Calculations

Calculations

• Point on a placed transition

  The project coordinates and direction at a distance along a transition element.

  p = p₀ + R(dir₀)·(x, ±y)

  Transition curves and sampled alignment geometry alignment.js

  • CivilCraft
  64-bit

• Nearest point on a transition

  The station on a transition closest to a given point, for station and offset.

  Transition curves and sampled alignment geometry alignment.js

  • CivilCraft
  64-bit

• Alignment as a polyline

  The alignment as vertices for linework and export: arcs and transitions become chords.

  pieces = max(1, ⌈turn ÷ maxTurn⌉, ⌈length ÷ maxSeg⌉); default maxTurn = 0.5°

  Transition curves and sampled alignment geometry alignment.js

  • CivilCraft
  64-bit

• Transitions as straight pieces

  Each transition cut into short lines so that crossings with other linework can be found; lines and arcs are kept exact.

  pieces = max(4, ⌈θ ÷ 0.25°⌉)

  Transition curves and sampled alignment geometry alignment.js

  • CivilCraft
  64-bit

• Meters per drawing unit

  The length of each $INSUNITS drawing unit in meters.

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  Exact

• Drawing units to project units

  The factor every imported coordinate is multiplied by.

  inch, yard, mile into feet: meters ÷ 0.3048; metric into feet: meters ÷ (1200 ÷ 3937); into meters: meters ÷ 1

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Object coordinate system

  The rotation from an entity's own coordinate system to world coordinates, from its extrusion direction.

  Az = N ÷ |N|; Ax = (Wy or Wz) × Az, normalized; Ay = Az × Ax

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Composing transforms

  The product of two 3×4 affine transforms, used for nested block references.

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Block reference placement

  The transform of one block reference: base point, scale, array spacing, rotation, insertion point and extrusion.

  M = parent · OCS · T(insert) · R(rotation) · T(column, row) · S(scale) · T(−base)

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Arcs and circles as vertices

  Points along a circular arc, at most 5° apart.

  n = max(2, ⌈sweep ÷ 5°⌉); p = c + r·(cos a, sin a)

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Polyline bulges as vertices

  The arc between two polyline vertices that carry a bulge, as intermediate points.

  θ = 4·atan(bulge); r = chord ÷ (2·sin(θ/2)); center = chord middle + r·cos(θ/2) along the normal

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Splines as vertices

  Points along a B-spline, rational or not, sampled evenly in its parameter.

  samples = min(4000, max(16, 32 × (control points − degree)))

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Splines stored as fit points only

  A smooth curve through the fit points when the file gives no control points.

  centripetal Catmull-Rom: knot step = √(distance between points); 8 vertices per span

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Ellipses as vertices

  Points along an ellipse or elliptical arc.

  minor = ratio × (N × major); p = c + major·cos s + minor·sin s

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• One elevation per object, and flat objects

  The ELEV attribute of an imported object, and whether its vertices keep a z at all.

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Feature lines read back from a drawing

  The vertices of a feature line written earlier by CivilCraft, scaled into project units.

  x, y, z × scale

  DWG and DXF linework into project units cad-linework.js

  • CivilCraft
  64-bit

• Survey point from a block's insertion point

  The world position of each block reference, and of each cell of an arrayed reference, in project units.

  world = OCS · insert; array cell offset rotated by the reference's rotation; × unit scale

  DWG and DXF linework into project units block-points.js

  • CivilCraft
  64-bit

• Number from attribute text

  The elevation or number read from a block attribute such as EL 105.32.

  DWG and DXF linework into project units block-points.js

  • CivilCraft
  64-bit

• Elevation kept for a block point

  Which elevation a point made from a block gets: the insertion z, an attribute, or none.

  DWG and DXF linework into project units block-points.js

  • CivilCraft
  64-bit

• Number from file text

  A coordinate, angle, distance or height read from a field of the file.

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Dotted degrees, minutes, seconds to radians

  An angle written as DDD.MMSSss, as many data collectors write it, as radians.

  angle = (D + M ÷ 60 + S ÷ 3600) × π ÷ 180

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Degrees or gons to radians

  A file angle in decimal degrees or gons as radians.

  degrees × π ÷ 180; gons × π ÷ 200

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• GSI word to a length or angle

  The value of a GSI data word from its digits and its unit code.

  millimeters ÷ 1000; 1/10 mm ÷ 10⁴; 1/100 mm ÷ 10⁵; gon or degree counts ÷ 10⁵; sexagesimal digits split into D, M, S

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Polar reduction

  Northing, easting and elevation of every shot from its setup.

  orientation = atan2(ΔE, ΔN) to the backsight − circle reading; hd = sd·sin(vz)·scale; N = N₀ + hd·cos(az), E = E₀ + hd·sin(az); Z = Z₀ + sd·cos(vz) + hi − hr

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Shots as adjustment observations

  Directions and horizontal distances with their standard deviations, and starting coordinates for the free points.

