Calculations

Calculations

• Conjugate gradient solve

  The displacement of every node under the loads.

  repeat until ‖r‖ ÷ ‖b‖ < 1e-8

  Stress analysis fea.js

  • PartCraft
  64-bit

• Von Mises stress

  One equivalent stress from the six stress components.

  σᵥ = √(½[(σ_x − σ_y)² + (σ_y − σ_z)² + (σ_z − σ_x)²] + 3(τ_xy² + τ_yz² + τ_zx²))

  Stress analysis fea.js

  • PartCraft
  64-bit

• Stress and displacement at each node, and their maximum

  The values the plot colors by, and the maximum the report states.

  σ at a node = mean of its corners; |u| = √(u_x² + u_y² + u_z²); maximum over the nodes

  Stress analysis fea.js

  • PartCraft
  32-bit in part

• Volume, surface area and bounding box

  The measured properties of the finished body.

  volume, area, genus and bounding box, asked of the kernel

  Solid modeling kernel.js

  • PartCraft
  64-bit

• Vertex positions of the body

  The mesh that faces, edges and the display are built from.

  positions = 32-bit copy of the kernel's vertices

  Solid modeling kernel.js

  • PartCraft
  32-bit in part

• Fast Fourier transform

  The transform behind the band filters and the convolution.

  X_k = Σ x_n e^(∓2πi kn ÷ N), N a power of two

  Room impulse response and listening acoustics-ir.js

  • BimCraft
  64-bit

• 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
  64-bit

• 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

• 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

• 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

• Speed of sound

  The speed of sound used for every delay.

  c = 343 m/s

  Geometric room acoustics geo.js

  • BimCraft
  64-bit

• Image sources of a box room

  The energy arriving at the listener from the source and every mirror image of it within the time limit.

  image = ((1 − 2p)·s + 2·i·L); e[round(d ÷ c × sr)] += Π (1 − α)^hits × exp(−m·d) ÷ (4π·d²)

  Geometric room acoustics geo.js

  • BimCraft
  64-bit

• Plane of a surface

  The unit normal and plane distance of each room surface, from its first three corners.

  n = (b − a) × (c − a) ÷ |…|; d = n · a

  Geometric room acoustics geo.js

  • BimCraft
  64-bit

• Is a hit inside the surface

  Whether a point on a surface's plane lies inside its convex outline.

  the sign of ((b − a) × (p − a)) · n is the same for every edge

  Geometric room acoustics geo.js

  • BimCraft
  64-bit

• Ray tracing of a room

  The energy arriving at a spherical receiver from rays sent out evenly from the source and reflected round the room.

  e[⌊t × sr⌋] += E × chord ÷ (4⁄3·π·r³) × exp(−m·c·t); after a hit E = E × (1 − α)

  Geometric room acoustics geo.js

  • BimCraft
  64-bit

• Reverberation and clarity from an echogram

  EDT, T20, T30, C50, C80, D50 and Ts per octave band, from the energy in each time bin.

  amplitude[i] = √e[i]; the measures are taken from the amplitudes

  Geometric room acoustics geo.js

  • BimCraft
  32-bit in part

• Vertices of one batch

  The positions, normals and texture coordinates of the triangles a batch shows.

  normal = (x, y, z) ÷ √(x² + y² + z²); uv = planar meters ÷ tile size

  Model for rendering (glTF export) glb-bim.js

  • BimCraft
  32-bit in part

• Bounds of a mesh

  The smallest and largest coordinate of a mesh, which glTF requires beside its positions.

  Model for rendering (glTF export) glb-bim.js

  • BimCraft
  32-bit in part

• Placement of a batch

  The world matrix written on each node.

  Model for rendering (glTF export) glb-bim.js

  • BimCraft
  64-bit

• Lamps

  Each lamp as a glTF light: its intensity, cone and position.

  candela = lumens ÷ 4π; outer cone = angle × π ÷ 360, held between 0.02 and π ÷ 2; inner = 0.8 × outer

  Model for rendering (glTF export) glb-bim.js

  • BimCraft
  64-bit

• Direction of a spot

  The rotation that points a spot light along its direction.

  q = (a × d, 1 + a · d) ÷ |…|, a = (0, 0, −1)

  Model for rendering (glTF export) glb-bim.js

  • BimCraft
  64-bit

• Placing each vertex of an element

  Moves an element's vertices and normals from its own axes into the scene with its placement matrix.

  p′ = M × p; n′ = (rotation part of M) × n ÷ |…|

  Measuring on the IFC view's mesh ifc-model.js

  • BimCraft
  32-bit in part

• Storing the mesh

  Turns the collected positions, normals, indices and element runs of a batch into typed arrays.

  Measuring on the IFC view's mesh ifc-model.js

  • BimCraft
  32-bit in part

• Area of a picked flat face

  The flat face a picked triangle belongs to and its area.

  area = Σ |(b − a) × (c − a)| ÷ 2 over the triangles in the picked plane

  Measuring on the IFC view's mesh measure.js

  • BimCraft
  32-bit in part

• Distance between two picked points

  The straight-line distance Measure reports.

  d = √(Δx² + Δy² + Δz²)

  Measuring on the IFC view's mesh measure.js

  • BimCraft
  32-bit in part

• Distance split along the IFC axes

  The measured difference as ΔX, ΔY and ΔZ in the file's Z-up axes.

  ΔX = Δx; ΔY = −Δz; ΔZ = Δy (the viewer is Y up)

  Measuring on the IFC view's mesh measure.js

  • BimCraft
  32-bit in part

• Room floor area and volume from its shape

  The floor area and volume of a space measured from its triangles, used when the file states neither.

  area = Σ −n_y ÷ 2 over triangles with n_y ÷ |n| < −0.5; volume = |Σ a · (b × c) ÷ 6|

  Measuring on the IFC view's mesh ifc-qto.js

  • BimCraft
  32-bit in part

• Room area and volume in the spaces schedule

  Chooses the file's stated value or the measured one for each room, and rounds the measured one.

  measured value kept as Number(value.toFixed(4))

  Measuring on the IFC view's mesh ifc-qto.js

  • BimCraft
  32-bit in part

• Bounding box of each element in a shared frame

  The box and triangle count of every element of a model, in coordinates both versions share.

  Measuring on the IFC view's mesh ifc-compare.js

  • BimCraft
  32-bit in part

• How far an element moved, and whether its shape changed

  The move of an element between two versions and a yes or no on a change of size or triangle count.

  moved = |center of box B − center of box A|, reported when > tolerance; reshaped when a box side differs by > tolerance

  Measuring on the IFC view's mesh ifc-compare.js

  • BimCraft
  32-bit in part

• Bounding box of chosen elements

  The smallest box round the vertices of the chosen elements.

  Measuring on the IFC view's mesh ifc-vis.js

  • BimCraft
  32-bit in part

• Wall faces in plan

  The two long faces of each wall as plan segments in model millimeters, with a normal pointing away from the wall.

  Wall faces and plan frames from element meshes ifc-place.js

  • BimCraft
  32-bit in part