (cos 2πj ÷ 24, sin 2πj ÷ 24)

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Riser and tread written to the model

  Writes the number of risers and treads, the riser height, the tread length and the required headroom.

  RiserHeight, TreadLength = round(value ÷ unit, 6)

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Stair settings written to the model

  Writes the stair's start point, angle, width, riser limit, tread, split and rail height.

  lengths = round(value ÷ unit, 6); Angle = round(angle, 6); Split = round(split, 4)

  Stair risers, treads and stairwell res-stair.js

  • BimCraft
  64-bit

• Stair from a sketched walking line

  Turns a walking line of one, two or three segments into a straight, L or U stair: its direction, width, gap, split and tread depth.

  n = max(2, ⌈H ÷ riser_max − 1e-9⌉); tread = max(50, line length ÷ (n − 1)); split = first leg ÷ total

  Stair risers, treads and stairwell stair-sketch.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

• Millimeters per survey unit

  The factor from a survey file's length unit to millimeters.

  m = 1000; ft = 304.8; US survey ft = 1200 ÷ 3937 × 1000

  Ground read from a survey file res-ui.js

  • BimCraft
  Exact

• Ground points from a LAS or LAZ cloud

  Takes the ground-class points of a cloud and thins them to the lowest point in each 1 m cell.

  x = pos[3i] + origin_x; cell = 1000 ÷ (mm per unit)

  Ground read from a survey file res-ui.js

  • BimCraft
  32-bit in part

• Thinning an elevation grid

  Chooses every how many cells of a GeoTIFF or ASCII grid to read so that about 15000 points remain.

  step = max(1, ⌈√(width × height ÷ 15000)⌉)

  Ground read from a survey file res-ui.js

  • BimCraft
  64-bit

• Unit, offset and datum of an imported ground

  Sets the unit factor, moves far-off coordinates to the building and picks the datum so the ground near the building sits 200 mm under the first floor.

  datum = median(z near the building) + 200 ÷ k

  Ground read from a survey file res-ui.js

  • BimCraft
  64-bit

• Roof plane area in Properties

  The sloped area of a manual roof plane shown in its properties.

  area = |½ Σ (xᵢ yᵢ₊₁ − yᵢ xᵢ₊₁)| ÷ cos θ

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit

• Cut list schedule

  The lumber schedule's rows: size, stock length, pieces and board feet, with totals.

  board feet shown = bf.toFixed(1)

  Figures shown in the residential panels and schedules res-ui.js

  • BimCraft
  64-bit