  σ(direction) = 5″ = (5 ÷ 3600) × π ÷ 180; σ(distance) = 0.005

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Section stations

  The stations at which the corridor is built.

  s = ⌈from ÷ step⌉·step, then s += step; each rounded to 6 decimals

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Lane edge and shoulder point (simple assembly)

  The edge of pavement and the shoulder's outer edge on one side of one section, with any width or elevation target applied.

  edge z = z₀ − lane width × slope; shoulder z = edge z − shoulder width × shoulder slope

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• One side of a section from its parts

  Every point of a side from the centerline out: lanes, gutter, curb, strip, walk, then the daylight point.

  t += width; z −= width × slope (curb: z += height)

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Where a section meets a target line

  The distance out along a section to the first crossing of a 3D polyline, and the line's elevation there.

  t = (w × d) ÷ (u × d); z = z_a + s·(z_b − z_a)

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Do two sections cross

  Whether neighboring sections intersect, which happens inside a curve tighter than the corridor is wide.

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Pavement course area and volume

  The plan area and the volume of each pavement course along the corridor.

  area = Σ (w₁ + w₂) ÷ 2 × Δstation; volume = area × thickness

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Systems the coordinates fit

  The catalog systems in which a project point falls inside the system's area of use.

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Latitude and longitude as degrees, minutes, seconds

  The status bar text for a latitude or longitude.

  seconds = round(|v| × 360000) ÷ 100, then split into D, M, S

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Latitude and longitude as decimal degrees

  The status bar text in decimal degrees.

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Typed latitude or longitude

  A typed angle, decimal or in degrees, minutes and seconds, with a sign or a hemisphere letter.

  value = ±(D + M ÷ 60 + S ÷ 3600)

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Local fit: project to grid

  Grid coordinates of a project point through a scale, rotation and shift.

  grid = to + scale · R(rotation) · (p − from)

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Misclosure of a third control point

  How far a two-point fit puts a third known point from its grid coordinates, as a distance and in parts per million.

  ppm = distance ÷ span × 10⁶

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Converting a project's coordinates

  Every stored x and y of the project (points, breaklines, boundary, alignment PIs, pads, structures) passed through a conversion.

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Runoff depth by curve number

  The depth of runoff from a depth of rain.

  S = 25400 ÷ CN − 254; Q = (P − 0.2S)² ÷ (P + 0.8S) for P > 0.2S

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Runoff hydrograph (triangular unit hydrograph)

  Flow against time from a catchment for a storm, with its peak and volume.

  Tp = Δt ÷ 2 + 0.6·Tc; qp = 0.208·A ÷ Tp; base = 2.67·Tp; Q(t) = Σ ΔQₖ·u(t − k·Δt)

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Runoff hydrograph (rational method)

  A trapezoid hydrograph from the rational method peak.

  Qp = C·i·A ÷ 360 (i in mm/h, A in hectares, Q in m³/s)

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Stage and storage table

  Water surface area and stored volume at each level of the pond.

  slopes: area = A₀ + P₀·m·h + π·m²·h²; storage = A₀·h + P₀·m·h² ÷ 2 + π·m²·h³ ÷ 3; table: V += h ÷ 3·(A₁ + A₂ + √(A₁·A₂))

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Storage of a low place in the ground

  Area and volume below each level inside a polygon on the ground surface.

  storage(z) = Σ cells below z of (z − ground) × cell area

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Flow through one outlet

  Discharge of an orifice, pipe, weir, spillway, V-notch or riser at a water level.

  orifice: Cd·A·√(2g·(h − D/2)); weir: Cw·(L − 0.2·n·H)·H^1.5; V-notch: (8 ÷ 15)·Cd·√(2g)·tan(θ/2)·H^2.5

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Table interpolation

  A value read from a table between two rows, used for storage, level and outflow.

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Modified Puls routing

  Storage and outflow at each time step from the inflow hydrograph.

  2S₂ ÷ Δt + O₂ = I₁ + I₂ + (2S₁ ÷ Δt − O₁)

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Pond routing results

  Peak inflow and outflow, the highest level, the greatest storage, attenuation, draw-down time and the volumes in and out.

  attenuation = 1 − peak out ÷ peak in; volume = Σ (q₁ + q₂) ÷ 2 × Δt

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Orifice diameter for a target outflow

  The orifice diameter at which the peak outflow just reaches the allowed flow.

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Pond checks

  Overtopping, peak above the target, no attenuation, slow draw-down and a dry pond.

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• A saved pond in project units

  Converts a saved pond to SI, runs it, and converts the results back for display.

  1 ft = 0.3048 m; 1 ft² = 0.09290304 m²; 1 acre = 4046.8564224 m²; 1 in = 25.4 mm; 1 ft³/s = 0.028316846592 m³/s

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit