Calculations

Calculations

• 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

• Local origin of the site

  The point subtracted from every element position so the file holds small coordinates.

  origin = round(first x ÷ 100) × 100, round(first y ÷ 100) × 100

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit

• Element position and rotation

  Each element's position relative to the site origin, in meters, and its rotation as a direction.

  p = ((x − oₓ) × k, (y − oᵧ) × k, z × k); direction = (cos rot, sin rot, 0)

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit

• Profiles and extrusions

  The circles, polygons and extrusion depths that make each element's body.

  point = (x × k, y × k); depth = max(1e-4, (z₁ − z₀) × k)

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit

• Mesh body

  A freeform object's vertices and triangles as a triangulated face set.

  vertex = (x × k, y × k, z × k), 6 decimals each

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit

• Quantity sets

  Areas, lengths and volumes converted to square meters, meters and cubic meters for the file.

  area × k²; volume × k³; length × k

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit

• Plant, bed and hedge bodies

  The simple solids and property values that stand for plants, beds and hedges in the file.

  tree: trunk r = max(0.05 m, 8% of crown radius) to 40% of height, crown above; bed height = share-weighted mean plant height

  Landscape IFC export landscape/ifc-landscape.js

  • CivilCraft
  64-bit

• Pressure and flow unit constants

  The factors between kPa and meters of water, kPa and psi, and L/min and US gallons per minute.

  kPa per m = 9.80665; kPa per psi = 6.894757; L/min per gpm = 3.785412

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Pipe inside diameters

  The inside diameter of each pipe size, from its outside diameter and dimension ratio.

  ID = (OD − 2 × OD ÷ SDR) × 0.0254 m (inch sizes); ID = (OD − 2 × OD ÷ 11) ÷ 1000 m (metric)

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Hazen-Williams loss in one pipe

  The head loss, pressure loss and velocity for a flow in a pipe.

  hf = 10.67 × L × q^1.852 ÷ (C^1.852 × d^4.8704), q in m³/s; kPa = hf × 9.80665; v = q ÷ (π d² ÷ 4)

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Loss in psi per 100 ft

  The US form of the Hazen-Williams formula.

  psi per 100 ft = 4.52 × Q^1.852 ÷ (C^1.852 × d^4.87) × 100

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Multiple-outlet factor

  The reduction in friction loss for a pipe that discharges through N evenly spaced outlets.

  F = 1 ÷ (m + 1) + 1 ÷ (2N) + √(m − 1) ÷ (6N²)

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Precipitation rate

  Millimeters of water per hour from a flow spread over an area.

  mm/h = 60 × L/min ÷ m²

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Precipitation rate, US form

  Inches of water per hour from gallons per minute over square feet.

  in/h = 96.3 × gpm ÷ ft²

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Flow of one head

  The flow of a sprinkler head, from its own listed flow or from its design precipitation rate.

  L/min = pr × r² × (arc ÷ 360) ÷ 60

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Precipitation rate at a head spacing

  The precipitation rate of heads of one type set out on a square or triangular grid.

  area = s² (square) or 0.866 × s² (triangular)

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Joining pipe ends into nodes

  Decides which pipe ends, heads and drip lines meet at the same point.

  same node when distance ≤ join tolerance ÷ meters per project unit

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Flow of a drip line

  The flow of a drip line from its length, emitter spacing and emitter rate.

  L/min = (⌊length ÷ spacing⌋ + 1) × (L/h per emitter ÷ 60)

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Pressure needed at the valve

  The loss from the valve to every head and the pressure the worst head needs.

  loss to node = loss to parent + friction kPa + (z node − z parent) × 9.80665; need = max(head nominal pressure + loss) + valve loss

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Pressure needed at the supply

  The loss along the mainline from the supply to a zone's valve and the pressure that zone needs at the supply.

  at supply = zone need + Σ (friction + elevation) along the main + supply loss

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Zone precipitation rate and weekly run time

  The precipitation rate of a zone and the minutes a week it must run for the weekly water depth.

  pr = 60 × Σ flow ÷ Σ (r² × arc ÷ 360); minutes = weekly mm ÷ pr × 60

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Bill of materials

  Counts of heads, total pipe length by size, drip length and emitter count.

  pipe length = Σ √(Δx² + Δy²) × meters per project unit

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Coverage grid and head-to-head check

  The share of the area reached by no head, one head or two and more, and the heads whose nearest neighbor is beyond their throw.

  cell = larger extent ÷ 200, grown by 1.5 until at most 200000 cells; far when nearest head > 1.0001 × throw

  Irrigation zones: flow, pressure and coverage landscape/irrigation.js

  • CivilCraft
  64-bit

• Unit text for labels, the check table and its CSV

  Turns kPa, L/min, meters and mm/h into the text shown, in US units for a feet project.

  psi = kPa ÷ 6.894757; gpm = L/min ÷ 3.785412; ft = m ÷ 0.3048; in/h = mm/h ÷ 25.4

  Irrigation zones: flow, pressure and coverage landscape/irr-ui.js

  • CivilCraft
  64-bit

• Head radius typed in feet

  Stores a head's throw radius, typed in project units, as meters.

  radius (m) = typed feet × 0.3048

  Irrigation zones: flow, pressure and coverage landscape/irr-ui.js

  • CivilCraft
  64-bit

• Supply pressure, flow and loss typed in US units

  Stores the supply's pressure, available flow and loss in kPa and L/min from values typed in psi and gpm.

  kPa = psi × 6.894757; L/min = gpm × 3.785412

  Irrigation zones: flow, pressure and coverage landscape/irr-ui.js

  • CivilCraft
  64-bit

• Irrigation quantities for takeoff

  Head counts and pipe and drip lengths passed to TakeoffCraft.

  LF = round(m ÷ 0.3048 × 100) ÷ 100

  Irrigation zones: flow, pressure and coverage landscape/irr-ui.js

  • CivilCraft
  64-bit

• Meters per project unit

  The length of one project unit in meters, used by every landscape calculation that works in meters.

  1 ft = 1200 ÷ 3937 m (US survey foot); 1 m = 1

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  Exact

• Bed area

  The plan area of a bed outline.

  A = |Σ (xⱼ + xᵢ)(yⱼ − yᵢ)| ÷ 2

  Planting: bed and hedge fills, planted areas and their quantities landscape/planting.js

  • CivilCraft
  64-bit