Calculations

Calculations

• Octave band weight

  How much of a frequency belongs to one octave band.

  w = cos(π ÷ 2 × |log₂(f ÷ f_band)|) within one octave, else 0

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  64-bit

• Zero-phase band filter

  Keeps one octave band of a signal.

  Room impulse response and listening acoustics-ir.js

  • BimCraft
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• Decaying reverberant tail

  The diffuse part of the response: noise that falls 60 dB in each band's reverberation time.

  tail(t) = Σ_bands noise_b(t) × e^(−k t), k = 6.907755 ÷ T_b; × (t ÷ onset)² up to onset = max(0.002, 2 × mean free path ÷ 343)

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  64-bit

• First reflections and the tail's level

  Places the six first reflections and sets the level of the tail against the direct sound.

  R = S a ÷ (1 − a); reflection gain = √(1 − a) × d₀ ÷ d at sample round((d − d₀) ÷ 343 × sr); tail energy = 16π d₀² ÷ R less the reflections; r_c = √(R ÷ 16π)

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  32-bit in part

• Reverberation time measured from a response

  The reverberation time of an impulse response in one band, by Schroeder's backward integration.

  E(t) = Σ over τ ≥ t of x²; L = 10 log₁₀(E(t) ÷ E(0)); T = 60 ÷ −slope of L between −5 and −35 dB

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  64-bit

• Convolution

  A dry sound passed through the room's impulse response.

  y = IFFT(FFT(x) × FFT(h)) ÷ N

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  32-bit in part

• Level matching

  Brings the sound in the room to the loudness of the dry sound, so switching between them changes the room and not the volume.

  k = rms(dry) ÷ rms(wet over the dry sound's length)

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  32-bit in part

• WAV file samples

  The numbers written to the downloaded sound file.

  s = round(clamp(x × k, −1, 1) × 32767), k = 1 ÷ peak when peak > 1

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  32-bit in part

• 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

• 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

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• Is this dimension already there

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

  Automatic plan dimensions autodim.js

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• Measured segment along an axis

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

  Automatic plan dimensions autodim.js

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• 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

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• 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
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• 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
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• 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
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• 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

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  • ModelCraft
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• 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
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• 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

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  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

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  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
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• 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

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• Clash tolerance as typed

  Reads the tolerance for the clash check, in meters.

  Measurements and typed values in the main window bimcraft.js

  • BimCraft
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• 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

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  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

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• 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