Calculations

Calculations

• Parcel outline with arcs as chords

  The parcel boundary as points, with each curved course replaced by short chords.

  n = max(2, ⌈Δ ÷ (π ÷ 36)⌉); point k = center + R·(cos, sin)(a₀ + turn·Δ·k ÷ n)

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• Assembly description text

  The road assembly written as words and numbers in the IFC properties.

  IFC export: geometry and quantities gathered from the project ifc-civil-model.js

  • CivilCraft
  64-bit

• A real number as IFC text

  Formats every number the export writes.

  text = v.toFixed(d) with trailing zeros removed; d = 6 unless stated

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Points and directions

  Writes a Cartesian point and a direction.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• File origin

  The local origin that coordinates are written from: the middle of the content rounded to 100 units.

  origin = round((min + max) ÷ 200) × 100

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  Exact

• Unit factor to SI

  Meters per file unit, and the conversion of areas and volumes to square and cubic meters.

  um = 1, 0.3048 or 1200 ÷ 3937; m² = a × um²; m³ = v × um³

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  Exact

• Conversion factor in the file

  Writes the foot's length in meters into the file's unit definition.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Property values and quantities

  Writes lengths, areas, volumes, ratios, speeds and counts in property sets and quantity sets.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Surface area written with a mesh

  The area of a surface, corridor part or slope in square meters.

  area = Σ |(b − a) × (c − a)| ÷ 2 × um²

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Triangle meshes

  Writes a surface or solid as a point list and triangles.

  x′ = x − origin_x, written with 6 decimals

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Site latitude and longitude

  Writes a latitude or longitude as degrees, minutes, seconds and millionths of a second.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Map conversion

  The grid easting and northing of the file origin, and the rotation and scale of a local ground system.

  E₀ = to_x + s·(cos r·Δx − sin r·Δy); N₀ = to_y + s·(sin r·Δx + cos r·Δy)

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• PI and PVI tables as text

  Writes each alignment's PIs and PVIs into a property set, which is what CivilCraft reads back from IFC4 and IFC2x3 files.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Continuity between horizontal segments

  Decides whether two neighboring segments are written as continuous, same direction, or same direction and curvature.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Spiral terms

  The constants of Bloss, cosine, sine and Helmert transition curves.

  A_i = L × |a_i|^(−1/n) × sign a_i; f = L ÷ R₁ − L ÷ R₀; a₀ = L ÷ R₀

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Clothoid constant

  The constant A of a clothoid transition.

  A = L ÷ √|f| × sign f

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Cubic parabola coefficient

  The coefficient of y = x³ ÷ (6·R·Lp) for a cubic transition.

  A₃ = 1 ÷ (6 × R × Lp)

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Horizontal segment parameters

  Writes a segment's start point, start direction, radii and length.

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Vertical segment parameters and curve

  Writes each grade or vertical curve: start distance, height, gradients, and the curve as a line or a polynomial.

  C = (g₁ − g₀) ÷ (2L); line length = L ÷ cos(atan g₀); curve length = parabola length

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Length along a parabola

  The true length of a vertical curve y = A + Bx + Cx² over its horizontal length.

  F(x) = (d·√(1 + d²) + asinh d) ÷ 4C, d = B + 2Cx; length = F(L) − F(0)

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Cant axis

  The leaning axis of a cant segment from the height difference of the two rails.

  dy = 2 × half difference; dz = √(max(0, base² − dy²)); axis = (0, dy ÷ base, dz ÷ base)

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Helmert cant halves

  The two second-order spirals of a Helmert cant transition and the slope where they meet.

  slope = (L ÷ 2)² × (2·(L ÷ 2) ÷ A₂³)

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Sleeper placement axes

  The three axes of each sleeper from its direction across the track and the cross slope.

  A₁ = (across_x, across_y, slope) ÷ |…|; A₂ = (−across_y, across_x, 0); A₃ = A₁ × A₂

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Pipe solid

  A pipe as a circle swept from the upstream to the downstream invert.

  L₃ = hypot(Δx, Δy, Δz); axis = Δ ÷ L₃; start z = invert + D ÷ 2

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Rail weight

  The weight of each rail from its length and section.

  weight = length × um × kg per meter

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• Design speed in meters per second

  Converts a design speed in km/h or mph for the road design property.

  m/s = km/h ÷ 3.6; m/s = mph × 0.44704

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  Exact

• Building mass footprint and height

  The footprint area, height and gross floor area written for each building mass.

  footprint = |Σ (x_i·y_j − x_j·y_i)| ÷ 2; height = floors × floor height

  IFC export: numbers written to the file ifc-civil.js

  • CivilCraft
  64-bit

• File units to project units

  The factor that turns a length in the file into a length in the project.

  k = file unit in meters ÷ (1 or 1200 ÷ 3937)

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• File coordinates to project coordinates

  Moves a point through the file's map conversion, or adds the file's stored origin, and scales it to project units.

  p′ = (M · p) × k or p′ = (p + origin) × k

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Where a horizontal segment ends

  The end point and end direction of a line, arc, cubic parabola or transition curve.

  arc: center = start ∓ r·(sin, −cos)(dir), end at angle a₀ + L ÷ r; transition: x = ∫cos θ(u) du, y = ∫sin θ(u) du

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Crossing of two tangents

  The PI: where the tangent into a curve meets the tangent out of it.

  s = ((q − p) × v) ÷ (u × v); PI = p + u·s

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Horizontal layout to PIs

  Turns a chain of lines, arcs and transitions into PIs with radius and spiral lengths.

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Vertical layout to PVIs

  Turns grades and vertical curves into PVIs with station, elevation and curve length.

  curve: sta = d₀ + L ÷ 2, z = z₀ + g₀·L ÷ 2; end: z = z₀ + (g₀ + g₁) ÷ 2 × L

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Horizontal segment values

  Reads a segment's start point, direction, radii and length into project units.

  length × (map scale × k); direction × angle unit + rotation

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Vertical segment values

  Reads a vertical segment's start distance, length, height and gradients.

  z₀ = (height × map scale + map height) × k

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• IFC 4x1 vertical curves

  Reads an IFC 4x1 vertical segment and works out the end grade of a curve from its radius.

  g₁ = g₀ ± L ÷ R_v

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Applied cant of a curve

  The cant of each curve from the constant-cant segment over its middle.

  E = right − left (or left − right); stored = round(E × 1000) ÷ 1000

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• CivilCraft's own PI and PVI tables

  Reads the PI and PVI tables CivilCraft wrote into an IFC4 or IFC2x3 file.

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Element geometry into project coordinates

  Moves each mesh vertex through its placement and then into project coordinates.

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• Terrain corners joined into points

  Turns a terrain's separate triangles into one point list and faces.

  IFC import: alignments, surfaces and units ifc-civil-read.js

  • CivilCraft
  64-bit

• A real number as IFC text

  Formats every number this file writes.

  text = v.toFixed(d) with trailing zeros removed; d = 9 unless stated

  Building masses as IFC ifc-massing.js

  • CivilCraft
  64-bit

• US survey foot

  Meters in a US survey foot, shared with the project IFC export.

  1200 ÷ 3937

  Building masses as IFC ifc-massing.js

  • CivilCraft
  Exact

• Latitude and longitude

  Writes an angle as degrees, minutes, seconds and millionths of a second.

  Building masses as IFC ifc-massing.js

  • CivilCraft
  64-bit

• Footprint area

  The signed area of a mass outline; its sign sets the direction the outline is written in.

  A = Σ (x_i·y_j − x_j·y_i) ÷ 2

  Building masses as IFC ifc-massing.js

  • CivilCraft
  64-bit

• File origin

  The origin footprints are written from: the middle of the masses rounded to 10 units, at the lowest ground floor level.

  origin = round((min + max) ÷ 20) × 10

  Building masses as IFC ifc-massing.js

  • CivilCraft
  Exact

• Height and areas of a mass

  The height, footprint area and gross floor area written in the mass's properties.

  H = floors × floor height; footprint (m²) = A × um²; gross = A × floors × um²

  Building masses as IFC ifc-massing.js

  • CivilCraft
  64-bit

• Simple curb return

  The circular arc joining two pavement edges at a corner: tangent points, center, arc length.

  ψ = acos(a · b); T = r ÷ tan(ψ ÷ 2); center = corner + bisector × r ÷ sin(ψ ÷ 2); length = r × |Δ|

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Three-center curb return

  A compound curve of three arcs (radii 2r, r, 2r by default) between two pavement edges.

  angles = share·Δ, (1 − 2·share)·Δ, share·Δ; T = p_x − p_y·cos h ÷ sin h; length = Σ chord lengths

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Intersection outline, area and curb length

  The closed pavement edge of an intersection, its area and the total length of its curb returns.

  corner: p_a + s·d_a = p_b + t·d_b, s = ((p_b − p_a) × d_b) ÷ (d_a × d_b); area = |shoelace(outline)|

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Polygon area

  The signed area of an outline.

  A = Σ (x_i·y_j − x_j·y_i) ÷ 2

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit