Calculations

Calculations

• Reproject points

  Every point of a file from one coordinate system to another.

  (x, y) in the source system → (x, y) in the target system, point by point

  Map coordinate reprojection reproject-batch.js

  • BimCraft
  • CivilCraft
  64-bit

• Map origin from latitude and longitude

  Eastings and northings of a typed latitude and longitude.

  (lon, lat) → (E, N), rounded to 0.000001 of the map unit

  Map coordinate reprojection crs-georef.js

  • BimCraft
  • CivilCraft
  64-bit

• Model to map conversion

  Where a model sits on the map: origin, rotation and scale.

  X axis = (cos a, sin a) rounded to 1e-12; scale = model unit ÷ map unit

  Map coordinate reprojection crs-georef.js

  • BimCraft
  • CivilCraft
  64-bit

• Sabine constant

  The constant both reverberation formulas multiply the volume by.

  C = 0.161 s/m

  Room reverberation time acoustics.js

  • BimCraft
  64-bit

• Sound absorbed by the air

  The attenuation of a pure tone in air, in dB per meter, at the room's temperature, humidity and pressure.

  α = 8.686 f² [1.84e-11 (p_r ÷ p) √(T ÷ T₀) + (T ÷ T₀)^−2.5 (0.01275 e^(−2239.1 ÷ T) ÷ (f_rO + f² ÷ f_rO) + 0.1068 e^(−3352 ÷ T) ÷ (f_rN + f² ÷ f_rN))]

  Room reverberation time acoustics.js

  • BimCraft
  64-bit

• Air absorption per meter

  Turns the dB figure into the energy absorption coefficient the formulas use.

  m = α ÷ 4.343

  Room reverberation time acoustics.js

  • BimCraft
  64-bit

• Reverberation time per band

  The Sabine and Eyring times of a room in each of six octave bands, and the mid-frequency mean.

  A = Σ Sᵢαᵢ + extra; ᾱ = min(0.999, A ÷ S); Sabine = C V ÷ (A + 4mV); Eyring = C V ÷ (−S ln(1 − ᾱ) + 4mV)

  Room reverberation time acoustics.js

  • BimCraft
  64-bit

• Reverberation over the target

  The finding raised when a room's mid-frequency time is over the person's target, with the absorption that would meet it.

  T = round(T_mid × 100) ÷ 100; need = round(max(0, V C ÷ target − (A₅₀₀ + A₁₀₀₀) ÷ 2))

  Room reverberation time acoustics.js

  • BimCraft
  64-bit

• Distance from a point to a room outline

  How far an opening's middle is from the room's outline, to decide which room the opening belongs to.

  d = min over edges of |P − (A + t (B − A))|, t clamped to 0…1

  Room reverberation time acoustics-model.js

  • BimCraft
  64-bit

• Room perimeter

  The length of the room's outline, used for the wall area when the walls' finishes are not read from the model.

  P = Σ |pᵢ₊₁ − pᵢ|

  Room reverberation time acoustics-model.js

  • BimCraft
  64-bit

• Is a point inside a room

  Decides whether a ceiling, a floor or a piece of furniture lies in a room.

  Room reverberation time acoustics-model.js

  • BimCraft
  64-bit

• Room height and opening areas

  The height the room is given and the area of the doors and windows in its walls.

  H = height ÷ 1000; opening area = (width ÷ 1000) × (height ÷ 1000)

  Room reverberation time acoustics-model.js

  • BimCraft
  64-bit

• Wall area per finish

  The area of wall each finish covers in a room, less its doors and windows.

  wall area = Σ edge length × H; net = max(0, gross − glass − doors); each finish × net ÷ gross

  Room reverberation time acoustics-model.js

  • BimCraft
  64-bit

• Room volume and the figures reported

  The volume passed to the formulas and the area, height and volume listed for each room.

  V = floor area × H; aspect = longest ÷ max(shortest, 0.1)

  Room reverberation time acoustics-model.js

  • BimCraft
  64-bit

• Length unit of the file

  The factor that takes the file's lengths to millimeters.

  toMm = prefix × 1000, or factor × base × 1000 for a converted unit

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Axis placement

  The three axes and the origin of one IFC placement.

  X = norm(X − Z (X·Z)); Y = Z × X

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Placement chain

  An element's position and axes in the model, through every placement it is relative to.

  M = M_parent ∘ M_local

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Rounded rectangle outline

  The outline of a hollow rectangular section with rounded corners.

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Circle outline

  The outline of a round bar or tube.

  pᵢ = r (cos 2πi ÷ 64, sin 2πi ÷ 64)

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• I-shape outline

  The outline of an I section with its root fillets.

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Is this I-shape a rolled section

  Matches an I-shape's name and sizes against the section table, to decide whether it is treated as rolled or welded.

  |a − b| ≤ max(0.5 mm, 0.01 × b) for d, bf, tw, tf

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Member axis, length and section

  The line a member is analyzed on and the section properties it carries.

  axis from the section centroid c₀ to c₀ + depth × ext; skipped when |ext·U| or |ext·V| > 0.001

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Concrete wall as a line, thickness and height

  Reads a concrete wall's plan outline as a center line and a thickness for the plate model.

  turn the outline by −θ of its longest edge; thickness = y₁ − y₀; kept when |area| ≥ 0.9 × box area

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Closest points of a line and a segment

  Where a member's own line passes nearest another member's axis, and how far apart they are there.

  s = (b e − c d) ÷ (a c − b²); t = (a e − b d) ÷ (a c − b²)

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Member ends carried onto the nearest axis

  Moves each member end along its own line onto the axis of the member it meets.

  accepted when d ≤ 0.6 × max(size) + 25 mm and |s| ≤ 0.6 × size + 150 mm; score = d + 0.01 |s|

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Node merging

  Decides whether a point is a new joint or an existing one.

  same node when |p − node| ≤ 10 mm

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Where members are split

  The stations along a member at which other members or point loads meet it.

  s = (Q − A)·u; split when 10 mm < s < L − 10 mm and |A + s u − Q| ≤ 10 mm

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Shared section records

  Groups members that have the same section so the model lists each section once.

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Section roll angle

  How far the drawn section is turned about the member's axis from the default local axes.

  roll = atan2(U·e_z0, U·e_y0) × 180 ÷ π + principal turn

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Supports at column feet

  Puts a support under every column that nothing continues below.

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Loads on split members

  Places point loads and cuts distributed loads onto the pieces a member was split into.

  w(s) = w + (w₂ − w)(s − a) ÷ (b − a)

  Frame model from a building model analysis-bim.js

  • BimCraft
  64-bit

• Cloud to plan matrix

  The one matrix that takes a cloud's points to a level's plan in millimeters.

  M = storey⁻¹ · S · C⁻¹ · model⁻¹ · layer, S taking meters with Y up to millimeters with Z up

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Slice of the cloud at the cut height

  The cloud's points near a level's cut height, in plan millimeters.

  kept when |z − cut| ≤ thickness ÷ 2

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Nearest slice point

  The slice point nearest a plan point, for snapping a drawn point to the scan.

  minimum of (x − xᵢ)² + (y − yᵢ)² within r

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Turn that sets the scan square

  The angle of the scan's walls against the plan's axes, and the point to turn about.

  angle = first estimate + the trial turn in −1°…1° with the highest sharpness

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Sharpness of a trial turn

  Scores how well the points line up along X and Y after a trial turn.

  score = Σ (count per 10 mm bin along X)² + Σ (count per 10 mm bin along Y)²

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Wall direction from line fits

  A first estimate of the walls' direction from a line fitted to the points in each cell.

  per cell: covariance c_xx, c_yy, c_xy; λ = tr ÷ 2 ± √(tr² ÷ 4 − det); angle = atan2(λ₁ − c_xx, c_xy), folded into 0…90°

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Floor height of a scan

  The height of the scan's floor above the level.

  floor = mean z of the points in the fullest 20 mm band of the lowest third

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Turn about a plan point

  The matrix that turns the scan by an angle about a point in the plan.

  x' = c x − s y + (x₀ − c x₀ + s y₀); y' = s x + c y + (y₀ − s x₀ − c y₀)

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• A plan change carried to the scene

  Re-expresses a turn or a lift made in the plan as a change of the cloud's own placement.

  A' = M⁻¹ · A · M

  Point cloud slice and scan alignment cloud-slice.js

  • BimCraft
  64-bit

• Unit factors for priced quantities

  The size of each pricing unit in m, m² or m³.

  1 yd³ = 0.764554858 m³; 1 ft³ = 0.0283168466 m³; 1 ft² = 0.09290304 m²; 1 ft = 0.3048 m

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Dollars to whole cents

  Rounds an amount to a whole number of cents.

  cents = round(dollars × 100)

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Whole cents to dollars

  The amount reported, in dollars.

  dollars = round(cents) ÷ 100

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Quantity in the price's unit

  An element's volume, area, length, weight or count in the unit its price is per.

  qty = quantity ÷ unit factor; weight = volume × density

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Cost of each element

  The material and labor cost of every element, and the total.

  line = round(qty × (1 + waste) × material rate × 100) + round(qty × labor rate × 100) cents

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Cost of each scheduled task

  Adds up the cost of a task's elements, sharing an element that is in several tasks.

  task cents = round(Σ element cents ÷ n), n = the tasks that hold the element

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Spending profile of a task

  The weight each day of a task gets: even, front-loaded, back-loaded or bell-shaped.

  even 1; front D − i; back i + 1; bell sin(π (i + 0.5) ÷ D)

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• A task's cost per day

  Divides a task's cost over its days in whole cents.

  dayᵢ = floor(cents × wᵢ ÷ W), then one more cent to the days with the largest remainders

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Cash flow curve

  The cost per day, week or month and the running total.

  period cost = Σ day cents; cumulative = running sum

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Planned, built and earned value on a day

  What the schedule plans to have spent by a day, what is built, running and remaining, and the earned value from typed progress.

  earned = Σ task cents × progress, progress clamped to 0…1

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit