Calculations

Calculations

• 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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• Is the item big enough

  Refuses a hatch with fewer than 3 corners or under 100 mm², and a line under 10 mm.

  L = Σ √(Δx² + Δy²); refuse when L < 10 mm or |area| < 100 mm²

  Drafting lines and hatch regions drafting.js

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• Move drafting items

  Every point of the picked items moved by one offset.

  (x, y) → (x + dx, y + dy)

  Drafting lines and hatch regions drafting.js

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• Is a point inside the region

  Whether a point lies inside the outline and outside its holes.

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

  Drafting lines and hatch regions drafting.js

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• Clip a stroke to the region

  The pieces of a straight stroke that lie inside the region.

  t = ((c − a) × e) ÷ (d × e), u = ((c − a) × d) ÷ (d × e); keep 0 < t < 1, 0 ≤ u ≤ 1

  Drafting lines and hatch regions drafting.js

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• Strokes of a hatch pattern

  The lines, dots or zigzags of a pattern inside a region, at its scale.

  line k of a family: n · p = ⌊(n_min − offset) ÷ gap⌋ × gap + k × gap, gap = pattern gap × scale

  Drafting lines and hatch regions drafting.js

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• Pattern scale

  The scale of a hatch pattern as it is kept.

  scale = min(50, max(0.1, v)), or 1 when v is not a positive number

  Drafting lines and hatch regions drafting.js

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• A typed point

  The next point of a drafting line from typed coordinates, a typed offset, a typed length and angle, or a typed length along the pointer's direction.

  polar: (x + L·cos(a·π ÷ 180), y + L·sin(a·π ÷ 180)); length only: last + L × (to − last) ÷ |to − last|

  Drafting lines and hatch regions drafting-ui.js

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• 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

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• 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

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• 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

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• 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

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• 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

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• Segments in an arc

  How many straight segments stand in for an arc.

  n = max(8, min(128, ⌈|sweep| ÷ 2π × 72⌉))

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

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• Points along an arc or circle

  An arc or circle as points on it.

  pᵢ = (cx + r·cos aᵢ, cy + r·sin aᵢ), aᵢ = a₀ ± sweep × i ÷ n

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

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• Points along an ellipse

  An ellipse or elliptical arc as points on it.

  p(t) = c + R(rot) · (L·cos t, L·ratio·sin t), L = |major axis|, rot = atan2(my, mx)

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

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• Polyline with bulge arcs

  A polyline whose segments may be arcs, as points.

  θ = 4·atan(bulge); r = chord ÷ (2·sin(θ ÷ 2)); center = chord middle + normal × r·cos(θ ÷ 2)

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

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• Points along a spline

  A spline as points: its fit points, or samples of the B-spline from its control points.

  de Boor: dⱼ = (1 − a)·dⱼ₋₁ + a·dⱼ, a = (u − kᵢ) ÷ (kᵢ₊ₚ₋ᵣ₊₁ − kᵢ); point = (Σ w·P) ÷ Σ w

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

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• What a sheet viewport looks at

  The model point at the middle of a viewport on a sheet.

  vx = target_x + cos(tw)·cx + sin(tw)·cy; vy = target_y − sin(tw)·cx + cos(tw)·cy

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

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