Calculations

Calculations

• Quantities file for TakeoffCraft

  The quantity rows in the format TakeoffCraft reads.

  qty = round(qty, 2)

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Meters per unit

  The length of each supported unit in meters.

  ft = 0.3048; US survey ft = 1200 ÷ 3937; in = 0.0254; yd = 0.9144; mi = 1609.344

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  Exact

• Scale from two points

  Project units per pixel from two points on the scan and the true distance between them.

  units per pixel = distance ÷ √(Δpx² + Δpy²)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Scale from a stated scale

  Project units per pixel from the scan's resolution and a scale such as 1 inch = 50 feet or 1:500.

  per ÷ dpi, or ratio × 0.0254 ÷ (m per unit) ÷ dpi

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Placement from a scale, origin and rotation

  The transform that puts the sheet's lower-left corner at a point, turned by an angle, at a given scale.

  c = s·cos θ, d = s·sin θ; X = x₀ − d·h + c·px + d·py; Y = y₀ + c·h + d·px − c·py

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Pixel to project coordinates

  The project position of a pixel.

  X = g₀ + g₁·px + g₂·py; Y = g₃ + g₄·px + g₅·py

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Inverse placement

  The transform from project coordinates back to pixels.

  det = g₁·g₅ − g₂·g₄; inverse = adjugate ÷ det

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Scale of a placement

  The project units per pixel a placement stands for, reported with every fit.

  scale = √|g₁·g₅ − g₂·g₄|

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Rotation of a placement

  The angle a placement turns the sheet by, in degrees.

  rotation = atan2(g₄, g₁) × 180 ÷ π

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• 3 × 3 linear solve

  Solves the normal equations of the affine fit.

  Gauss-Jordan elimination with partial pivoting

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Least-squares fit to matched points

  The placement that best matches points picked on the scan to their project coordinates, with each point's residual and the root mean square.

  similarity: c = Σ(u·X + v·Y) ÷ Σ(u² + v²), d = Σ(u·Y − v·X) ÷ Σ(u² + v²); rms = √(Σ r² ÷ n)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Traced arc to points

  Turns an arc found on the scan into points for a line layer.

  n = max(2, ⌈|sweep| ÷ 5°⌉); point = center + r·(cos t, sin t)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Traced lines in project coordinates

  The lines and arcs traced on the scan as one line layer in project coordinates.

  each end point through the placement; kept when its length > the minimum

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Frame of a member

  The origin, the unit direction, the two section axes and the length of a member line.

  x = (e − s) ÷ |e − s|; v = unit(Z − x·x_z); u = v × x; u′ = cos a·u + sin a·v, v′ = −sin a·u + cos a·v

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Local point to model point

  The model coordinates of a point given along the member and across its section.

  p = o + x·x̂ + u·û + (v + voff)·v̂

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Model point to local point

  Where a model point lies along a member and across its section.

  d = p − o; x = d·x̂, u = d·û, v = d·v̂ − voff

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• End face position on a plane-cut end

  How far along the part its end face is at a given point of the section, for square ends and mitre cuts.

  x = x0 + ku·u + kv·v

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Section outline clipped at a height

  The part of a section outline below or above a line, used for coped ends.

  t = (limit − a_v) ÷ (b_v − a_v); new point = (a_u + (b_u − a_u)·t, limit)

  Member frames and local coordinates geom.js

  • DetailCraft
  64-bit

• Distance from a point to a member line

  The shortest distance from a point to the segment between a member's two ends.

  k = clamp((P − a)·(b − a) ÷ |b − a|², 0, 1); d = |P − (a + k·(b − a))|

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Is a member vertical

  Whether a member stands vertical, the condition for a column to take a connection.

  |Δx| < 1 mm and |Δy| < 1 mm and |Δz| ≥ 1 mm

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Members end to end in line

  Pairs of member ends that meet in line, with the gap between them.

  along = d·d̂_a; off = |d − d̂_a·along|; in line when |d̂_a·d̂_b| ≥ 0.9999, off ≤ 1 mm, |d| ≤ 50 mm

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Beam end at a column

  Which beam ends land on a column, and whether they meet its flange, its web or come in skewed.

  flange when |away·v̂| > 0.9999; web when |away·û| > 0.9999; else skew

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Members meeting at an angle

  Pairs of I-shaped member ends that share a point and are not in line, with the angle between them.

  angle = acos(clamp(ê_A·ê_B, −1, 1)) × 180 ÷ π

  Finding joints between members connections.js

  • DetailCraft
  64-bit

• Steel and bar weight in the status line

  The total weight of all steel parts and of all reinforcing bars, shown under the drawing.

  steel = Σ part weight; bars = Σ row total weight

  Weight totals in the status line and panels detailcraft.js

  • DetailCraft
  64-bit

• Steel weight of a selection

  The weight of the selected members plus the main plate of each selected connection.

  steel = Σ weight of selected members and connection plates

  Weight totals in the status line and panels detailcraft.js

  • DetailCraft
  64-bit

• Cut length and weight of one part

  The cut length, weight and weight per meter shown for a selected member.

  Weight totals in the status line and panels detailcraft.js

  • DetailCraft
  64-bit

• Numbers in the model file

  How the model's numbers are written to the file.

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• A point of a member

  Checks and stores a member's start or end point.

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• Member rotation and minimum length

  Brings a member's rotation into 0 to 360 degrees and refuses a member shorter than 1 mm.

  rotation = ((r mod 360) + 360) mod 360; length = √(Δx² + Δy² + Δz²) ≥ 1 mm

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• Grid lines from spacings

  The position of each grid line from the list of spacings typed.

  at_i = at_{i−1} + spacing_{i−1}

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• Spacings shown for existing grid lines

  The spacings text filled into the grid dialog from the stored grid positions.

  spacing = (at_i − at_{i−1}) to 3 decimals

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• A loose bolt as stored

  The diameter, length, head point and direction kept for a bolt that is not part of a connection.

  d, length, head: round(v × 1000) ÷ 1000; axis_i = round(a_i ÷ |a| × 10⁶) ÷ 10⁶

  The model file and what it stores model.js

  • DetailCraft
  64-bit

• Viewport scale from 1:n

  Paper units per model unit for a drawing scale 1:n.

  s = mm per model unit ÷ mm per paper unit ÷ n

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Scale 1:n from a viewport scale

  The n of 1:n that a viewport's stored scale stands for.

  n = mm per model unit ÷ mm per paper unit ÷ s

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• List of standard and custom scales

  The scales offered for a drawing: the standard ones and the drawing's own that the standard list lacks.

  custom n = drawing ÷ paper; kept when |n − listed n| ≥ 1e-6 × n for every listed scale

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Name of a viewport scale

  The text a viewport scale reads as: a standard name when it is one, else 1:n.

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Ratio text for a scale that is not listed

  Writes 1:n or n:1 for a scale with no standard name.

  n ≥ 1: "1:n"; n < 1: "(1 ÷ n):1"

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Largest standard scale that fits

  Picks the largest listed scale at which the window still fits the viewport.

  largest s with s ≤ sFit × (1 + 1e-9)

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Viewport center and scale for a model window

  The model point a viewport looks at and the scale at which a model window fits it.

  sFit = min(w ÷ Δx, h ÷ Δy); center = ((minX + maxX) ÷ 2, (minY + maxY) ÷ 2)

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Standard paper for a sheet size

  Finds the standard paper a sheet of w × h is, either way round.

  |standard side − side| ≤ 0.005 × side, both sides in mm

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Space for viewports on a sheet

  The rectangle inside the border and above the title block, in paper units.

  x0 = sheet x0 + 15 mm × k; y0 = sheet y0 + 47 mm × k; x1 = sheet x0 + (W − 15 mm) × k; y1 = sheet y0 + (H − 15 mm) × k; k = 1 ÷ mm per paper unit

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Viewport of a new sheet

  The size, paper position, model center and scale of the viewport a new sheet starts with.

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Clusters of the model

  Groups the model's visible objects whose bounding boxes are within a gap of each other, and returns each group's box.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Gap that separates parts

  The distance below which two objects count as one part.

  gap = max(Δx, Δy, 1e-9) × 0.04

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Size of a part's viewport at a scale

  The paper width and height a part needs at a scale 1:n, with padding and a caption band.

  w = Δx × s + 2 × 4 mm × k; h = Δy × s + 2 × 4 mm × k + 7 mm × k; k = 1 ÷ mm per paper unit

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Shelf packing

  Places boxes in rows inside the free zone and returns each box's lower-left corner, or nothing when they do not fit.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Scale and place for every part on one paper

  Chooses the scale or scales and the position of each viewport on a given paper.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Scale on automatic paper

  With no scale given and automatic paper, the scale the largest part gets on the default paper.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Viewport placed for a part

  The viewport stored for each part: paper size and center, model center and scale.

  h = packed h − 7 mm × k; paper center = (x + w ÷ 2, y + 7 mm × k + h ÷ 2); model center = midpoint of the window

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Frame a sheet maps onto

  The drawing area a redline sheet is mapped onto: a given box, or the extents of everything drawn.

  Redline items placed in the drawing redline.js

  • CadCraft
  64-bit