Calculations

Calculations

• Affine through three points

  The affine transform that carries three source points onto three destination points.

  det = (u₁ − u₀)(v₂ − v₀) − (u₂ − u₀)(v₁ − v₀); a = ((x₁ − x₀)(v₂ − v₀) − (x₂ − x₀)(v₁ − v₀)) ÷ det

  Map pictures warped onto the plan basemap.js

  • CadCraft
  • BimCraft
  • CivilCraft
  32-bit, display only

• Cells of a warped picture

  The cells a picture is cut into so that each can be drawn with one affine transform.

  split while max |affine(p) − exact(p)| > tol over the fourth corner, the middle and the four edge midpoints

  Map pictures warped onto the plan basemap.js

  • CadCraft
  • BimCraft
  • CivilCraft
  32-bit, display only

• Tile level for the screen

  Which level of a tile grid is drawn at the current zoom.

  the coarsest level with res ≤ 1.5 × screen resolution

  Map pictures warped onto the plan basemap.js

  • CadCraft
  • BimCraft
  • CivilCraft
  32-bit, display only

• 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

• A group value by its code

  Turns one group's text into a real number, a whole number, a true or false, or text.

  codes 10–59, 110–149, 210–239, 460–469, 1010–1059: parseFloat; 60–99, 160–179, 270–289, 370–389, 400–409, 420–429, 440–459, 1060–1071: parseInt

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Arc angles

  An arc's start and end angles in radians.

  angle = degrees × (π ÷ 180)

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Multi-line text direction

  The direction vector of multi-line text, from the file's vector or from its rotation angle.

  x axis = group 11 when present; otherwise (cos(a), sin(a)), a = degrees × (π ÷ 180)

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Hatch arc and ellipse edges

  The center, radius or axes, and start and end angles of the curved edges of a hatch boundary.

  angle = degrees × (π ÷ 180); missing end angle = 360 degrees

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• abs, round, ceil and floor

  The four functions an expression may call.

  round(x) = floor(x + 0.5) for x ≥ 0, −floor(−x + 0.5) for x < 0; ceil(x) = ⌈x − 1e-9·max(1, |x|)⌉; floor(x) = ⌊x + 1e-9·max(1, |x|)⌋

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Adding and subtracting

  Sums and differences of lengths, left to right.

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Multiplying and dividing

  Products and quotients of a length and plain numbers, left to right.

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• The answer

  The final value and whether it is a length or a plain number.

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Unit sizes

  Builds each unit's row: its fraction of the base unit and the factor used for quick conversion.

  factor = n ÷ d (× π for degrees and gons)

  Unit table: reading and writing values unit-table.js Every app
  Exact

• Numbers and fractions

  Reads 6, 6.5, 6 1/2, 6-1/2 or 1/2 as a number.

  whole + numerator ÷ denominator

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Feet and inches

  Reads 12'6", 12'-6 1/2" or 6" as inches.

  inches = feet × 12 + inches

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Degrees, minutes and seconds

  Reads 45°30'15" or 45d30m15s as degrees.

  degrees + minutes ÷ 60 + seconds ÷ 3600

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Slopes

  Reads 2%, 3H:1V, 1:3 or 6/12 as a grade (rise over run).

  percent ÷ 100; H:V → V ÷ H; rise:run → rise ÷ run

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Writing feet and inches

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

  n = round(|inches| × den); feet = ⌊n ÷ 12den⌋; inches = ⌊rest ÷ den⌋; fraction = rest ÷ den, reduced

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Writing degrees, minutes and seconds

  Writes an angle as degrees, minutes and seconds.

  t = round(|degrees| × 3600 × 10^dec); split by 3600 and 60

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• Writing decimals

  Writes a number with a fixed count of decimals.

  text = v.toFixed(dec)

  Unit table: reading and writing values unit-table.js Every app
  64-bit

• A level written as text

  Reads a level such as 104.37, +104,37 or EL 104.37 from a text.

  value = Number(whole digits . decimal digits) × sign

  Survey levels from text and the survey check survey.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Levels into project units

  A level point's x, y and z in project units.

  x·k, y·k, z·k

  Survey levels from text and the survey check survey.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Extent and distance from the origin

  How far the data spans and how far it lies from zero, in meters.

  span = |(maxX − minX, maxY − minY)| × m per unit; far = max |coordinate| × m per unit

  Survey levels from text and the survey check survey.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Median

  The middle value of a list of levels.

  odd count: the middle value; even: mean of the two middle values

  Survey levels from text and the survey check survey.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Level outliers

  Counts levels that are far from the rest, and levels of exactly 0 that look like missing heights.

  MAD = median(|z − median|) × 1.4826; limit = max(6 × MAD, 5 m); outlier when |z − median| > limit

  Survey levels from text and the survey check survey.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Duplicate points

  Counts points that sit on top of another point, with the same or a different level.

  cell = 1 mm; key = (round(x ÷ cell), round(y ÷ cell)); same level when |Δz| ≤ cell

  Survey levels from text and the survey check survey.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Height unit factor

  The factor that turns a file's heights into the project's unit.

  factor = meters per file unit ÷ meters per project unit

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Cell center in the file's coordinates

  The x and y of a raster cell's center.

  x = g₀ + (col + 0.5)·g₁ + (row + 0.5)·g₂; y = g₃ + (col + 0.5)·g₄ + (row + 0.5)·g₅

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Cells inside a box

  The range of columns and rows whose centers can fall inside a picked box.

  (col, row) = G⁻¹·(x − g₀, y − g₃) − 0.5; c₀ = ⌈min − 1e-9⌉, c₁ = ⌊max + 1e-9⌋ + 1

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• A box through a coordinate conversion

  The box round a rectangle after its outline is converted to another coordinate system.

  17 points along each side, converted, then minimum and maximum

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Survey points from a grid

  One survey point per grid node that has a height.

  (x, y) = conversion(cell center); z = file height × unit factor

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Grid surface

  A triangulated surface from the grid: two triangles per cell.

  cell corners a (SW), b (SE), c (NE), d (NW): triangles a–b–c and a–c–d

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• 1-2-5 step

  Rounds a step up to 1, 2 or 5 times a power of ten.

  p = 10^⌊log₁₀ x⌋; m = x ÷ p; 1, 2, 5 or 10 × p

  Elevation grids into survey points and a grid surface terrain.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Guard on every written measure

  Decides what is written when a value is missing or not a number.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit