Calculations

Calculations

• Labor and machine hours

  The labor hours from the count of each cabinet kind, and the machine hours from the number of sheets.

  hours = Σ count × hours per kind + frames × extra; machine = sheets × minutes per sheet ÷ 60

  Cabinet job cost estimate addons/cabinetcraft/lib/estimate.js

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• Subtotal, markup, tax and total

  The totals of the estimate and the cost per cabinet.

  subtotal = Σ amounts; markup = subtotal × rate; tax = (subtotal + markup) × rate; total = subtotal + markup + tax

  Cabinet job cost estimate addons/cabinetcraft/lib/estimate.js

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• A rate read from a shop's table

  Turns one cell of an imported rate table into a number.

  Cabinet job cost estimate addons/cabinetcraft/lib/estimate.js

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• Rate table lines

  Splits each line of a text rate table into a path and a value.

  Cabinet job cost estimate addons/cabinetcraft/lib/estimate.js

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• Rounding to a number of decimals

  Rounds a value to dp decimals, 6 by default.

  round(v, dp) = Math.round(v × 10^dp) ÷ 10^dp

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Cut size of a part

  The size to cut a part so it measures its finished size once the banding is on.

  cut width = width − (t_L1 + t_L2) + premill × banded L edges; cut length = length − (t_W1 + t_W2) + premill × banded W edges

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Pieces and areas per material

  The piece count, finished area and cut area of each material and thickness.

  area = Σ qty × length × width; cut area = Σ qty × cut length × cut width

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Edge banding length

  The length of each banding, the number of edges, and the length with trim waste.

  length = Σ qty × edge; with waste = Σ qty × (edge + waste per edge)

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Rough sheet count

  An estimate of the sheets a material needs, from area only.

  estimate = ⌈round(cut area × (1 + 0.15) ÷ sheet area, 9 decimals)⌉

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Parts handed to nesting

  Each part as a rectangle at its cut size for the nesting engine.

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Cut list CSV numbers

  Writes the cut list as CSV text.

  number cell = round(v, dp), dp = 2 by default

  Cut list sizes, areas and banding lengths addons/cabinetcraft/lib/cutlist/cutlist.js

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• Arcs to chords

  Turns a loop with bulges into points, with each arc as chords no further than the sag from it.

  θ = 4 atan(b); r = chord ÷ (2 sin(|θ| ÷ 2)); steps = ⌈|θ| ÷ (2 acos(1 − min(sag, r) ÷ r))⌉

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Area of a loop with arcs

  The signed area of a closed loop, with each arc's segment included.

  2A = Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ) + Σ sign(θ) r² (|θ| − sin|θ|)

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Area of a part

  A part's area: its outline less its holes.

  area = |A₀| − Σ |Aₖ|

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• A part moved to its place

  Rotates, mirrors and moves a part's loops to their position on the sheet.

  q = (x, y) + R(rot) · (m pₓ, p_y), m = −1 when mirrored; bulge × m

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Turns a part may take

  The rotation angles tried for a part, from its grain and the turn step.

  no grain: rot = k × 2π ÷ n, n = round(360 ÷ step); grain: rot = −g (+ π) ± tolerance

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• A shape on the raster

  Marks every grid cell a part touches.

  cell i = ⌊(x − oₓ) ÷ res⌋; edge cells from the segment's lowest and highest point in each column

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Raster cell size and clearance

  The cell size of the raster, the arc sag, and the number of cells kept clear around each part.

  res = max((h − 2 margin) ÷ 750, 1e-6), at most smallest ÷ 4; sag = min(res ÷ 8, 0.1); grow = ⌈(spacing + 2 sag) ÷ res − 1e-9⌉

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Placed position of a part

  The position of each placed part in sheet coordinates.

  x = margin + gₓ × res − shape origin x; y = margin + g_y × res − shape origin y

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Used length and efficiency

  The length used on each sheet and the share of the sheet area the parts cover.

  used = max x of the placed outlines + margin; efficiency = Σ part area ÷ (sheets × w × h), or ÷ (used × h) on a roll

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Distance between two edges

  The shortest distance between two segments, 0 when they cross.

  0 when the cross-product signs differ on both segments; else min of the four end-point-to-segment distances

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Re-check of a nest

  Checks that no two placed parts overlap or come closer than the spacing, and that all lie inside the margins.

  outside when the bounding box passes a margin by more than eps; overlap when d ≤ eps or one part's first point is inside the other; close when d < gap − eps

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Lines and arcs joined into loops

  Joins separate line and arc pieces into closed loops where their ends meet.

  ends meet when their distance ≤ 1.5 × tol

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Bulge of an arc

  The bulge value of an arc from its sweep in degrees.

  bulge = tan(sweep × π ÷ 180 ÷ 4)

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Flat pattern pieces to loops

  Turns line, arc, circle and polyline pieces of a flat pattern into closed loops with bulges.

  arc end = c + r (cos a, sin a); sweep = (a₁ − a₀) mod 360; circle = two bulges of 1

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Arcs and ellipses read from DXF

  Reads ARC and ELLIPSE entities into pieces or loops.

  ellipse: n = max(8, ⌈sweep ÷ (2π ÷ 96)⌉) points at equal parameter steps

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Joining tolerance for a DXF

  The distance within which loose line and arc ends of a DXF are joined.

  tol = max(1e-6, 1e-7 × largest absolute coordinate)

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Outlines and their holes

  Sorts loops into parts: an outline and the holes directly inside it.

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Numbers written to the DXF

  Formats every coordinate, bulge and text height of the nest DXF.

  text = v.toFixed(6) with trailing zeros removed; |v| < 1e-12 written as 0

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Sheets stacked in the DXF

  The y offset of each sheet in the written DXF.

  offset₀ = 0; offsetₛ₊₁ = offsetₛ − (Hₛ + gap), gap = 0.1 × tallest sheet by default

  Sheet nesting addons/cabinetcraft/lib/nest/nest.js

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• Cross-section of the cables

  The total cross-sectional area of a set of cables.

  area = Σ (π ÷ 4) × od² × n

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Conduit fill

  The percentage of a conduit's inside area the cables take, and whether it is within the limit.

  pct = 100 × used ÷ (π ÷ 4 × id²); free = area × limit ÷ 100 − used

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Smallest conduit that holds the cables

  The first trade size, going up, whose fill is within the limit.

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Cable tray fill

  The fill of a tray by area, or by the sum of cable diameters when the cables lie in one layer.

  area mode: pct = 100 × used ÷ (width × depth); layer mode: pct = 100 × Σ (od × n) ÷ width

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Shortest way through the carriers

  The shortest path between two nodes of the tray and conduit network, and its length.

  Dijkstra: d = dist[u] + segment length × 1000

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Cable length through each run

  For each cable, the runs it passes through and its length in each.

  length in a run = Σ segment length × 1000 over that run's segments on the path

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Cable schedule length

  The length of each cable in the schedule, with slack and an allowance at each end.

  length m = (route mm × (1 + slack) + 2 × ends mm) ÷ 1000, rounded to 0.1

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Cable list read from CSV

  Reads cable tags, outside diameters and counts from a CSV file.

  Conduit and tray fill, cable schedule addons/electrical/lib/mep/carrier.js

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• Numbers read from an IES file

  Splits the numeric part of an IES file into numbers.

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• IES candela values and luminaire size

  Scales the candela table and converts the luminous opening to millimeters.

  cd = value × multiplier × ballast factor; lumens = lamps × lumens per lamp; size mm = value × 304.8 (feet) or × 1000 (meters)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Full set of horizontal planes

  Mirrors the horizontal planes of a symmetric IES file to cover 0 to 360 degrees.

  quadrant: a, 180 − a, 180 + a, 360 − a; bilateral: a, 360 − a

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• EULUMDAT lamp flux and watts

  Adds up the lamp flux and wattage of the lamp sets in an EULUMDAT file.

  lumens = Σ |count| × flux; watts = Σ watts

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• EULUMDAT candela scale

  Turns the file's cd per 1000 lm values into candela.

  cd = value × (lumens ÷ 1000) × (LORL ÷ 100) × conversion factor

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Position in an angle table

  Finds the two table angles on either side of an angle and the fraction between them.

  f = (x − a_lo) ÷ (a_hi − a_lo)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Candela in a direction

  The luminous intensity at a vertical and horizontal angle, interpolated from the table.

  I = (1 − f_h) (I₀₀ (1 − f_v) + I₀₁ f_v) + f_h (I₁₀ (1 − f_v) + I₁₁ f_v)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Luminaire axes

  The nadir, C0 and C90 directions of an aimed and rotated luminaire.

  n = aim ÷ |aim|; r₀ = axis − (axis·n) n, normalized; r = r₀ cos t + (n × r₀) sin t

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Illuminance at a point

  The direct illuminance in lux at a point on a surface from all luminaires.

  E = LLF × Σ I(γ, C) × scale × cos θ ÷ d², d in meters

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Calculation grid

  The points the illuminance is computed at: cell centers inside the area at the working height.

  nₓ = max(1, round(width ÷ spacing)); x = x₀ + (width ÷ nₓ) × (i + 0.5)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Minimum, average, maximum and uniformity

  The statistics of the grid values.

  avg = Σ E ÷ n; uniformity = min ÷ avg; min ÷ max

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Area and lighting power density

  The area in square meters, the total lumens and watts, and the watts per square meter.

  area m² = |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)| ÷ 2e6; LPD = watts ÷ area

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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