Calculations

Calculations

• Quantity with waste

  A quantity increased by a waste percentage.

  qtyW = qty × (1 + bp ÷ 10000)

  Rates, percentages and extended amounts units.js

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• Cents as dollars text

  Writes whole cents as $1,234.56.

  Rates, percentages and extended amounts units.js

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• Typed bid amount to cents

  Reads an amount typed into the bid leveling sheet as whole cents.

  cents = round(rate4 ÷ 100)

  Rates, percentages and extended amounts takeoffcraft.js

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• Typed pitch to rise per 12

  Reads 6:12, 6/12, 4:10, a bare rise, or an angle in degrees.

  rise = tan(a·π ÷ 180) × 12; rise = rise ÷ run × 12

  Roof pitch and slope factors units.js

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• Slope factor of a roof plane

  Surface length or area per unit of plan length or area.

  f = √(1 + (rise ÷ 12)²)

  Roof pitch and slope factors units.js

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• Hip and valley factor

  True length of a hip or valley per unit of its plan length.

  f = √(1 + (rise ÷ 12)² ÷ 2)

  Roof pitch and slope factors units.js

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• Pitch as text

  Writes the rise as 6:12 or 6.5:12.

  Roof pitch and slope factors units.js

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• Signed coordinate length

  Reads one typed coordinate, which may be negative or zero, into feet.

  Typed distances and coordinates while drawing typein.js

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• Sheet direction of a screen direction

  The unit vector on the sheet that points along a given direction on the screen.

  u = M⁻¹·(sx, −sy); u ÷ |u|

  Typed distances and coordinates while drawing typein.js

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• Point from typed text

  Works out the next point from a distance, a distance and angle, or coordinates.

  p = last + dir × ft × k, k = 1 ÷ ftPerUnit

  Typed distances and coordinates while drawing typein.js

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• Circle radius typed while drawing

  Places a circle's edge point at a typed radius from its center, toward the pointer.

  edge = c + (to − c) ÷ |to − c| × ft ÷ ftPerUnit

  Typed distances and coordinates while drawing takeoffcraft.js

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• Typed spot elevation

  Reads the elevation typed on a count mark, in decimal feet, feet-inches or meters.

  Typed distances and coordinates while drawing takeoffcraft.js

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• One CAD object as points and bulges

  The run or outline that stands for a line, arc, circle, polyline, ellipse, spline or 2D solid.

  arc: p = c + r·(cos a, sin a), b = tan(sweep ÷ 4); ellipse: n = max(24, ⌈1440·sweep ÷ 2π⌉) chords

  Lengths and areas taken from CAD objects cadgeom.js

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• Hatch as outlines with holes

  The outer loops of a hatch, each with the loops inside it as cut-outs.

  Lengths and areas taken from CAD objects cadgeom.js

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• Object placed on the sheet

  Applies the sheet or viewport matrix to an object's points and decides whether a viewport shows it.

  p′ = T·(mirror·x, y); b′ = b × sign(det T × mirror)

  Lengths and areas taken from CAD objects cadgeom.js

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• Marks made from picked objects

  The point lists a linear or an area item takes from the picked objects.

  Lengths and areas taken from CAD objects cadgeom.js

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• Length and area of what is picked

  The total length or net area of the picked objects in page units.

  len = Σ length; area = Σ (gross − cut-outs)

  Lengths and areas taken from CAD objects cadgeom.js

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• Picked objects in real units

  The length or area of the picked CAD objects shown above the sheet.

  SF = area × k²; ft = len × k

  Lengths and areas taken from CAD objects takeoffcraft.js

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• Product of two transforms

  Combines two 2 × 3 affine matrices.

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

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• Place of a block reference and its array cells

  The point of each copy of a block reference, and the transform its contents get.

  p = M·(insert + R(rot)·(c·dx, r·dy))

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

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• Point that stands for a shape

  The one point a shape is placed and counted by: a center, a middle, or the middle of its box.

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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• Room around a point

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

  Room outline by flood fill roomfill.js

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• Outline traced along pixel edges

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

  Room outline by flood fill roomfill.js

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• 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

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• 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

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• 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

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• Symbol turned to an angle

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

  Automatic count by symbol matching match.js

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• 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

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• 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

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• Search at each angle

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

  Automatic count by symbol matching match.js

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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