Calculations

Calculations

• Learned symbol saved and read back

  Stores an accepted symbol in the file and reads it back for a later search.

  byte = round(ink × 255); ink′ = byte ÷ 255

  Automatic count by symbol matching learn.js

  • TakeoffCraft
  32-bit in part

• Same symbol as one already learned

  The normalized correlation of two symbols over their common area.

  ncc = Σ(a − ā)(b − b̄) ÷ √(Σ(a − ā)² · Σ(b − b̄)²)

  Automatic count by symbol matching learn.js

  • TakeoffCraft
  64-bit

• Find placed on the sheet

  Maps a find's pixel box back to sheet coordinates and takes its middle as the count mark's point.

  p = T⁻¹·((x + w ÷ 2) ÷ wt, (y + h ÷ 2) ÷ wt)

  Automatic count by symbol matching takeoffcraft.js

  • TakeoffCraft
  64-bit

• Similarity from two point pairs

  The move, turn and uniform scale that take two points of the old sheet to two points of the new one.

  c + i·s = (b₂ − b₁) ÷ (a₂ − a₁); t = b₁ − (c + i·s)·a₁

  Revision overlay: lining up two sheets and moving the takeoff overlay.js

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  64-bit

• Scale of an alignment

  How much longer a length becomes under the alignment.

  scale = √(m₀² + m₁²)

  Revision overlay: lining up two sheets and moving the takeoff overlay.js

  • TakeoffCraft
  64-bit

• Marks moved onto the new sheet

  Applies the alignment to every point of a mark.

  p′ = A·p; b′ = b

  Revision overlay: lining up two sheets and moving the takeoff overlay.js

  • TakeoffCraft
  64-bit

• Old sheet's pixels under the new sheet

  The matrix from a pixel of the new sheet's raster to a pixel of the old one.

  Revision overlay: lining up two sheets and moving the takeoff overlay.js

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  64-bit

• Applying, multiplying and inverting a transform

  The 2 × 3 matrix operations behind sheet transforms.

  det = m₀·m₃ − m₁·m₂; M⁻¹ = adj(M) ÷ det

  Revision overlay: lining up two sheets and moving the takeoff geom.js

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  64-bit

• Alignment from four picks

  Collects two points on the old sheet and two on the new one and fits the alignment.

  Revision overlay: lining up two sheets and moving the takeoff takeoffcraft.js

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  64-bit

• Scale carried to the new sheet

  The scale the moved marks are measured with on the new sheet.

  ftPerUnit′ = ftPerUnit ÷ scale(A)

  Revision overlay: lining up two sheets and moving the takeoff takeoffcraft.js

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  64-bit

• Where the two sheets differ

  Marks each pixel as removed, added or unchanged, and counts both kinds.

  removed: old ≥ 0.35 and max(new within r) < 0.2; added: the reverse

  Revision overlay: what changed under a mark overlay.js

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  64-bit

• How much changed along a mark

  The share of a mark's path with changed ink beside it, whether a corner changed, and the changed pixels near it.

  share = samples with changed ink within the buffer ÷ samples

  Revision overlay: what changed under a mark overlay.js

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  64-bit

• Changed pixels in a box

  How many changed pixels lie in a rectangle of the mask.

  n = S[y₁+1][x₁+1] − S[y₀][x₁+1] − S[y₁+1][x₀] + S[y₀][x₀]

  Revision overlay: what changed under a mark overlay.js

  • TakeoffCraft
  Exact

• Raster sizes and the mark test

  Chooses the two raster scales, builds the pixel map between them and tests every mark of the old sheet.

  px = min(2, √(12,000,000 ÷ (W × H)))

  Revision overlay: what changed under a mark takeoffcraft.js

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  64-bit

• Sheet coordinates to feet on the ground

  Maps a point of the sheet to feet in the 3D view.

  k = ftPerUnit ÷ √|det T|; (x, y) → (dx·k, (height − dy)·k)

  3D check view: walls, slabs and their quantities scene3d.js

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  64-bit

• Wall area of a run

  The area of the wall a run with a height stands for.

  wall area = L × H

  3D check view: walls, slabs and their quantities scene3d.js

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  64-bit

• Net area and volume of a slab

  An area's net square feet after back-outs, and its volume when it has a depth.

  net = max(0, A − cut); V = net × D

  3D check view: walls, slabs and their quantities scene3d.js

  • TakeoffCraft
  64-bit

• Totals over stacked sheets

  Adds the totals of each sheet when several sheets are stacked as floors.

  3D check view: walls, slabs and their quantities scene3d.js

  • TakeoffCraft
  64-bit

• Outline of a wall with a thickness

  Offsets a run half the thickness to each side, with mitred corners, into one closed outline.

  offset = min(half ÷ max(cos, 1e-6), 4 × half) along the bisector

  3D check view: walls, slabs and their quantities scene3d.js

  • TakeoffCraft
  64-bit

• Solid from an outline and its cut-outs

  Triangulates the top and bottom faces and builds the side faces of a slab or wall.

  3D check view: walls, slabs and their quantities scene3d.js

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  64-bit

• Feet to meters, Z up to Y up

  Converts one vertex from the view's feet to glTF's meters and axes.

  (x, y, z) ft → (0.3048·x, 0.3048·z, −0.3048·y) m

  3D check view exported as glTF glb.js

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  64-bit

• Vertex positions and normals written

  Fills the position and normal buffers of an object.

  n = (b − a) × (c − a) ÷ |…|

  3D check view exported as glTF glb.js

  • TakeoffCraft
  32-bit in part

• Bounds of each position buffer

  The minimum and maximum of a position buffer, written beside it.

  3D check view exported as glTF glb.js

  • TakeoffCraft
  32-bit in part

• Quantities carried with each object

  Attaches each object's mark, item, kind and measured values to its node.

  3D check view exported as glTF glb.js

  • TakeoffCraft
  64-bit

• Arcs as Bézier curves for drawing

  Turns a run or an outline into move, line and curve commands.

  k = 4 ÷ 3 × tan(φ ÷ 4); c₁ = p₀ + k·r·tangent₀; c₂ = p₃ − k·r·tangent₁

  Marks and sheets written to PDF geom.js

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  64-bit

• A mark's path written to the page

  Writes a mark's commands as PDF path operators.

  Marks and sheets written to PDF pdfmarks.js

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  64-bit

• Quantities printed in the legend

  The quantity of each item on that sheet, as text in the page's legend.

  Marks and sheets written to PDF pdfmarks.js

  • TakeoffCraft
  64-bit

• A drawing's lines written as vector paths

  Writes each batch of the drawing's lines to the PDF page under the sheet's matrix.

  width = max(0.25, lw × 72 ÷ 25.4 [× 0.5]) ÷ scale

  Marks and sheets written to PDF cadpdf.js

  • TakeoffCraft
  64-bit

• Unit conversions to the factor table's basis

  How many meters, square meters, cubic meters or items one of each takeoff unit is.

  CY → m³: × 0.764554858 (exact: 0.9144³ = 0.764554857984)

  Embodied carbon from quantities carbon.js

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  64-bit

• Quantity in the factor's basis

  Converts a line's quantity with waste into the unit its carbon factor is given in.

  qty = qtyW × factor; kg basis: qtyW × factor × density

  Embodied carbon from quantities carbon.js

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  64-bit

• Kilograms per line and the total

  The carbon of each line for the chosen modules, and their sum.

  kg = qty × (A1–A3 + A4 + A5); total = Σ kg

  Embodied carbon from quantities carbon.js

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  64-bit

• Carbon lines written to a file

  Writes each line's quantity and kilograms to a CSV file.

  written = round(v × 100) ÷ 100

  Embodied carbon from quantities carbon.js

  • TakeoffCraft
  64-bit

• Unit conversions for the price table

  The table unit and factor for each takeoff unit.

  Rates exported as a price table carbon.js

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  Exact

• Rates converted and rounded

  One table row per priced item, with its material rate, labor rate and waste.

  rate = round(rate4 ÷ 10000 × factor × 10⁶) ÷ 10⁶

  Rates exported as a price table carbon.js

  • TakeoffCraft
  64-bit

• Quantity rounded for the package

  Rounds a quantity to 4 decimals before it is sent.

  qty = round(v × 10000) ÷ 10000

  Quantities sent in a bid package bidsend.js

  • TakeoffCraft
  64-bit

• Scope lines of a package

  Builds the lines of a bid package: item, quantity, unit and sheets.

  Quantities sent in a bid package bidsend.js

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  64-bit

• Vertex buffers for the 3D view

  Copies an object's triangles into a buffer for the graphics card.

  Drawing the 3D check view and CAD sheets on screen view3d.js

  • TakeoffCraft
  32-bit, display only

• Canvas paths for a CAD sheet

  Builds the canvas paths of one batch of lines and fills.

  Drawing the 3D check view and CAD sheets on screen cadset.js

  • TakeoffCraft
  32-bit, display only