Calculations

Calculations

• 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

• Intersection sight distance

  The sight distance along the major road for a driver turning out of the minor road, in meters.

  ISD = 0.278 × V × (t_g + 0.5 × extra lanes)

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Sight triangle

  The three corners of the sight triangle from the driver's position and the two leg lengths.

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Obstacles in the sight triangle

  Which obstacle outlines reach into the sight triangle.

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Offset line

  A polyline moved sideways by a distance, with mitred corners.

  corner shift = d × min(4, 1 ÷ max(cos(half turn), 0.25)) along the mitre

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Part of a line between two distances

  Cuts a polyline to the stretch between two distances along it.

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Dash positions

  The painted lengths of a dashed line.

  dash k starts at from − phase + k × (dash + gap)

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Striping and its quantities

  Lays out center, lane and edge lines and totals the painted length and painted area.

  length per kind = Σ line lengths; painted area = Σ length × width

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Crosswalk bars

  The number and position of crosswalk bars across a road.

  count = max(1, ⌊(width + gap) ÷ (bar + gap)⌋); bar i starts at −used ÷ 2 + i × (bar + gap)

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Sign positions

  The plan position and facing of each sign from its station, side and offset.

  position = point at station + normal × side × offset; repeating signs every `every` from `from`

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• Road quantities

  Totals intersection pavement area, curb return length, striping length, painted area and sign count.

  Road intersections, striping and signs intersection.js

  • CivilCraft
  64-bit

• A number as LandXML text

  Formats every number the export writes.

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

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Northing, easting and elevation

  Writes a point as northing, easting and elevation.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Spiral element

  Writes a transition curve: length, radii, station, angle, total X and Y, long and short tangents, constant.

  theta (degrees) = θ × 180 ÷ π; constant = √(r × L_s)

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Curve element

  Writes a circular curve: radius, length, station, chord, delta, tangent, external and middle ordinate.

  delta (degrees) = Δ × 180 ÷ π

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Existing-ground profile

  Writes the ground line along an alignment as station and elevation pairs.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Surface definition

  Writes a surface's plan area, surface area and highest and lowest elevations, then its points and faces.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Pipe length and slope

  Writes each pipe's plan length and slope.

  length = hypot(Δx, Δy); slope = (invert up − invert down) ÷ length

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Feature-line arc from a bulge

  The center, radius, sweep and length of an arc segment of a feature line.

  k = (1 − b²) ÷ 4b; r = c(1 + b²) ÷ 4|b|; sweep = 4·atan b; L = r × |sweep|

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Reading numbers

  Splits a text list on spaces and commas and parses each number.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Units of a file

  Decides whether the file is metric or in feet from its linear unit.

  LandXML export and import landxml.js

  • CivilCraft
  Exact

• Alignment elements to PIs

  Turns lines, curves and spirals into PIs with radius and spiral lengths.

  PI = p₁ + d₁·a, a = ((p₂ − p₁) × d₂) ÷ (d₁ × d₂)

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• PI of a plain curve without one

  Where the tangents at a curve's start and end meet, from its center.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Curve to bulge

  The bulge of a feature-line arc from its start, center and end.

  sweep = (a₁ − a₀) mod 2π; bulge = ± tan(sweep ÷ 4)

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Sump depth of a structure

  The depth of a structure's sump below its lowest pipe invert.

  sump depth = max(0, lowest invert − sump elevation)

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Joining feature-line pieces

  Joins consecutive lines and curves of a plan feature into one line.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Scaling an import to project units

  Multiplies every coordinate, elevation, station, radius and length of an import by one factor.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Mass ordinate

  The running total of earth along the alignment, and the cut and fill totals.

  m_i = m_(i−1) + cut_i × factor − fill_i

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Balance points

  The stations where the mass ordinate crosses zero.

  sta = sta_a + (sta_b − sta_a) × m_a ÷ (m_a − m_b)

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Volume moved and average haul

  For each balanced stretch, the volume moved and the average distance it travels.

  volume = |peak| − |end level|; haul = ∫ (|m| − |end level|)⁺ d(sta) ÷ volume

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Totals and what is left over

  Total cut, adjusted cut, fill, the end ordinate, and whether the job wastes, borrows or balances.

  balanced when |end| < 1e-6 × max(1, cut + fill)

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• CSV export

  Writes the stations, ordinates and spans as a CSV file in cubic yards or cubic meters.

  cubic yards = cubic feet ÷ 27

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Footprint and floor area of an option

  The footprint area and gross floor area of each alternative, in square meters.

  area (m²) = |A| ÷ 10⁶; gross = area × floors

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Is the footprint a simple polygon

  Refuses a footprint whose edges cross.

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Turning and moving a footprint

  Rotates a footprint about its centroid and moves it to a position.

  x′ = t_x + (x − c_x)·cos a − (y − c_y)·sin a; y′ = t_y + (x − c_x)·sin a + (y − c_y)·cos a

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Placing an option in the envelope

  The position and rotation at which as much of the footprint as possible lies inside the buildable envelope.

  k = 0.001 ÷ meters per project unit; inside = area(envelope ∩ footprint) ÷ area(footprint)

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Option to a mass

  Makes a project mass from a placed option, with its floor height in project units.

  floor height = mm × 0.001 ÷ meters per project unit

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Envelope file

  Writes the buildable envelope in millimeters, turned so its longest edge lies along x.

  mm = meters per project unit × 1000; value = round(v × 10) ÷ 10

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Footprint area

  The signed area of a mass outline.

  A = Σ (x_i·y_j − x_j·y_i) ÷ 2

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Gross floor area and height

  The floor area of all floors and the height of the mass.

  GFA = |A| × floors; height = floors × floor height

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Centroid

  The center of area of the outline.

  c_x = Σ (x_i + x_j)·k_ij ÷ 6A, k_ij = x_i·y_j − x_j·y_i

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Ground under a mass

  The lowest, highest and mean ground elevation under the footprint, and the samples used for earthwork.

  sample (i, j) at x₀ + (i + 0.5)·dx, y₀ + (j + 0.5)·dy; dA = |A| ÷ samples; mean = Σ z ÷ n

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Ground floor level

  The level the mass is set at: the mean ground, the highest ground (podium) or the lowest (cut in).

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Cut and fill under a mass

  The earth to remove above the ground floor level and to place below it.

  fill = Σ (z₀ − z)·dA where z < z₀; cut = Σ (z − z₀)·dA otherwise

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Floor levels

  The elevation of each floor and its top.

  z_i = z₀ + i × floor height

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Floors for a pulled height

  The floor count nearest to a height set by push and pull.

  floors = clamp(round(H ÷ floor height), 1, 200)

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  Exact