Calculations

Calculations

• Recognizing copies of a part

  Folds parts that are rigid moves of one another into one part with several placements.

  copy when fit error ≤ 1e-5 × size and largest corner difference ≤ 4e-5 × size

  Manual: imported product meshes, copies and part volume illustrate/import.js

  • PartCraft
  64-bit

• Largest corner difference after a move

  How far the moved corners of one mesh are from another's.

  Manual: imported product meshes, copies and part volume illustrate/import.js

  • PartCraft
  64-bit

• Placement moved to millimeters

  A 3MF placement with its move in millimeters.

  Manual: imported product meshes, copies and part volume illustrate/import.js

  • PartCraft
  64-bit

• Mesh in the manual file

  A part's mesh as written into the manual file.

  Manual: imported product meshes, copies and part volume illustrate/manual.js

  • PartCraft
  32-bit in part

• Explode offsets

  How far each part has moved at a point in an exploded view.

  offset = Σ dir × dist × clamp(t × n − k, 0, 1) over the steps k

  Manual: imported product meshes, copies and part volume illustrate/manual.js

  • PartCraft
  64-bit

• Where each part is drawn

  Each instance's matrix in a view.

  M = translation(explode offset + view move) × placement

  Manual: imported product meshes, copies and part volume illustrate/manual.js

  • PartCraft
  64-bit

• Moving parts in a view

  Adds a move to parts in one view.

  Manual: imported product meshes, copies and part volume illustrate/manual.js

  • PartCraft
  64-bit

• Part volume and area

  The volume and surface area of a part's mesh.

  V = |Σ a·(b × c) ÷ 6|; A = Σ |(b − a) × (c − a)| ÷ 2

  Manual: imported product meshes, copies and part volume illustrate/manual.js

  • PartCraft
  32-bit in part

• Picture to ink darkness

  Turns the canvas pixels of a sheet into darkness from 0 (paper) to 1 (black).

  ink = 1 − (lum·a + (1 − a)), lum = (0.299R + 0.587G + 0.114B) ÷ 255

  Automatic count by symbol matching match.js

  • TakeoffCraft
  32-bit in part

• Symbol turned to an angle

  Rotates the symbol's raster for a search at an angle.

  Automatic count by symbol matching match.js

  • TakeoffCraft
  32-bit in part

• Integral images

  Running sums of ink and of ink squared, so any window's sum costs four lookups.

  sum(window) = S[e] − S[b] − S[c] + S[a]

  Automatic count by symbol matching match.js

  • TakeoffCraft
  64-bit

• Match score at every position, and its peaks

  Scores how well the symbol matches at each position and keeps the local best ones.

  score = Σ (t − t̄)·img ÷ (σₜ·√n × √(v·n)), v = Σimg² ÷ n − (Σimg ÷ n)²

  Automatic count by symbol matching match.js

  • TakeoffCraft
  32-bit in part

• Search at each angle

  Runs the match at every angle asked for and collects the finds.

  Automatic count by symbol matching match.js

  • TakeoffCraft
  32-bit in part

• Angle of a find refined

  Tries angles within 7.5° of a find in 1.5° steps and keeps the best.

  Automatic count by symbol matching match.js

  • TakeoffCraft
  32-bit in part

• Finds kept at the threshold

  Keeps the finds at or above the threshold, best first, and drops any that overlaps a kept one.

  keep when score ≥ threshold and IoU with every kept find ≤ 0.25

  Automatic count by symbol matching match.js

  • TakeoffCraft
  32-bit in part

• Raster scale for a search

  The pixels per sheet unit that make the symbol's longer side about 40 pixels.

  w = clamp(40 ÷ max(boxW, boxH), 0.2, 4)

  Automatic count by symbol matching match.js

  • TakeoffCraft
  64-bit

• How alike two symbols are

  The best normalized correlation of two symbols over shifts of up to one pixel.

  likeness = max over shifts of Σ(p − p̄)(q − q̄) ÷ √(Σ(p − p̄)² · Σ(q − q̄)²)

  Automatic count by symbol matching legend.js

  • TakeoffCraft
  64-bit

• One find per spot across symbols

  Merges overlapping finds of one symbol, and gives a spot two symbols match to the higher score.

  Automatic count by symbol matching legend.js

  • TakeoffCraft
  32-bit in part

• Counts per symbol and per sheet

  Counts the kept finds for each symbol, in total and on each sheet.

  Automatic count by symbol matching legend.js

  • TakeoffCraft
  Exact

• Raster sizes for a sheet at another scale

  The pixel sizes to search a sheet at so a symbol drawn to scale keeps its size in pixels.

  w′ = w × tgtFt ÷ srcFt when |tgtFt ÷ srcFt − 1| > 0.01

  Automatic count by symbol matching legend.js

  • TakeoffCraft
  64-bit

• 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

• 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

  • TakeoffCraft
  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