Calculations

Calculations

• Frame of an interior elevation

  The width and height of the wall shown, and how deep the view looks.

  x₀, x₁ = min, max of p·right; depth from the room's middle to max(p·dir) + 50 mm

  Interior elevations and their dimensions comforts-views.js

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• Dimension values on elevations and sections

  The widths, heights and level spacings written on a view.

  width = x₁ − x₀; height = y₁ − y₀; level spacing = yᵢ₊₁ − yᵢ

  Interior elevations and their dimensions comforts-views.js

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• Where a door or window is tagged

  The plan point, the height range and the outward side of each opening.

  middle station = offset + width ÷ 2; top = sill + height

  Interior elevations and their dimensions comforts-views.js

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• Views placed at scale on the sheet

  Takes view millimeters to paper millimeters at the sheet's scale.

  k = 1 ÷ scale ratio; paper = origin + view × k

  Interior elevations and their dimensions comforts-views.js

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• Where a drag puts an item

  The position and turn saved when a placed item is dragged or turned by its grip.

  turn = round(atan2(dy, dx) × 180 ÷ π ÷ step) × step, step 15° or 1° with Shift

  Interior elevations and their dimensions comforts-ui.js

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• Room height on the interior elevations

  The floor-to-floor height the elevations are framed to, and the height of each tagged item.

  height = next level − this level, else the level's own height

  Interior elevations and their dimensions comforts-ui.js

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• Project origin and survey point

  Where the site's survey point is in the file's coordinates, with its elevation and map grid position.

  survey point = site placement origin × file unit in mm; elevation in m = RefElevation × unit ÷ 1000

  Coordinate readouts and survey point coords.js

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• Level a height is on

  Picks the level whose floor is at or just below a height.

  the highest level with elevation ≤ z + 1 mm

  Coordinate readouts and survey point coords.js

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• Foot and US survey foot

  The two sizes of foot a map's unit is compared with.

  ft = 0.3048 m; US ft = 1200 ÷ 3937 m

  Coordinate readouts and survey point coords.js

  • BimCraft
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• Map grid coordinates as text

  A point's eastings and northings in the map's own unit.

  value = meters ÷ map unit in meters, written with 3 decimals

  Coordinate readouts and survey point coords.js

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• Height above the level

  The lines of a readout: the level and the height above its floor, X and Y from the project origin, Z, and the map position.

  height above the level = z − level elevation

  Coordinate readouts and survey point coords.js

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• Plan point to file coordinates

  A point in a storey's plan, in the file's coordinates.

  q = M (x, y, 0)

  Coordinate readouts and survey point coords.js

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• File coordinates to plan point

  A point in the file's coordinates, in a storey's plan.

  p = M⁻¹ q

  Coordinate readouts and survey point coords.js

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• File coordinates to the 3D view

  Where a point of the file sits in the 3D view, to draw the origin and survey markers.

  (x, y, z) × unit → (x, z, −y) → C → placement

  Coordinate readouts and survey point coords.js

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• Unit factors for priced quantities

  The size of each pricing unit in m, m² or m³.

  1 yd³ = 0.764554858 m³; 1 ft³ = 0.0283168466 m³; 1 ft² = 0.09290304 m²; 1 ft = 0.3048 m

  Costs on the schedule cost5d.js

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• Dollars to whole cents

  Rounds an amount to a whole number of cents.

  cents = round(dollars × 100)

  Costs on the schedule cost5d.js

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• Whole cents to dollars

  The amount reported, in dollars.

  dollars = round(cents) ÷ 100

  Costs on the schedule cost5d.js

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• Quantity in the price's unit

  An element's volume, area, length, weight or count in the unit its price is per.

  qty = quantity ÷ unit factor; weight = volume × density

  Costs on the schedule cost5d.js

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• Cost of each element

  The material and labor cost of every element, and the total.

  line = round(qty × (1 + waste) × material rate × 100) + round(qty × labor rate × 100) cents

  Costs on the schedule cost5d.js

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• Cost of each scheduled task

  Adds up the cost of a task's elements, sharing an element that is in several tasks.

  task cents = round(Σ element cents ÷ n), n = the tasks that hold the element

  Costs on the schedule cost5d.js

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• Spending profile of a task

  The weight each day of a task gets: even, front-loaded, back-loaded or bell-shaped.

  even 1; front D − i; back i + 1; bell sin(π (i + 0.5) ÷ D)

  Costs on the schedule cost5d.js

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• A task's cost per day

  Divides a task's cost over its days in whole cents.

  dayᵢ = floor(cents × wᵢ ÷ W), then one more cent to the days with the largest remainders

  Costs on the schedule cost5d.js

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• Cash flow curve

  The cost per day, week or month and the running total.

  period cost = Σ day cents; cumulative = running sum

  Costs on the schedule cost5d.js

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• Planned, built and earned value on a day

  What the schedule plans to have spent by a day, what is built, running and remaining, and the earned value from typed progress.

  earned = Σ task cents × progress, progress clamped to 0…1

  Costs on the schedule cost5d.js

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• Grand total

  Runs the whole calculation and states the total cost.

  grand = scheduled + unscheduled

  Costs on the schedule cost5d.js

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• Rates read from TakeoffCraft

  Turns TakeoffCraft's stored rates into prices per unit.

  rate = stored whole number ÷ 10000

  Costs on the schedule cost5d.js

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• Costs in the CSV export

  The amounts written to the exported table.

  Costs on the schedule cost5d.js

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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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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