Calculations

Calculations

• Is a ray to the sun blocked

  Whether the line from a point toward the sun meets a triangle of the model.

  det = e₁ · (d × e₂); u = (t · (d × e₂)) ÷ det; v = (d · (t × e₁)) ÷ det; hit if 0 ≤ u, 0 ≤ v, u + v ≤ 1 and distance > tMin

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Sample points on the modules

  The points on each module from which rays are cast.

  p = bilinear blend of the four corners at ((a + ½) ÷ k, (b + ½) ÷ k) + normal × lift

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Shade fraction by month and hour

  The share of the sample points in shadow at each of 12 × 24 sun positions.

  frac = shaded points ÷ points

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Beam light lost to shadows

  The share of the direct sunlight the array loses to shading, over the year or chosen months.

  loss = Σ beam × frac ÷ Σ beam

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Module voltage at a temperature

  The open-circuit voltage of a module at a cell temperature.

  V(T) = V × (1 + β × (T − 25))

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• Longest and shortest string

  The most and the fewest modules a string may have.

  nMax = min(⌊V_limit ÷ (Voc,cold × f) + 1e-9⌋, ⌊MPPT max ÷ Vmp,cold + 1e-9⌋); nMin = ⌈MPPT min ÷ Vmp,hot − 1e-9⌉

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• String length and number of strings

  The string length inside the window that leaves the fewest modules over.

  count = ⌊modules ÷ n⌋; left = modules − count × n

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  Exact

• String voltage checks

  The string's cold and hot voltages against the inverter's and the system's limits.

  V_string = round(n × round(V_module, 2 decimals), 2 decimals)

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• Strings per inverter input

  How many strings one input can carry by its current limits, and how many inputs are needed.

  per input = min(⌊I_dc max ÷ Imp + 1e-9⌋, ⌊I_sc max ÷ Isc + 1e-9⌋); inputs needed = ⌈count ÷ per input⌉

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• DC to AC ratio

  The array's peak power against the inverter's AC rating.

  kWp = n × count × Wp ÷ 1000; DC ÷ AC = kWp ÷ (P_ac × inverters)

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• Cell temperature

  The temperature of the cells from the air temperature and the light on the module.

  T_cell = T_amb + (NOCT − 20) ÷ 800 × G

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Module DC power

  The power of one module at a given irradiance and cell temperature.

  P = Wp × G ÷ 1000 × (1 + γ × (T_cell − 25))

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Loss chain

  The share of the DC energy left after soiling, mismatch, wiring, downtime and the inverter.

  chain = (1 − soiling) × (1 − mismatch) × (1 − wiring) × (1 − availability) × inverter efficiency

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Power in one hour

  The light on the array, the cell temperature and the DC and AC power for one hour of a month's representative day.

  G = beam × (1 − shade) + sky + ground; P = n × max(0, module power); AC before clipping = P ÷ 1000 × chain

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Monthly figures

  A month's light, shade loss and DC energy from its representative day.

  month = day × days in month; shade loss % = (unshaded − shaded) ÷ unshaded × 100

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Inverter clipping and monthly AC energy

  The AC energy of each month after the inverter's rating limits the hourly power.

  scale = P_ac ÷ Σ P when Σ P > P_ac; month AC = Σₕ P × scale × days, rounded to 0.1 kWh

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Annual energy, specific yield and performance ratio of an array

  An array's yearly DC and AC energy, kWh per kWp and performance ratio.

  AC = Σ rounded months; specific yield = AC ÷ kWp; PR = AC ÷ (kWp × POA)

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Plant totals

  The energy, specific yield, performance ratio, clipping and shade loss of all arrays together.

  PR = Σ AC ÷ Σ(kWp × POA); clipped % = clipped ÷ unclipped × 100

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit

• Stair parameters

  The sizes and counts the stair family is made with.

  Width, Height, Gap = round(v × 100) ÷ 100; Tread, Rise = round(v × 1e4) ÷ 1e4; Rise = Height ÷ Steps

  Stair family from a sketch stair-family.js

  • BimCraft
  64-bit

• Where the stair family is placed

  The insertion point and rotation that put the family on the sketch.

  rot = ((angle mod 360) + 360) mod 360

  Stair family from a sketch stair-family.js

  • BimCraft
  64-bit

• Tag values of an element

  An element's tags as their kinds keep them, lengths in millimeters.

  length in mm = round(value × unitMm × 1e6) ÷ 1e6

  Length tags and tag schedules tags.js

  • BimCraft
  64-bit

• Tag value written to the file

  A tag as the IFC property that holds it.

  stored length = round(u(value) × 1e6) ÷ 1e6

  Length tags and tag schedules tags.js

  • BimCraft
  64-bit

• Schedule rows and groups

  The rows of a tag schedule and the groups they fall in.

  length column = round(value × unitMm × 1e6) ÷ 1e6

  Length tags and tag schedules tags.js

  • BimCraft
  64-bit

• Mesh points of an element

  The vertices of each element as the USD file stores them.

  (x′, y′, z′) = P · (x, y, z, 1); stored as (x′, −z′, y′)

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  32-bit in part

• Inverse of a placement

  The matrix that undoes a model's placement.

  R⁻¹ = Rᵀ ÷ s², s² = m₀² + m₁² + m₂²; t⁻¹ = −R⁻¹ · t

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  64-bit

• Site transform back to the file's coordinates

  The transform on each Site that returns the exported points to the IFC file's own coordinates.

  toFile = A · (P · C)⁻¹ · A⁻¹

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  64-bit

• Storey elevation in meters

  Each storey's elevation as an attribute of the USD file.

  elevation in m = elevation × (mm per file unit ÷ 1000)

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  64-bit

• Inverse of a placement (hand-off)

  The matrix that undoes a model's placement, for the render hand-off.

  R⁻¹ = Rᵀ ÷ s²; t⁻¹ = −R⁻¹ · t

  USD export and render hand-off handoff-bim.js

  • BimCraft
  64-bit

• Viewer scene to the USD stage

  The transform that takes camera, sun and lamp positions from the viewer's scene to the exported file's world.

  toStage = A · (P · C)⁻¹; A alone when the model has no coordination matrix

  USD export and render hand-off handoff-bim.js

  • BimCraft
  64-bit

• Sizes a spec allows

  The pipe sizes between the spec's smallest and largest.

  min − 1e-9 ≤ nominal ≤ max + 1e-9

  Pipe spec rules addons/plant/lib/spec.js

  • BimCraft
  64-bit

• How a branch is made

  Whether a branch on a header is a tee, a reducing tee or a stub-in.

  ratio = branch ÷ header; rule = first with ratio ≤ limit + 1e-9

  Pipe spec rules addons/plant/lib/spec.js

  • BimCraft
  64-bit

• Bend radius of a spec

  The center-line radius of the spec's elbows for a size, in inches.

  short: max(nominal size, outside diameter); long: the table's radius

  Pipe spec rules addons/plant/lib/spec.js

  • BimCraft
  64-bit

• Adding tile results to the picture

  The sums of red, green, blue and sample count of every pixel after a pass.

  out[pixel] += tile[pixel]

  Rendered picture: sample sums and color tables compute/cpu-render.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Mean radiance of each pixel

  The picture as the average of its samples.

  color = Σ ÷ n

  Rendered picture: sample sums and color tables compute/cpu-render.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Color through a .cube table

  A color after the table's 1D and 3D look-ups.

  x = clamp((r − lo) ÷ (hi − lo)); trilinear: c = c₀ + (c₁ − c₀) × d along each axis in turn

  Rendered picture: sample sums and color tables exr/cube.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Table rows read from a .cube file

  The entries of a color table as they are held in memory.

  Rendered picture: sample sums and color tables exr/cube.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Numbers written to a .cube file

  A table entry as text in a saved color table.

  text = Number(v.toPrecision(7))

  Rendered picture: sample sums and color tables exr/cube.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Starter door sizes

  Width and height of each starter door type in millimeters.

  width = inches × 25.4

  Starter door and window sizes opening-types.js

  • BimCraft
  64-bit

• Starter window sizes

  Width, height and sill height of each starter window type in millimeters.

  size = inches × 25.4

  Starter door and window sizes opening-types.js

  • BimCraft
  64-bit

• Reading time of a line

  How long a spoken line takes, for placing the next one.

  max(2, round(words ÷ 2.5, 1 decimal))

  Narration cue times narration.js

  • BimCraft
  64-bit

• Cue times from a script

  The start time of each cue from a typed script, and the squeeze when the speech is longer than the walk.

  t = round(min × 60 + s, 1 decimal); squeezed t = round(t × duration ÷ end, 1 decimal)

  Narration cue times narration.js

  • BimCraft
  64-bit

• Subtitle timestamp

  A cue time as an SRT or WebVTT timestamp.

  ms = round(s × 1000); h, m, s, ms by integer division

  Narration cue times narration.js

  • BimCraft
  64-bit

• Stored size, roughness and bump

  The numbers saved with a photo material.

  x = round(clamp(x) × 100) ÷ 100

  Photo material settings photo-materials.js

  • BimCraft
  64-bit

• Width and height in pixels

  The pixel size of the picture.

  h = round(w × vh ÷ vw); k = min(1, MAX ÷ w, MAX ÷ h)

  Rendered picture size render-tools.js

  • BimCraft
  64-bit

• Value and time of one reading

  A single reading of a feed with its time.

  t = tt × 1000 if tt < 1e11, else tt

  Live feed values and times assets-bim-live.js

  • BimCraft
  64-bit

• Outside diameter handed to the router

  The pipe's outside diameter in millimeters for a route between two ports.

  od = od in × 25.4

  Pipe route clearance size addons/plant/main.js

  • BimCraft
  64-bit

• Mesh handed to the solid kernel

  Welds the mesh's corners and passes it to manifold-3d.

  weld grid = 10⁻⁶ × max(Δx, Δy, Δz); positions → Float32Array

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Boolean of two solids

  The difference, union or intersection of two element meshes.

  c = center of a's box; R = (a − c) OP (b − c); result = R + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Element minus all its openings

  Subtracts every opening from an element, one after another.

  A₀ = base − c; Aᵢ = Aᵢ₋₁ − (cutterᵢ − c); result = Aₙ + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Face planes of a convex cutter

  Finds the outward planes of a cutter and decides whether it is convex.

  n = (b − a) × (c − a) ÷ |…|; d = n · a; convex when n · p − d ≤ 10 ε for every corner p

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit