Calculations

Calculations

• Volume printed after a 3D command

  The total volume of the solids a command just made, in drawing units cubed.

  V = Σ volumeᵢ ÷ (k × k × k)

  3D solid commands: sizes, paths and reported volume commands3d.js

  • CadCraft
  64-bit

• Number text in 3D command messages

  How heights, radii, angles and volumes are written on the command line.

  |n| < 1e-10 → 0; otherwise n rounded to 4 decimals

  3D solid commands: sizes, paths and reported volume commands3d.js

  • CadCraft
  64-bit

• Sweep path from a 2D object

  The points a profile is swept along, taken from a line, polyline, arc, circle or ellipse.

  n = max(2, ⌈sweep ÷ (π ÷ 24)⌉); pᵢ = c + r × (cos aᵢ, sin aᵢ), aᵢ = a₀ ± sweep × i ÷ n

  3D solid commands: sizes, paths and reported volume commands3d.js

  • CadCraft
  64-bit

• Extrude: outline, height and taper to model units

  Converts the picked outline and the typed height and taper angle into the numbers the solid is made from.

  ring = (x × k, y × k); height = h × k; taper = degrees × π ÷ 180

  3D solid commands: sizes, paths and reported volume commands3d.js

  • CadCraft
  64-bit

• Revolve angle

  The angle a profile is turned through; no angle means a full turn.

  θ = 2π if |angle| < 1e-9, else angle

  3D solid commands: sizes, paths and reported volume commands3d.js

  • CadCraft
  64-bit

• Meters per unit

  The length of a meter, an international foot and a US survey foot in meters.

  m = 1; ft = 0.3048; ftUS = 1200 ÷ 3937

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  Exact

• Local system to grid and back

  Moves a point between project (ground or assumed) coordinates and grid coordinates.

  grid = to + k × R(θ) × (p − from); p = from + R(θ)ᵀ × (grid − to) ÷ k

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Project point to longitude and latitude and back

  The longitude and latitude (WGS 84) of a project point, and the project point of a longitude and latitude.

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Grid scale factor, convergence and elevation factor

  At a project point: the grid scale factor, the meridian convergence in degrees, the elevation factor and the combined factor.

  k_N = |p(φ+d) − p(φ−d)| ÷ (2 M d); k_E = |p(λ+d) − p(λ−d)| ÷ (2 N cos φ d); k = (k_N + k_E) ÷ 2; γ = −atan2(Δx, Δy); elevation = R ÷ (R + h), R = √(M N)

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Local system from two control points

  The scale and rotation that carry two points known in both local and grid coordinates onto each other.

  scale = |B − A| ÷ |b − a|; rotation = atan2(grid) − atan2(local), in degrees, brought into −180 to 180

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Ground coordinates about a base point

  A local system that scales by a combined factor about one base point, with no rotation.

  scale = combined; rotation = 0; from = to = base

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Any system to any system

  Converts a coordinate pair from one system's definition to another's.

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Matching a .prj to a catalog system

  Decides whether the projection in a .prj file is one of the catalog's systems, and if so uses the catalog's definition.

  |a − a′| < 1e-3; |e² − e′²| < 1e-9; distance at each of 3 probe points < 1e-3 (1e-9 for geographic)

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Probe points for matching

  Three longitude and latitude points inside a projection's zone, used to compare two definitions.

  (λ₀, φ), (λ₀ + 0.5°, φ + 0.5°), (λ₀ − 0.5°, φ + 0.25°)

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Linear unit of a .prj

  Decides whether a projection is in meters, international feet or US survey feet.

  |k − 1| < 1e-12 → m; |k − 0.3048| < 1e-10 → ft; |k − 1200 ÷ 3937| < 1e-10 → ftUS

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Extent of a grid shift file

  The west, south, east and north limits, in degrees, of the area a loaded grid shift file covers.

  east = −λ_ll × 180 ÷ π; west = −(λ_ll + (n_λ − 1) × Δλ) × 180 ÷ π; north = (φ_ll + (n_φ − 1) × Δφ) × 180 ÷ π

  Coordinate reference systems crs.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• UTM zone to EPSG code

  The EPSG number of a UTM zone typed as text such as UTM 33N.

  WGS 84: 32600 + zone (north), 32700 + zone (south); NAD83: 26900 + zone; ETRS89: 25800 + zone; GDA94: 28300 + zone; GDA2020: 7800 + zone

  Coordinate reference systems crs-pick-shared.js

  • CadCraft
  • BimCraft
  • CivilCraft
  Exact

• Linear unit of a typed definition

  Decides whether a typed projection definition is in meters, international feet, US survey feet or degrees.

  |k − 1| < 1e-12 → m; |k − 0.3048| < 1e-10 → ft; |k − 1200 ÷ 3937| < 1e-10 → ftUS

  Coordinate reference systems crs-pick-shared.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Probe points for a typed definition

  Three longitude and latitude points inside the definition's zone, used to compare it with catalog systems.

  Coordinate reference systems crs-pick-shared.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Matching a typed definition to the catalog

  Finds the catalog systems that give the same easting and northing as a typed definition.

  same projection family; |a − a′| ≤ 1e-3; |e² − e′²| ≤ 1e-9; distance at each of 3 probe points < 1e-3

  Coordinate reference systems crs-pick-shared.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Round-trip check of a typed definition

  Refuses a typed projection that does not return its own probe point.

  |inverse(forward(λ, φ)) − (λ, φ)| < 1e-6 degrees in each of λ and φ

  Coordinate reference systems crs-pick-shared.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Do two systems give the same coordinates

  Says whether two systems give the same easting and northing.

  same unit and distance at each of 3 probe points < 1e-3

  Coordinate reference systems crs-pick-shared.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Block size from its label

  The width and height of a diagram block.

  w = longest line × th × 0.62 + 3 × th; h = (lines × 1.3 + 1.7) × th; diamond: w × 1.5, h × 1.6; minimum width 8 × th (diamond 10 × th)

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Symbol scale in a block

  The factor that fits a symbol drawing into a box of six text heights.

  k = 6 × th ÷ max(w, 1.4 × h)

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Symbol geometry scaled and moved

  Scales a symbol's lines, circles, arcs, polylines, hatches and text by k and moves them to the block.

  x′ = x × k + dx; y′ = y × k + dy; r′ = r × k

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Block coordinates

  The x and y of every block in a layered diagram.

  x = previous edge + w ÷ 2, gap 2.5 × th; y = Σ (layer height + 4 × th); then x → mean of neighbors' x, kept in order with the gap

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Sequence diagram positions

  The x of each lifeline and the y of each message row in a sequence diagram.

  gap ≥ 2.5 × th and ≥ (label length × th × 0.8 × 0.62 + 2 × th) ÷ lifelines crossed; row = 3.4 × th; top = box height + 2.6 × th

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Layout to drawing coordinates

  Places the laid-out diagram at a point in the drawing, turning y from downward to upward.

  X = x + px − minX; Y = y − (py − minY)

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Arrowhead triangle

  The three corners of a connector's filled arrowhead.

  u = (to − from) ÷ |to − from|; corners: to, to − u × s ± n × 0.35 × s

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Measured value

  The length, radius, diameter or angle a dimension reports.

  linear = |(p₂ − p₁) · (cos r, sin r)|; aligned = |p₂ − p₁|; radius = |p₁ − c|; diameter = 2 × |p₁ − c|; angular = sweep

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Sector of an angular dimension

  The start angle, end angle and counterclockwise sweep an angular dimension measures.

  a₁ = atan2(p₁ − c); a₂ = atan2(p₂ − c); sweep = (end − start) mod 2π

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Ends of the dimension line

  Where the two extension lines meet the dimension line, square or at an obliquing angle.

  square: q = loc + u × ((p − loc) · u); oblique: q = p + d × ((loc − p) · n) ÷ (d · n)

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Angular dimension between two lines

  The vertex where two lines cross and a point on each leg bounding the sector that holds the text point.

  den = d₁ × d₂; t = ((l₂ − l₁) × d₂) ÷ den; c = l₁ + d₁ × t

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Linear and aligned dimension parts

  The extension lines, dimension line, arrowheads and text point of a linear or aligned dimension.

  extension line: from p + exo to q + exe; arrows inside when length ≥ 2 × asz; text at the middle, offset by gap

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Angular dimension parts

  The arc, extension lines, arrowheads and text point of an angular dimension.

  R = |loc − c|; arc from a₀ to a₁ at R; arrows outside when R × sweep < 2 × asz; text at c + (R + gap) at a₀ + sweep ÷ 2

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Radius and diameter dimension parts

  The center mark, leader or dimension line, arrowheads and text point of a radius or diameter dimension.

  r = |p₁ − c|; P = c + r × (cos u, sin u); Q = c − r × (cos u, sin u); center mark half-length = asz ÷ 2

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Closed arrowhead

  The three corners of the default filled arrowhead.

  base = tip − asz along the arrow; corners = base ± asz ÷ 6 across

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Text for a measurement

  The main text, alternate-unit text and tolerance text a dimension style writes for a measured value.

  m = round(v × |lfac|, rnd); alternate = round(m × altf, altrnd); limits: upper = base + tp, lower = base − tm

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Decimal number text

  Writes a value with a fixed number of decimal places and the style's zero suppression.

  d = clamp(round(dec), 0, 8); |v| < 0.5 × 10⁻ᵈ → 0; text = v to d places

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Round-off to a multiple

  Rounds a value to the nearest multiple of the style's round-off.

  r > 0: Math.round(v ÷ r) × r; else v

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Length text

  Writes a length as a decimal number or, for other unit formats, through the shared length formatter.

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Angle text

  Writes an angle in decimal degrees, degrees-minutes-seconds, grads or radians.

  degrees = radians ÷ (π ÷ 180); minutes = (degrees − ⌊degrees⌋) × 60; seconds = (minutes − ⌊minutes⌋) × 60; grads = degrees ÷ 0.9

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Millimeters in each text unit

  The size of the units a dimension can write its value in.

  mm = 1; cm = 10; m = 1000; km = 1 000 000

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  Exact

• Measurement scale for a text unit

  Sets the scale that makes a dimension write its value in mm, cm, m or km.

  lfac = mmPerUnit ÷ mm in the unit

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Which text unit a style writes

  Recognizes a style's scale and suffix as mm, cm, m or km, as drawn, or custom.

  |lfac − mmPerUnit ÷ unit| ≤ 1e-9 × max(1, lfac); as drawn: |lfac − 1| < 1e-12

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Millimeters in one drawing unit

  The size of a drawing unit, or of a sheet's paper unit, in millimeters.

  paper in inches: 25.4; paper in mm: 1; model: mmPerDrawingUnit; unitless: 1 (assumed)

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Refit after the drawing units change

  Gives dimensions that write in mm to km a new scale when the drawing's unit changes.

  lfac′ = new mm per unit ÷ mm in the unit

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Arrowhead shapes

  The lines, circle or filled outline of each arrowhead style at a tip, direction and size.

  half-width = size ÷ 6; open 30°: tan(15°) × size; dot radius = size ÷ 4 (small: size ÷ 8), drawn with 16 sides; tick at 45°, half-length size ÷ 2

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Number rounded for comparison

  The text a number is compared by: its value on a grid of 0.0001.

  Math.round(v ÷ 0.0001) × 0.0001, written with at most 4 decimals

  Drawing compare drawing-compare.js

  • CadCraft
  64-bit

• Center and size of an object

  The middle of an object's bounding box and the length of its diagonal, used to pair objects.

  cx = (minX + maxX) ÷ 2; cy = (minY + maxY) ÷ 2; d = √((maxX − minX)² + (maxY − minY)²)

  Drawing compare drawing-compare.js

  • CadCraft
  64-bit