Calculations

Calculations

• Grand total

  Runs the whole calculation and states the total cost.

  grand = scheduled + unscheduled

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Rates read from TakeoffCraft

  Turns TakeoffCraft's stored rates into prices per unit.

  rate = stored whole number ÷ 10000

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Costs in the CSV export

  The amounts written to the exported table.

  Costs on the schedule cost5d.js

  • BimCraft
  64-bit

• Rounding of stored map values

  Rounds an easting, northing or height before it is stored.

  round(v × 10⁶) ÷ 10⁶

  Placing a model on the map crs-georef.js

  • BimCraft
  64-bit

• Latitude and longitude of a grid point

  The longitude and latitude of an easting and northing in the chosen system.

  Placing a model on the map crs-georef.js

  • BimCraft
  64-bit

• Map conversion as a matrix

  The matrix that takes model coordinates to map coordinates.

  x' = s (a x − b y) + E; y' = s (b x + a y) + N; z' = s z + H, with (a, b) the normalized X axis

  Placing a model on the map crs-georef.js

  • BimCraft
  64-bit

• Rotation of the model on the grid

  The angle of the model's X axis from grid east, in degrees.

  θ = atan2(ordinate, abscissa) × 180 ÷ π

  Placing a model on the map crs-georef.js

  • BimCraft
  64-bit

• True north in the model

  The direction of true north in the model's own X and Y.

  g = grid direction of a 0.0001° step north; true north = (cos(g − m), sin(g − m)), m the model's rotation

  Placing a model on the map crs-georef.js

  • BimCraft
  64-bit

• Map conversion moved to another system

  The same place on the earth described in a different coordinate system: new origin, rotation and scale.

  origin' = T(E, N); p₁ = T(origin + 10 m along the X axis); axis' = (p₁ − origin') ÷ D; scale' = scale × D ÷ step

  Placing a model on the map crs-georef.js

  • BimCraft
  64-bit

• Illuminance of the whole sky

  The horizontal illuminance of an unobstructed overcast sky, which every component is divided by.

  E_h = 7π ÷ 9, in units of the zenith luminance

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Overcast sky integrated in altitude

  The light a vertical plane gets from the sky between the horizon and an altitude.

  F(θ) = (θ ÷ 2 + sin 2θ ÷ 4) ÷ 3 + (2 ÷ 9)(1 − cos³θ)

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Overcast sky luminance

  The sky's brightness at an altitude, relative to the zenith.

  L(θ) = (1 + 2 sin θ) ÷ 3

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Hidden altitude intervals joined

  Joins the altitude ranges hidden by separate objects into one list.

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• What hides the sky in one direction

  The altitudes hidden along one level direction from a window.

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Sky profile of a window

  For each direction across the window's front, the altitudes that are hidden.

  φᵢ = −90° + step ÷ 2 + i × step, i = 0 … 180 ÷ step − 1

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Weight of an azimuth band

  How much a band of directions counts, by how squarely it faces the window.

  w = sin(φ + step ÷ 2) − sin(φ − step ÷ 2)

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Vertical sky component

  The share of the unobstructed sky's light that reaches the window, in percent.

  VSC = 100 × Σ over bands of w × Σ over visible intervals of (F(b) − F(a)) ÷ (7π ÷ 9)

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Share of a uniform sky seen

  The share of a uniform sky's light a window still gets, used for diffuse sun gain.

  fraction = Σ w × Σ (G(b) − G(a)) ÷ Σ w × G(π ÷ 2), G(θ) = θ ÷ 2 + sin 2θ ÷ 4

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Angle of obstruction

  The altitude of the top of whatever hides the horizon square to the window.

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Is a ray hidden

  Decides whether a ray from a point through the window meets sky or an obstruction.

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Floor of a room

  Picks the floor triangles out of a room's shell.

  floor when |n_z| > 0.7 |n| and the triangle's mean height is below the shell's middle

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Is a grid point over the floor

  Tests a plan point against one floor triangle.

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Grid of points in a room

  The points at working-plane height where the daylight factor is worked out.

  spacing = max(0.25, ceil(√(area ÷ max) × 20) ÷ 20) m; points at lo + s ÷ 2, then every s

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Window opening as a rectangle

  The rectangle that stands for a window's opening.

  k = √(area ÷ (width × height)); half sizes = k × width ÷ 2 and k × height ÷ 2

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Sky and externally reflected components at a point

  The light a point gets through one window straight from the sky and from obstructions, in percent.

  SC = 100 ÷ E_h × Σ over patches of L(θ) sin θ × dA cos ω ÷ r²

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• C factor by angle of obstruction

  The coefficient C of the internally reflected component.

  straight lines between table rows at 0°, 10° … 80°

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Internally reflected component

  The light a room gets by reflection from its own surfaces, in percent.

  IRC = T W ÷ (A (1 − R)) × (C R_fw + 5 R_cw) × M

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Daylight factor on the grid

  The daylight factor at every grid point of a room and its mean, median, minimum, maximum and uniformity.

  DF = (SC + ERC) × T × glazed share × M + IRC; uniformity = min ÷ mean

  Sky view and daylight factor daylight-bim-sky.js

  • BimCraft
  64-bit

• Solar constant

  The sun's irradiance outside the atmosphere at the mean earth–sun distance.

  G_sc = 1367 W/m²

  Sun gain through windows daylight-bim-sky.js

  • BimCraft
  64-bit

• Clear-sky irradiance

  Beam and diffuse irradiance under a clear sky for a day of the year and a sun height.

  τ_b = a₀ + a₁ e^(−k ÷ cos θz); G_on = 1367 (1 + 0.033 cos(2π n ÷ 365)); τ_d = 0.271 − 0.294 τ_b

  Sun gain through windows daylight-bim-sky.js

  • BimCraft
  64-bit

• Climate factors for the date

  Picks the row of climate factors that fits the latitude and the month.

  Sun gain through windows daylight-bim-sky.js

  • BimCraft
  64-bit

• Sun gain through one day

  The gain through each window at every time step, each room's peak and when it falls, and the day's energy.

  gain = g × A × (G_bn cos i unless shaded + G_dh × 0.5 × sky fraction + (G_bh + G_dh) × ρ × 0.5); kWh = Σ gain × step ÷ 1000

  Sun gain through windows daylight-bim-sky.js

  • BimCraft
  64-bit

• Total blocked angle

  The total of the angle intervals that obstructions hide, with overlaps counted once.

  total = Σ (hiᵢ − loᵢ) over the merged intervals, each clipped to 0°…90°

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Sky angle in one section

  The angle of sky, from the horizon to straight up, that is still visible from a point on the window's outer face.

  cut point = a + t · (b − a), t = d_a ÷ (d_a − d_b); angle = atan2(v, u); θ = 90° − blocked total

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Mean reflectance of the room

  The area-weighted mean reflectance of floor, walls, ceiling and glass.

  R = (A_floor·ρ_floor + A_wall·ρ_wall + A_ceiling·ρ_ceiling + A_glass·0.1) ÷ (A_floor + A_wall + A_ceiling + A_glass)

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Average daylight factor

  The room's average daylight factor in percent.

  ADF = Σ (T × A_g × θ × M) ÷ (A × (1 − R²))

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Triangle area and tilt

  The area of one triangle of a room's shell and how far its normal points up or down.

  area = |AB × AC| ÷ 2; nz = (AB × AC)_z ÷ |AB × AC|

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Closest point of a triangle

  The point of a triangle nearest to a given point, used to find which room a window belongs to.

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Direction a window faces

  The level direction across which a window's triangles are thinnest.

  width(α) = max(x·cos α + y·sin α) − min(x·cos α + y·sin α); the α with the least width

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Floor, wall and ceiling areas of a room

  The inside surface areas of a room from the triangles of its space.

  A = A_floor + A_wall + A_ceiling

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Window area

  The area of one window and the point on its outer face that the sky angle is measured from.

  area = OverallWidth × k × OverallHeight × k, k = file length unit in mm ÷ 1000

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Sky angle of a window

  The window's sky angle: the mean of five sections across its width.

  θ = (θ₁ + θ₂ + θ₃ + θ₄ + θ₅) ÷ 5, at 10, 30, 50, 70 and 90 % of the width

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Glass taken out of the walls

  The glass area of a room and the wall area left beside it.

  A_glass = min(Σ window areas, A_wall); A_wall = A_wall − A_glass

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Result per room

  Each room's mean reflectance, glazed areas, daylight factor and guidance band for the inputs given.

  A_g = window area × glazed share; band: below 2 % low, below 5 % mid, else high

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Daylight table as CSV

  The rooms' results written as a CSV file.

  Average daylight factor of rooms daylight-bim.js

  • BimCraft
  64-bit

• Combine two transforms

  The product of two plan transforms, each six numbers.

  [a b c d e f]: x′ = a·x + c·y + e, y′ = b·x + d·y + f

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Block insert transform

  Where the content of a block lands: insertion point, rotation, scale, base point and its place in a row and column array.

  M = T(insert) · R(rotation) · S(sx, sy) · T(−base + (col × colSpacing ÷ sx, row × rowSpacing ÷ sy))

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Tilted block seen from above

  The plan transform of an insert whose extrusion direction is neither up nor down.

  Ax = unit(Wz × N) (or Wy × N when |Nx| and |Ny| < 1/64); Ay = unit(N × Ax); offset = N·z

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Downward extrusion

  Mirrors an entity in X when its extrusion direction points down.

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Transform points

  A list of points moved through a transform into the space's coordinates.

  x′ = a·x + c·y + e; y′ = b·x + d·y + f

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit