Calculations

Calculations

• Flow update and convergence test

  Updates every link flow from the new heads and decides when the network is solved.

  stop when Σ|Q_new − Q_old| ÷ Σ|Q_new| < 1e−7 and no valve or pump changed status

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Linear solve for the heads

  Solves the symmetric positive definite system for the unknown node heads.

  A = L·Lᵀ, forward and back substitution; or conjugate gradient with z = r ÷ diag(A)

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Heads, pressures, velocities and head loss per 1000

  The numbers shown for each node and pipe, converted back to project units, and the limit checks on them.

  pressure = (H − z) × p factor; v = |Q| ÷ (π D² ÷ 4); loss per 1000 = |Hₐ − H_b| ÷ (L ÷ 1000)

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Available fire flow

  The largest draw at one node that keeps the lowest pressure in the network at or above the residual pressure.

  bisection on the draw: 40 halvings of [lo, hi], each one a full network solve

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Tank levels over time

  Steps the network through the day and moves each tank level by the flow into it.

  level₊ = level + inflow × Δt ÷ (π d² ÷ 4), clamped to [min level, max level]

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• EPANET-format export

  Writes the network as EPANET-format text for other programs.

  written value = round(v × 10⁴) ÷ 10⁴

  Water mains network: heads, flows and pressures water.js

  • CivilCraft
  64-bit

• Lot outline with arcs as chords

  The lot as a counter-clockwise ring of points, each tagged with the lot line it starts.

  chord angle = 2·acos(1 − 0.01 ÷ R); n = ⌈Δ ÷ chord angle⌉, 2 ≤ n ≤ 400

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Setback distance for each lot line

  Assigns the front, side or rear distance, or a typed distance, to every lot line, and picks the rear line when none is named.

  rear = the line with −cos(dir − front dir) > 0.5 whose midpoint is farthest from the front line's midpoint

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Buildable envelope and its area

  The lot taken in from every line by that line's setback, with its area, or the reason it cannot be built.

  area = |shoelace(envelope)|; lot area = |shoelace(lot ring)|

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Mitred inset with a distance per line

  Moves each lot line in by its own distance and finds each new corner where two moved lines meet.

  s = ((q − p) × u_q) ÷ (u_p × u_q); corner = p + s·u_p

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Allowed height under a sky-exposure plane

  The lowest height the cap and the sky-exposure plane allow over a footprint.

  s = ((p − a) × (b − a)) ÷ |b − a|; h = h₀ + rise × max(0, s); allowed = min over corners and lines

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Footprint area inside the envelope

  How much of a building footprint lies inside the buildable envelope.

  area = Σ over envelope triangles of |shoelace(footprint clipped to the triangle)|

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Clip a footprint to one triangle

  The part of a polygon inside a convex, counter-clockwise piece.

  side(p) = (b − a) × (p − a); crossing at u = s_p ÷ (s_p − s_q)

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Coverage, floor area ratio, setback and height checks

  Compares the masses on a lot with every limit typed for it and lists each result.

  coverage = Σ footprint ÷ lot area; FAR = Σ floor area ÷ lot area; outside = footprint − inside area

  Zoning envelope and limit checks zoning.js

  • CivilCraft
  64-bit

• Signed polygon area

  The signed area of a closed outline.

  A = −½ Σ (xⱼ + xᵢ)(yⱼ − yᵢ)

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Point inside a polygon

  Whether a point lies inside an outline, used to keep or drop each boundary piece.

  count edges with (aᵧ > y) ≠ (bᵧ > y) and x < x on the edge at height y

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Where two segments cross

  The position along one edge where another edge crosses or touches it.

  t = ((c − a) × s) ÷ (r × s); u = ((c − a) × r) ÷ (r × s)

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Area by slabs

  The area of the outline with every hole removed, overlaps counted once.

  area = Σ over slabs of (width inside the outline and outside all holes at mid-height) × slab height

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Outline and cut lengths

  The pieces of the outline that remain and the pieces of the holes that cut it, with their total lengths.

  length = Σ |b − a| over kept pieces; a = e.a + t₀(e.b − e.a), b = e.a + t₁(e.b − e.a)

  Outline minus holes: area and boundary lengths landscape/areas.js

  • CivilCraft
  64-bit

• Fingerprint of the source points

  A short code that changes when the source linework moves, so the linked object knows to update.

  hash of round(x × 10⁶), round(y × 10⁶) for every point

  Linework checks for linked landscape objects landscape/links.js

  • CivilCraft
  64-bit

• Clean and check a line or outline

  Drops repeated points, closes an outline and refuses linework that is too short, too far away, open or self-crossing.

  Linework checks for linked landscape objects landscape/links.js

  • CivilCraft
  64-bit

• Self-crossing test

  Whether any two edges of the line cross away from their ends.

  Linework checks for linked landscape objects landscape/links.js

  • CivilCraft
  64-bit

• STL reader

  Turns a binary or ASCII STL file into a mesh with shared vertices, scaled to millimeters.

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Volume, surface area, footprint and height

  The quantities of a mesh object that schedules and the IFC export report.

  V = |Σ v₀·(v₁×v₂)| ÷ 6; A = Σ |(v₁−v₀)×(v₂−v₀)| ÷ 2; height = z max − z min

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Convex hull of the plan points

  The outline used as the object's footprint on the plan.

  keep a turn when (a − o) × (b − o) > 0

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Mesh millimeters to project coordinates

  Places a mesh point on the site: scaled to project units, turned by the object's rotation and moved to its insertion point.

  x = x₀ + (x·cos a − y·sin a) × k; k = 1 ÷ (1000 × meters per project unit)

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Base elevation and volume below ground

  The elevation the object's base sits at, its points in project coordinates, and an estimate of how much of it is below the existing ground.

  follow: base = lowest ground sample; cut: base = typed level or mean of the samples; below ≈ Σ (ground − base) × cell²

  Freeform mesh objects: quantities and placement on the ground landscape/freeform.js

  • CivilCraft
  64-bit

• Positions and indices from an accessor

  Reads a primitive's vertex positions and triangle indices from the file's binary chunk.

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only

• Node transform

  The 4×4 matrix of a node from its matrix, or from its translation, rotation and scale.

  M = T · R(q ÷ |q|) · S

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only

• Transform to the model's frame, Y up to Z up

  Applies each node's transform to its vertices and gathers all triangles into one mesh.

  p′ = M·p; (x, y, z) → (x, −z, y)

  Plant 3D models for the 3D view landscape/glb.js

  • CivilCraft
  32-bit, display only

• Scale a model to the unit box

  Centers a model in plan, sets its base at zero and scales it to one unit wide and one unit tall, with a normal per triangle.

  x′ = (x − cx) ÷ w; z′ = (z − z min) ÷ h; n = (b − a) × (c − a) ÷ |…|

  Plant 3D models for the 3D view landscape/symbols.js

  • CivilCraft
  32-bit, display only

• Scale a symbol into the unit circle

  Centers the symbol's entities and scales them so the farthest point is at radius 1.

  x′ = round((x − cx) ÷ R × 10⁴) ÷ 10⁴

  Plant symbols from SVG files and CAD blocks landscape/symbols.js

  • CivilCraft
  64-bit

• SVG path to polylines

  Reads an SVG path's commands into straight-line polylines.

  Bézier point at t = k ÷ 8, k = 1 … 8

  Plant symbols from SVG files and CAD blocks landscape/symbols.js

  • CivilCraft
  64-bit

• Scale a symbol to a plant

  The symbol's entities at the plant's radius on the plan.

  x = x′ × R

  Plant symbols from SVG files and CAD blocks landscape/symbols.js

  • CivilCraft
  64-bit

• Corner elevations of a sloped platform

  The elevation of each corner of a platform that falls at a given percent in a given direction.

  z = z₀ − (pct ÷ 100) × ((x − cx)·cos a + (y − cy)·sin a)

  Landscape grading: platforms, swales, slope classes and ponding landscape/grade.js

  • CivilCraft
  64-bit

• Mean ground elevation under an outline

  The level used for a platform, berm or paving when none is typed.

  mean of ground elevations at every vertex and edge midpoint

  Landscape grading: platforms, swales, slope classes and ponding landscape/grade.js

  • CivilCraft
  64-bit

• Swale sections along a line

  The bottom elevations and the left and right daylight lines of a swale, as a patch of the proposed surface.

  z bottom = z start − depth − (fall ÷ 100) × s, or ground − depth, never rising; step = max(0.5 m or 1.5 ft, min(L ÷ 200, max(bottom, 1 m or 3 ft)))

  Landscape grading: platforms, swales, slope classes and ponding landscape/grade.js

  • CivilCraft
  64-bit

• Edge of a free grading area

  The outline of a grading area with ground elevations, plus the spot elevations and contours inside it.

  edge spacing = √|area| ÷ 20

  Landscape grading: platforms, swales, slope classes and ponding landscape/grade.js

  • CivilCraft
  64-bit

• Triangles and area by slope class

  Sorts the surface's triangles into slope bands and totals the plan area in each.

  class = number of limits the slope exceeds; area = |(b − a) × (d − a)| ÷ 2

  Landscape grading: platforms, swales, slope classes and ponding landscape/grade.js

  • CivilCraft
  64-bit

• Ponds: depth, area and volume

  Where water would stand on the surface, and each pond's depth, area, volume and spill level.

  W(v) = max(Z(v), lowest level reached from the edge); volume = Σ triangle area × mean depth of its 3 corners

  Landscape grading: platforms, swales, slope classes and ponding landscape/grade.js

  • CivilCraft
  64-bit

• Length along a line

  The plan length of a path, wall, curb or ramp line, and the point and direction at any distance along it.

  L = Σ √(Δx² + Δy²)

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Stations along a line

  The distances along a line where the ground is read and sections are built.

  0, step, 2·step, … , L, and every bend; each rounded to 6 decimals

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Paving levels and falls

  The elevation of each corner of a paved area for a level surface, a cross fall, or a fall to a drain.

  drain: z = z₀ + (pct ÷ 100) × distance to the drain; cross: the platform plane

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Path edges and steepest grade

  The center line and edges of a path on the ground, its length, and the steepest grade along it.

  grade = |Δz| ÷ Δs × 100 between stations; edge z = ground ± (crossfall ÷ 100) × width ÷ 2

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Wall heights, face area and volume

  The top, ground and footing level of a wall at each station, with its maximum height, face area and volume.

  footing = ⌊(ground − depth) ÷ step⌋ × step; face = Σ Δs × (hₐ + h_b) ÷ 2; volume = Σ Δs × thickness × mean(top − footing)

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Ramp grade and landings

  A ramp's rise, the number of runs and landings, its grade and the length it needs.

  runs = ⌈rise ÷ landing interval⌉; grade = rise ÷ (L − landings × landing length) × 100; need = rise ÷ (max grade ÷ 100) + landings × landing length

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Risers, goings and run of steps

  The number of risers, the riser height, the going and the run of a flight of outdoor steps.

  n = ⌈H ÷ riser max⌉; riser = H ÷ n; going = max(going min, comfort − 2 × riser); run = treads × going + landings × (landing − going)

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Ground strip under a retaining wall

  The two edges of the strip under a retaining wall, with the high side held at the ground or the typed top and the low side at the foot level.

  high side = left when Σ (ground left − ground right) ≥ 0

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Hardscape quantities for takeoff

  The areas, layer volumes and lengths of paving, paths, walls, curbs and ramps passed to TakeoffCraft.

  qty = round(v × 100) ÷ 100; layer volume = area × thickness (÷ 27 for cubic yards)

  Hardscape: paving, paths, walls, ramps and steps landscape/hardscape.js

  • CivilCraft
  64-bit

• Number format in the file

  Turns a number into the text written to the IFC file.

  text = v.toFixed(6), trailing zeros removed

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit