Calculations

Calculations

• 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

• Plan extents and edge tolerance

  The outside box of the level's walls and how close to it a wall must lie to count as an outside edge.

  T = 1.2 × max(150 mm, thickest wall)

  Automatic plan dimensions autodim.js

  • BimCraft
  64-bit

• Dimension line offset

  How far the dimension line sits from the two points it measures.

  offset = round((target − a)·n × 10) ÷ 10, n = (−dy, dx) ÷ |b − a|

  Automatic plan dimensions autodim.js

  • BimCraft
  64-bit

• Reference station on a wall

  The saved position of a dimension's end along its wall, 0 at one end and 1 at the other.

  station = round(station × 10⁶) ÷ 10⁶

  Automatic plan dimensions autodim.js

  • BimCraft
  64-bit

• Is this dimension already there

  Compares two references so the same dimension is not made twice.

  Automatic plan dimensions autodim.js

  • BimCraft
  64-bit

• Measured segment along an axis

  Makes one dimension between two points, measured along X or along Y.

  Automatic plan dimensions autodim.js

  • BimCraft
  64-bit

• Stops along an outside edge

  The wall ends, opening edges and meeting walls that a row of dimensions runs between.

  opening stations = offset ÷ L and (offset + width) ÷ L

  Automatic plan dimensions autodim.js

  • BimCraft
  64-bit

• Inverse of a 4 × 4 matrix

  The inverse of the model's coordination matrix.

  M⁻¹ = adj(M) ÷ det(M)

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Viewer point to model point

  A camera position or a point on a section plane in the model's own coordinates, in meters with Z up.

  (x, y, z) = C⁻¹ v; IFC = (x, −z, y)

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Viewer direction to model direction

  A camera direction, up vector or section plane normal in the model's own axes.

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Model point to viewer point

  A point read from an issue file, placed in the viewer.

  v = C (x, z, −y)

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Model direction to viewer direction

  A direction read from an issue file, in the viewer's axes.

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Numbers written to the file

  How each coordinate, direction, field of view and scale is written in a viewpoint.

  round(v × 10⁶) ÷ 10⁶

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Numbers read from the file

  Reads the X, Y and Z of a point or direction.

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Camera read from a viewpoint

  The camera of an issue as BimCraft keeps it.

  Issue viewpoints in BCF files bcf.js

  • BimCraft
  • ModelCraft
  64-bit

• Distance and area measured in 3D

  The length between two picked points with its X, Y and Z parts, or the area of a picked face.

  distance = |b − a|; area = the picked face's area

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  32-bit in part

• Map position of a picked point

  The map grid coordinates, height, latitude and longitude of a point picked on the model.

  picked point → file coordinates → map grid (IfcMapConversion) → latitude and longitude (proj4)

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  32-bit in part

• Latitude and longitude as text

  How a located point's latitude and longitude are written in the readout and the label.

  round(v × 10ⁿ) ÷ 10ⁿ, then n decimals

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• Lengths shown in Properties

  A length property or quantity shown in the person's display unit.

  shown = file value × file unit in mm

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• A typed length written to the file

  Converts a length typed in Properties from the display unit to the file's own unit.

  file value = round(mm ÷ file unit × 10⁹) ÷ 10⁹

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• Numbers in the quantity tables

  How a total or a quantity is written in the on-screen quantity tables.

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• Height of a ceiling-mounted item

  How far above its level a library item is placed when it hangs from the ceiling.

  z = max(0, top − item height)

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• Clash tolerance as typed

  Reads the tolerance for the clash check, in meters.

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• Offset of an added model

  The X, Y and Z move typed for a model added beside the first one.

  offset in m = typed length in mm ÷ 1000

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
  64-bit

• Which stated quantity is used

  Picks an element's volume, area or length from the quantities the file states.

  Element quantities for carbon and cost carbon-calc.js

  • BimCraft
  64-bit

• Volume of a mesh

  The volume of an element from its triangles, used when the file states none.

  V = |Σ a·(b × c)| ÷ 6 × (unit ÷ 1000)³

  Element quantities for carbon and cost carbon-calc.js

  • BimCraft
  64-bit

• Share of the volume per material

  How an element's volume is divided between the materials it is made of.

  layer share = tᵢ ÷ Σt; constituent share = fᵢ ÷ Σf; otherwise 1 ÷ n

  Element quantities for carbon and cost carbon-calc.js

  • BimCraft
  64-bit

• Floor area of the building

  The floor area the carbon total is divided by when the person has not typed one.

  area = Σ space floor areas, else Σ floor slab areas

  Element quantities for carbon and cost carbon-calc.js

  • BimCraft
  64-bit

• Quantities per material part

  The volume, area and length handed on for each material of an element.

  part volume = element volume × share

  Element quantities for carbon and cost carbon-calc.js

  • BimCraft
  64-bit

• World triangles and box of each element

  Each element's triangles in the scene's coordinates and the box round them.

  p' = M p

  Clash check clash.js

  • BimCraft
  32-bit in part

• Overlap of two boxes

  How far two elements' boxes overlap, the figure reported as the clash depth.

  depth = min over X, Y, Z of (min of the two maxima − max of the two minima)

  Clash check clash.js

  • BimCraft
  64-bit

• Candidate pairs and the result list

  Pairs one element from each set whose boxes overlap by more than the tolerance, tests them and lists the clashes deepest first.

  candidate when depth > tolerance

  Clash check clash.js

  • BimCraft
  64-bit

• Do two elements' surfaces cross

  Looks for a pair of triangles, one from each element, that cross.

  Clash check clash.js

  • BimCraft
  32-bit in part

• Triangle against triangle

  Decides whether two triangles cross and gives a point on the crossing.

  dᵢ = n₂·pᵢ + d₂ for each corner; crossing when each triangle has corners on both sides of the other's plane and their intervals on the line n₁ × n₂ overlap

  Clash check clash.js

  • BimCraft
  32-bit in part

• 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

• Middle of a room

  The point the interior elevation cuts through.

  middle = (min + max) ÷ 2 on each axis

  Interior elevations and their dimensions comforts-views.js

  • BimCraft
  64-bit