Calculations

Calculations

• Count of block references

  How many references of the named blocks there are, in total, by variant and by layer.

  total = number of matching references

  Counting blocks, shapes and texts in a CAD drawing cadcount.js

  • TakeoffCraft
  Exact

• Which sheet shows an object, and where

  The page point of a drawing object on a sheet, through the first viewport that contains it.

  Counting blocks, shapes and texts in a CAD drawing cadset.js

  • TakeoffCraft
  64-bit

• Bézier curves cut into chords

  Turns each cubic or quadratic curve of the page into 8 straight segments.

  B(t) = u³p₀ + 3u²t·c₁ + 3u·t²·c₂ + t³p₃, u = 1 − t, t = s ÷ 8

  Snapping to and measuring the sheet's own linework snap.js

  • TakeoffCraft
  64-bit

• Where two segments cross

  The crossing point of two segments, offered as a snap point.

  u = ((c − a) × s) ÷ (r × s); point = a + r·u

  Snapping to and measuring the sheet's own linework snap.js

  • TakeoffCraft
  64-bit

• Snap point for a picked point

  The end point, midpoint, intersection or nearest point on a line within the snap distance.

  Snapping to and measuring the sheet's own linework snap.js

  • TakeoffCraft
  64-bit

• Connected path through a segment

  The segment that was clicked and everything joined to it end to end within the gap tolerance.

  Snapping to and measuring the sheet's own linework pickpath.js

  • TakeoffCraft
  64-bit

• Next segment at a junction

  Chooses which segment a path continues along from an end point.

  score = turn angle + (0.01 when the ends are more than 1e-9 apart)

  Snapping to and measuring the sheet's own linework pickpath.js

  • TakeoffCraft
  64-bit

• Vertices of a picked path

  The points of the path in order, as they will be stored in the mark.

  Snapping to and measuring the sheet's own linework pickpath.js

  • TakeoffCraft
  64-bit

• Length of a picked path

  The length of the path in sheet units.

  L = Σ |pᵢ − pᵢ₋₁|

  Snapping to and measuring the sheet's own linework pickpath.js

  • TakeoffCraft
  64-bit

• Area of a picked loop

  The area inside a closed path in square sheet units.

  A = |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| ÷ 2

  Snapping to and measuring the sheet's own linework pickpath.js

  • TakeoffCraft
  64-bit

• Closed loops around a clicked point

  Finds the closed paths that have the clicked point inside, smallest first.

  Snapping to and measuring the sheet's own linework pickpath.js

  • TakeoffCraft
  64-bit

• A CAD sheet's lines for snapping

  The drawing's own line segments in page units, through the sheet and viewport matrices.

  Snapping to and measuring the sheet's own linework cadset.js

  • TakeoffCraft
  64-bit

• Picked path in real units

  The length and area of what is picked, shown while picking.

  ft = L × k; SF = A × k²

  Snapping to and measuring the sheet's own linework takeoffcraft.js

  • TakeoffCraft
  64-bit

• Room around a point

  Flood-fills the room and returns its outline in pixel corners.

  Room outline by flood fill roomfill.js

  • TakeoffCraft
  64-bit

• Outline traced along pixel edges

  Walks the outer boundary of the filled region, corner by corner.

  Room outline by flood fill roomfill.js

  • TakeoffCraft
  Exact

• Outline simplified

  Removes corners that lie within a tolerance of the line between their neighbors.

  d = |(p − a) × (b − a)| ÷ |b − a| ≤ 1.0 px

  Room outline by flood fill roomfill.js

  • TakeoffCraft
  64-bit

• Room outline back in sheet units

  Sets the raster scale and the door gap in pixels, and maps the outline's pixel corners back to sheet coordinates.

  gapPx = gap ÷ ftPerUnit × per × w; p = T⁻¹·(q ÷ w)

  Room outline by flood fill takeoffcraft.js

  • TakeoffCraft
  64-bit

• 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

• 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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • TakeoffCraft
  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

  • 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