Calculations

Calculations

• Point in triangle

  Whether a point lies inside or on a triangle.

  three cross products of (corner − point) pairs, each ≥ 0

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Bridge from a hole to the outer ring

  The point of the outer ring a hole is connected to.

  x = p.x + (h.y − p.y) × (p′.x − p.x) ÷ (p′.y − p.y); tan = |h.y − p.y| ÷ (h.x − p.x)

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Do two segments cross

  Whether two edges intersect, including touching and collinear overlap.

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Is the middle of a diagonal inside the polygon

  Whether a diagonal between two corners runs through the inside of the polygon.

  midpoint = ((a.x + b.x) ÷ 2, (a.y + b.y) ÷ 2); even-odd count of edges crossed by a ray

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Mesh handed to the solid kernel

  Welds the mesh's corners and passes it to manifold-3d.

  weld grid = 10⁻⁶ × max(Δx, Δy, Δz); positions → Float32Array

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Boolean of two solids

  The difference, union or intersection of two element meshes.

  c = center of a's box; R = (a − c) OP (b − c); result = R + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Element minus all its openings

  Subtracts every opening from an element, one after another.

  A₀ = base − c; Aᵢ = Aᵢ₋₁ − (cutterᵢ − c); result = Aₙ + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Face planes of a convex cutter

  Finds the outward planes of a cutter and decides whether it is convex.

  n = (b − a) × (c − a) ÷ |…|; d = n · a; convex when n · p − d ≤ 10 ε for every corner p

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Polygon split by a plane

  Cuts a convex polygon into the part in front of a plane and the part behind it.

  t = dₐ ÷ (dₐ − d_b); x = a + (b − a) t

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Mesh clipped by a plane

  Keeps the part of a mesh on one side of a plane and closes the cut.

  dᵢ = (pᵢ − p) · n; ε = 10⁻⁹ × (d_max − d_min); cut point = a + (b − a) dₐ ÷ (dₐ − d_b)

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Cap of a cut

  Joins the cut segments into loops, sorts outer loops from holes and fills them.

  key = round(x ÷ tol), round(y ÷ tol), round(z ÷ tol); area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Half-space cut

  Removes the part of an element behind a plane, optionally only inside a polygon boundary.

  L = 4 × max(1, box diagonal) + |P₀ − box min|; prism height = 2 L

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Vertex data of one geometry

  Returns a geometry's positions and normals for drawing and for measuring.

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Placement matrix of each piece

  The matrix that takes a geometry's vertices to model space in meters, Y up.

  M = C × Y-up × scale(u) × placement

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Shift to the origin

  Finds the translation that brings the model near the origin.

  c = (box min + box max) ÷ 2 of the first element; C = translate(−(Y-up × scale(u) × placement × c))

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• File units to meters, Z up to Y up

  Scales a placement by the file's length unit and turns its axes.

  M′ = Y-up × scale(u) × M

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Length of a linear mark

  The counted, deducted and gross length of a run in feet, along the slope where a segment is a rake or a hip.

  segment ft = segment length × ftPerUnit; sloped = segment ft × slope factor; length = Σ counted sloped segments; gross = length + deducted

  Takeoff quantities from marks model.js

  • TakeoffCraft
  64-bit

• Area and perimeter of an area mark

  The net area of an outline minus its cut-outs in square feet, on the slope when the mark or its item has a pitch, and its perimeter in feet.

  area = net × ftPerUnit × ftPerUnit × √(1 + (pitch ÷ 12)²); perimeter = perimeter × ftPerUnit

  Takeoff quantities from marks model.js

  • TakeoffCraft
  64-bit

• Totals per item and per sheet

  Each item's total length, area, perimeter and count, and the same per sheet, with back-outs taken out and typical groups counted as many times as they repeat.

  item total = Σ marks (measure × repeat); area mark = max(0, area − back-out × slope factor)

  Takeoff quantities from marks model.js

  • TakeoffCraft
  64-bit

• Back-out area taken from an area mark

  How many square feet the back-out marks on the same sheet cover of one area mark.

  cut = (Σ overlap areas in sheet units) × ftPerUnit × ftPerUnit

  Takeoff quantities from marks model.js

  • TakeoffCraft
  64-bit

• Totals in the item's unit

  An item's length, area, perimeter, height and count in the unit the item reports in, as the values assembly formulas use.

  L = feet × 0.3048 for a metric item; A = square feet × the unit's factor; wall area = length × height

  Takeoff quantities from marks model.js

  • TakeoffCraft
  64-bit

• Quantity of a second condition

  The quantity of an item's second kind of mark in that condition's own unit.

  Takeoff quantities from marks model.js

  • TakeoffCraft
  64-bit

• One priced row

  A row's quantity with waste and its material, labor and total amounts in cents.

  qtyW = qty × (1 + waste ÷ 10000); amount = round(qtyW × rate ÷ 100) cents; total = material + labor

  Priced estimate model.js

  • TakeoffCraft
  64-bit

• Crew hours and labor

  The crew hours, worker hours, crew days and labor amount for a quantity, and the labor rate per unit it comes to.

  hours = qtyW ÷ production; worker hours = hours × size; days = hours ÷ 8; labor = round(worker hours × wage ÷ 100) cents; rate = round(size × wage ÷ production)

  Priced estimate model.js

  • TakeoffCraft
  64-bit

• Estimate rows and totals

  A row for every item, second condition and assembly part, and the material, labor, hours and grand totals.

  material total = Σ row material; labor total = Σ row labor; total = material + labor; days = hours ÷ 8

  Priced estimate model.js

  • TakeoffCraft
  64-bit

• Estimate of each bid area

  A separate estimate for each bid area, from that area's own marks.

  Priced estimate model.js

  • TakeoffCraft
  64-bit

• Alternates

  What taking each alternate adds to or takes from the base bid.

  amount = + Σ row totals for an add; − Σ row totals for a deduct

  Priced estimate model.js

  • TakeoffCraft
  64-bit

• Rounding of exported quantities and amounts

  How a quantity, an amount in cents and a rate become the numbers written to a file.

  quantity → 4 decimals; dollars = cents ÷ 100 → 2 decimals; rate = rate ÷ 10000

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Estimate as CSV

  The estimate's rows, totals, alternates and bid summary as values in a CSV file.

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Per-sheet quantities as CSV

  Each item's quantity on each sheet as a CSV row.

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Material list

  Every part and priced item added up by name and unit across the takeoff.

  per name and unit: qty = Σ row qty; qty with waste = Σ row qtyW; material = Σ row cents

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Estimate by division

  Material, labor and total per division, from the first two digits of each item's CSI number.

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Spot elevation point file

  The count marks of one sheet that carry an elevation, as northing, easting and elevation in feet.

  northing = y × ftPerUnit; easting = x × ftPerUnit; elevation = z

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Estimate worksheet row

  One priced row of the Estimate sheet: values, live formulas and the cached results.

  F = D × (1 + E); I = ROUND(F × G, 2); J = ROUND(F × H, 2); K = I + J

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Per-mark quantities on the Marks sheet

  Each mark's own length or area in its unit, with its segments, cut-outs and perimeter as text.

  length = feet × 0.3048 for a metric unit; area = square feet × the unit's factor

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Markup rows under the estimate total

  Labor burden, tax, overhead, profit and bond as live rows: base, percent and amount.

  amount = ROUND(base × percent, 2); percent = basis points ÷ 10000

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• By bid area worksheet

  Each bid area's rows, a subtotal per area and the sum of the subtotals.

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Alternates worksheet

  The base bid, each alternate's rows and amount, and the base bid with every add taken.

  base with adds = base total + Σ add amounts

  Estimate and quantity exports (CSV and XLSX) export.js

  • TakeoffCraft
  64-bit

• Our cost of each item

  The sum of an item's estimate rows: the item, its second conditions and its assembly parts.

  cost = Σ row totals

  Bid packages and leveling level.js

  • TakeoffCraft
  64-bit

• Package scope and cost

  The items of each CSI division with their quantity, unit and cost, and the package's cost.

  package cost = Σ item costs

  Bid packages and leveling level.js

  • TakeoffCraft
  64-bit

• Leveled bids and the low bid

  Each bid with plugs for what it leaves out, its difference from our cost, and which bid is low.

  leveled = bid + Σ plugs; difference = leveled − our cost; low = smallest leveled

  Bid packages and leveling level.js

  • TakeoffCraft
  64-bit

• Package scope file

  The scope sent to a subcontractor: item, CSI number, quantity, unit and sheets, without prices.

  quantity = round(q × 10000) ÷ 10000

  Bid packages and leveling level.js

  • TakeoffCraft
  64-bit

• Base bid with the chosen bids

  The estimate with each awarded package priced at its chosen bid instead of our own rates.

  total = material + labor + Σ chosen bids

  Bid packages and leveling level.js

  • TakeoffCraft
  64-bit

• Paper length of a notation in inches

  Reads a fraction, a mixed number or a decimal as inches.

  1-1/2 → 1 + 1 ÷ 2; 1/4 → 1 ÷ 4

  Sheet scale read from the sheet's text scaletext.js

  • TakeoffCraft
  64-bit

• Ratio of a notation and its listed scale

  Every scale notation in the text, each matched to a listed scale.

  ratio = (feet × 12 + inches) ÷ paper inches, rounded to 3 decimals

  Sheet scale read from the sheet's text scaletext.js

  • TakeoffCraft
  64-bit

• Which scale a sheet gets

  The most frequent scale on the sheet, and the other scales found.

  Sheet scale read from the sheet's text scaletext.js

  • TakeoffCraft
  Exact

• Stock figure from text

  Reads a stock cell such as 1,200 or Out of stock as a number, or as in stock or not.

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Lead time in days

  Reads a lead time such as 2-3 weeks or 5 business days as a number of days.

  weeks × 7; months × 30; business days → ⌈n × 7 ÷ 5⌉; result rounded to 0.1 day

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• Price from text

  Reads a price cell as a whole number of 1/10000 dollar.

  price = round(n × 10000)

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit

• A need in the supplier's unit

  The needed quantity in the unit the supplier's row uses.

  tonnes = kilograms ÷ 1000

  Supplier stock and lead-time check lib-supply/supply.js

  • TakeoffCraft
  • DetailCraft
  64-bit