Calculations

Calculations

• Is a point in the room

  Whether a point lies inside the room's outline.

  even-odd count of edges crossed by a ray toward +x

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Does a piece fit in the room

  Whether a rectangle lies inside the room and outside its holes.

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Which way the outline runs

  The signed area of the room's outline, used to turn it counter-clockwise.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Zone kept clear at a door

  The rectangle round a door where nothing is placed.

  width = door width + 300 mm; depth = one door width on each side of the wall

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• A piece against a wall

  The first free place for a piece along a wall, with its back on the wall.

  t = w ÷ 2 + side, then every 100 mm; (x, y) = wall start + direction × t + inward normal × depth; kept: round(x), round(y), rotation to 0.001°

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• A piece in the middle of the room

  The first free place for a free-standing piece, starting at the middle of the room.

  middle of the outline's box, then offsets of k × 150 mm (k = 1…20) along ±x and ±y, at the longest wall's angle and at 90° to it

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Footprint of a placed piece

  The four plan corners of a piece from its stored position.

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• 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

• Map conversion as a matrix

  The transform from model units to map units, from the conversion's numbers.

  (ax, ay) = (XAxisAbscissa, XAxisOrdinate) ÷ |…|; E = Eastings + s·(ax·x − ay·y); N = Northings + s·(ay·x + ax·y); H = Height + s·z

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Meters per map unit

  The size of the map's length unit in meters, from its name.

  US survey foot = 1200 ÷ 3937 m; foot = 0.3048 m; otherwise 1

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Length unit of the map system

  Finds or makes the IFC unit for the map's coordinates.

  wanted mm per unit: m 1000, ft 304.8, US survey ft 1200 ÷ 3937 × 1000; match when |unit − wanted| < 10⁻⁹ × wanted

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Latitude and longitude as degrees, minutes, seconds

  An angle in decimal degrees split into the four whole numbers the IFC site stores.

  d = ⌊|deg|⌋; m = ⌊(|deg| − d) × 60⌋; s = ⌊rest × 60⌋; millionths = round((rest − s) × 10⁶)

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• Map conversion written to the file

  The six conversion numbers written into IfcMapConversion, new or in place.

  Georeference written to the IFC file georef-model.js

  • BimCraft
  64-bit

• 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

• Room depth at each time sample

  The water depth in every room at each time step, from the outside level and the openings the water has passed.

  level(t) = linear between hydrograph points; depth = max(0, level − floor) for a room the water reaches

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Maximum depth, first wet time and wet duration

  For each room: the deepest water, the first sample time it was wet and how long it stayed wet.

  maxDepth = round(max × 1000) ÷ 1000; wetFor = (number of wet samples) × dt

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Hydrostatic push on a wall

  The force of standing water on one meter of wall, from the depth.

  F = ½ × ρ × g × d² (ρ = 1000 kg/m³, g = 9.80665 m/s²)

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Wind force, shear and moment by story

  The wind force on each story and the shear and overturning moment summed from the top story down.

  V = V10 × (max(z, 5) ÷ 10)^α; q = ½ ρ V²; force = q × G × (Cp,w + Cp,l) × width × h; shear = Σ force above; moment = Σ force × z

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Eigenvalues of a symmetric matrix

  The eigenvalues and eigenvectors behind the building's periods and mode shapes.

  t = sign(θ) ÷ (|θ| + √(θ² + 1)), θ = (a_qq − a_pp) ÷ (2 a_pq); c = 1 ÷ √(t² + 1); s = t × c

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Stiffness matrix of a shear building

  Builds the tridiagonal floor stiffness matrix from one stiffness per story.

  K[i][i] = k[i] + k[i+1]; K[i][i+1] = K[i+1][i] = −k[i+1]

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Periods, mode shapes and effective mass

  The natural periods, the mode shapes scaled to 1 at the top floor, the participation factor and the effective mass of each mode.

  S = K[i][j] ÷ √(mᵢ mⱼ); ω = √max(λ, 0); T = 2π ÷ ω; Γ = Σ m φ ÷ Σ m φ²; effective mass = (Σ m φ)² ÷ Σ m φ²

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Story stiffness for a chosen first period

  The single story stiffness that gives the building the first period the person typed.

  k = (2π ÷ T₁)² ÷ ω₁², ω₁ = first frequency with k = 1

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Made ground acceleration record

  A Ricker pulse or filtered noise record scaled to the peak ground acceleration asked for.

  Ricker: a = (1 − 2x²) × e^(−x²), x = π f (t − 1.5 ÷ f); then a × pga ÷ max|a|

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Newmark time stepping

  The floor displacements, velocities and accelerations at every time step of the record.

  K* = K + c₁ M + c₂ C, c₁ = 1 ÷ (β Δt²), c₂ = γ ÷ (β Δt), β = 1/4, γ = 1/2; C = a₀ M + a₁ K

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Peak drift, floor acceleration, base shear and roof displacement

  The largest values over the run that the person reads.

  drift = uᵢ − uᵢ₋₁; floor acceleration = ü + a_g; base shear = k₀ u₁ (shear building) or Σ m (ü + a_g) (full matrix)

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Sway under static floor forces

  Floor displacements and story drifts under static sideways forces, used for the wind sway.

  shear building: driftᵢ = (Σ F above) ÷ kᵢ, u = running sum of drifts; full matrix: K u = F

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit

• Floor heights from the frame's nodes

  Groups the frame's nodes into floors by height and takes the lowest group as the base.

  nodes whose heights differ by ≤ tol join one group; floor height = mean of the group

  Earthquake time-history of a building hazard-frame.js

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• Inverse of the flexibility table

  Turns the floors' flexibility table into their stiffness matrix.

  Earthquake time-history of a building hazard-frame.js

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• Floor stiffness of a frame

  The stiffness the frame gives each floor sideways, and one stiffness per story for the drift check.

  F[i][j] = (mean sideways move of floor i under 1000 N on floor j) ÷ 1000 ÷ 1000; K = F⁻¹; k_story = V ÷ drift under forces ∝ height

  Earthquake time-history of a building hazard-frame.js

  • BimCraft
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• Floor masses from the frame

  The mass on each floor: half of each member's weight at each end, plus a load per square meter over the floor's plan box.

  member mass = ρ × A × L × 1e-9; floor area = (x extent ÷ 1000) × (y extent ÷ 1000); m = max(1, self + area × load)

  Earthquake time-history of a building hazard-frame.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

• Reading a property value

  Turns an IFC property or quantity value into the number or text the index, the totals and the comparison use.

  number kept = round(x × 10⁶) ÷ 10⁶

  Quantity totals and schedules from IFC properties ifc-props.js

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