Calculations

Calculations

• Arc move length

  The length of a G2 or G3 move in the XY plane, with any Z change.

  r = |start − center|; sweep = a₁ − a₀ wrapped to the move's direction; len = √((r × |sweep|)² + Δz²)

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Arc move extent

  The bounding box of an arc move.

  extent = end points ∪ {center + r × (cos q, sin q)} for q = 0°, 90°, 180°, 270° inside the sweep

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Straight move length

  The length and extent of a straight move.

  len = √(Δx² + Δy² + Δz²)

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Extent of the whole program

  The smallest and largest X, Y and Z any move reaches.

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Total cutting and rapid length

  The summed length of the cutting moves and of the rapid moves.

  cutLen = Σ len over cutting moves; rapidLen = Σ len over rapids

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Deepest cut and cut through the stock

  The lowest Z of any cutting move and how far it goes below the bottom of the sheet.

  deepest = min z; through = max(0, −deepest − thickness)

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Cutting and rapid time

  The minutes the cutting moves and the rapids take at their feed rates.

  minutesCut = Σ len ÷ feed; minutesRapid = rapidLen ÷ rapid rate

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Hole edge distance

  How close the rim of each face hole comes to the edge of its panel.

  e = min(x − r, L − x − r, y − r, W − y − r), r = d ÷ 2

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Rounding of reported values

  Rounds a value of the report to 3 decimals.

  r3(v) = round(v × 1000) ÷ 1000

  G-code dry run and hole check addons/cabinetcraft/lib/dryrun.js

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• Amount of one estimate row

  The amount of a row from its quantity and rate.

  amount = round(qty × rate × 100) ÷ 100; shown qty = round(qty × 1000) ÷ 1000

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

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• Price of one sheet

  The price of a sheet of the job's size from the price of the stock sheet.

  rate = round(base × (w × h × k²) ÷ (2440 × 1220), 2 decimals), k = 25.4 for an inch job

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

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• Number of sheets

  How many sheets of a material the job needs.

  nested: sheets used; else n = max(1, ⌈cut area × 1.15 ÷ (w × h)⌉)

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

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• Edge banding length priced

  The meters of each edge banding, with waste, and its rate.

  meters = length ÷ 1000 × k × (1 + waste), k = 25.4 for an inch job

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

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• Frame stock priced

  The price per meter of face-frame stock scaled from a 38 × 19 mm board, and the meters needed.

  rate = base × (width ÷ 38) × (thickness ÷ 19), in mm; meters = length ÷ 1000 × k × 1.1

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

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• Countertop priced

  The price of each countertop from its length and width.

  amount = (length ÷ 1000 × k) × round(base × (width × k ÷ 600), 2 decimals)

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

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• 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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