Calculations

Calculations

• 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
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• 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

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• 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

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• 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

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• Hidden altitude intervals joined

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

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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• Is a grid point over the floor

  Tests a plan point against one floor triangle.

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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• Daylight table as CSV

  The rooms' results written as a CSV file.

  Average daylight factor of rooms daylight-bim.js

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• A length as text

  Millimeters as feet and inches to 1/16 inch, or as a decimal number in mm, cm, m, inches or feet.

  sixteenths = round(|mm| ÷ 25.4 × 16); feet = ⌊sixteenths ÷ 192⌋; inches = ⌊rest ÷ 16⌋

  Lengths, areas and volumes as text display-units.js

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• Unit factors

  How many millimeters, square millimeters and cubic millimeters one display unit is.

  in = 25.4 mm; ft = 12 × 25.4 mm; cm = 10 mm; m = 1000 mm

  Lengths, areas and volumes as text display-units.js

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• A coordinate as a number

  A coordinate in millimeters as a number in the display unit, with a fixed count of decimals.

  value = mm ÷ factor, to 1 (mm), 2 (cm, in) or 3 (m, ft) decimals

  Lengths, areas and volumes as text display-units.js

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• A small length to three figures

  A tolerance or a scale per pixel as text with three significant figures.

  value = mm ÷ factor, toPrecision(3)

  Lengths, areas and volumes as text display-units.js

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• An area or a volume as text

  Square or cubic millimeters as text in the matching square or cubic display unit.

  value = v ÷ factor, to the unit's decimals; in² = 25.4² mm²; ft² = (12 × 25.4)² mm²; ft³ = (12 × 25.4)³ mm³

  Lengths, areas and volumes as text display-units.js

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• From meters, square meters and cubic meters

  What calculations give in SI, handed to the same formatters.

  mm = m × 1000; mm² = m² × 10⁶; mm³ = m³ × 10⁹

  Lengths, areas and volumes as text display-units.js

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• Lengths inside a message

  Rewrites plain "N mm" and "N m" inside a message into the display unit.

  Lengths, areas and volumes as text display-units.js

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• Quantities inside a sentence

  Rewrites lengths, areas and volumes inside a calculation's sentence into the display unit.

  Lengths, areas and volumes as text display-units.js

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• A paper size as text

  A sheet's width and height in the display unit.

  value = mm ÷ factor, to 1 (mm, cm), 2 (in) or 3 (m, ft) decimals

  Lengths, areas and volumes as text display-units.js

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• Area of a region

  The signed area of a closed outline, used to refuse a hatch with no area.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Drafting lines and hatch regions drafting.js

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• Points taken from a drawing gesture

  The points of a new line or region, without repeats.

  Drafting lines and hatch regions drafting.js

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• Points read from the file

  A drafting item's points in millimeters, from the IFC polyline that stores them.

  mm = stored coordinate × file length unit in mm

  Drafting lines and hatch regions drafting.js

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• Hatch spacing and angle written to the file

  The IFC fill style of a pattern: one hatching per line family with its spacing and angle.

  spacing = gap × scale in file units; angle = degrees × π ÷ 180 (× 180 ÷ π when the file's angles are degrees)

  Drafting lines and hatch regions drafting.js

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