Calculations

Calculations

• Cut-out inside its area

  Checks that a cut-out lies fully inside the outline and does not overlap another cut-out.

  Outline checks: inside, crossing, cut-outs geom.js

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• Convex outline test

  Whether a closed outline has no inward corner.

  Back-outs clipped out of areas geom.js

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• Polygon clipped to a convex polygon

  The part of a polygon that lies inside a convex polygon.

  t = d₁ ÷ (d₁ − d₂); corner = p + (q − p)·t

  Back-outs clipped out of areas geom.js

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• Area a back-out covers

  How much of an area mark (outline minus cut-outs) a convex back-out covers, in square PDF units.

  overlap = max(0, A(outline ∩ b) − Σ A(cut-out ∩ b))

  Back-outs clipped out of areas geom.js

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• Net area shown for a mark

  The area in a mark's properties after its back-outs are taken off.

  net = max(0, area − cut); plan area = max(0, plan − cut ÷ factor)

  Back-outs clipped out of areas takeoffcraft.js

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• Typed length to feet

  Normalizes what was typed and reads it as one length, or as arithmetic over lengths.

  Typed lengths and item units units.js

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• One length with a metric unit, or feet and inches

  Reads one normalized length into feet.

  ft = meters ÷ 0.3048

  Typed lengths and item units units.js

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• Numbers and fractions in a typed length

  Splits the text into numbers, fractions and foot or inch marks.

  fraction = a ÷ b (integers)

  Typed lengths and item units units.js

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• Feet and inches combined

  Combines a feet part and an inches part (whole number plus fraction) into feet.

  ft = feet + (inches + fraction) ÷ 12

  Typed lengths and item units units.js

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• Bare number in the default unit to feet

  Converts a number in feet, inches, meters, centimeters or millimeters to feet.

  ft = v ÷ 12; ft = v ÷ 0.3048; ft = v ÷ 1000 ÷ 0.3048

  Typed lengths and item units units.js

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• Item unit factors

  The factor from feet or square feet to each unit an item can be reported in.

  Typed lengths and item units units.js

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• Feet and square feet into an item's unit

  Converts a length in feet or an area in square feet to the unit that goes with an item.

  m = ft × 0.3048; area = sf × perSqFt

  Typed lengths and item units units.js

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• Round half away from zero

  Rounds a number to a given count of decimals.

  r = ⌊|v|·10ᵈ + 0.5 + 1e-9·max(1, |v|·10ᵈ)⌋ ÷ 10ᵈ

  Rounding for display and for money units.js

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• Grouped fixed-point text

  Writes a number with a fixed count of decimals and thousands separators.

  Rounding for display and for money units.js

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• Feet and inches to the nearest fraction

  Writes a length in feet as feet, inches and a fraction of an inch.

  n = round(|ft|·12·denom + 1e-9); feet = ⌊n ÷ (12·denom)⌋; inches = ⌊rem ÷ denom⌋

  Rounding for display and for money units.js

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• Length in a chosen display unit

  Writes a length in feet-inches, decimal feet, inches, meters or millimeters.

  m = ft × 0.3048; mm = ft × 0.3048 × 1000

  Rounding for display and for money units.js

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• Feet per sheet unit for a named scale

  The scale number for a preset such as 1/4 inch = 1 foot or 1:100.

  ftPerUnit = (userUnit ÷ 72) × ratio ÷ 12

  Sheet scale: presets, calibration and drawing units units.js

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• Scale from two points and a typed distance

  The scale that makes the distance between two picked points equal a typed real distance.

  ftPerUnit = realFt ÷ |b − a|

  Sheet scale: presets, calibration and drawing units units.js

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• Named scale a number matches

  Finds the preset scale closest to a scale number, if any is close enough.

  err = |ftPerUnit − s| ÷ s ≤ 0.005

  Sheet scale: presets, calibration and drawing units units.js

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• Feet per drawing unit by INSUNITS code

  The table that turns a drawing's unit code into feet per drawing unit.

  code 6: 1 ÷ 0.3048; code 21 as written: 1200 ÷ 3937

  Sheet scale: presets, calibration and drawing units cadcount.js

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• The drawing's length unit

  Reads the INSUNITS code and looks up feet per drawing unit.

  Sheet scale: presets, calibration and drawing units cadcount.js

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• Viewport transform, model to paper

  The matrix that places model space on the paper through a layout's viewport.

  k = h ÷ viewHeight; M = [k·c, k·s, −k·s, k·c, cx − k(c·vx − s·vy), cy − k(s·vx + c·vy)]

  Sheet scale: presets, calibration and drawing units cadset.js

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• Sheet size and the drawing-to-page transform

  Puts a layout on a page in points, or fits model space to a page about 2000 units on its longest side.

  layout: page = (paper − min) × ptU; model: k = 2000 ÷ extent, page = k·x + (24 − k·minX)

  Sheet scale: presets, calibration and drawing units cadset.js

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• Scale a drawing's sheet starts with

  Feet per page unit for a model sheet or a layout.

  model: f = ft ÷ k; layout: f = (1 ÷ ptU) ÷ s × ft, s = h ÷ viewHeight

  Sheet scale: presets, calibration and drawing units cadset.js

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• Drawing scale taken over by the takeoff

  Gives each sheet of an opened drawing the scale the drawing itself states, when the sheet has none yet.

  Sheet scale: presets, calibration and drawing units takeoffcraft.js

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• Calibration stored on the sheet

  Reads the typed distance, computes the scale and stores it with the two points and the text.

  Sheet scale: presets, calibration and drawing units takeoffcraft.js

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• Typed unit rate

  Reads a rate such as $1,234.5 into whole 1 ÷ 10000 dollars.

  rate4 = round(roundTo(v, 4) × 10000)

  Rates, percentages and extended amounts units.js

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• Typed percentage

  Reads a percentage such as 7.5 % into whole basis points.

  bp = round(roundTo(v, 2) × 100)

  Rates, percentages and extended amounts units.js

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• Quantity × rate to the cent

  The extended amount of a line in whole cents.

  cents = round(qty × rate4 ÷ 100)

  Rates, percentages and extended amounts units.js

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• 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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