Calculations

Calculations

• Polygon area in square meters

  The area of a polygon with holes, scaled to square meters.

  A = (Σ |outer ring| − Σ |holes|) × kx × ky

  Address to site: parcel area, distances and shares site-sources.js

  • CivilCraft
  64-bit

• Meters per degree at the site

  The factors that turn longitude and latitude differences into meters, and the search window.

  kx = 111320 × cos(lat); ky = 111320

  Address to site: parcel area, distances and shares site-sources.js

  • CivilCraft
  64-bit

• Distance to each building

  The distance from the point to each building and the building's footprint area.

  d = √(((cx − x)·kx)² + ((cy − y)·ky)²), c = center of the building's bounding box

  Address to site: parcel area, distances and shares site-sources.js

  • CivilCraft
  64-bit

• Shares of the parcel by sampling

  The share of the parcel that lies in each zoning district, soil unit and flood zone.

  share = points in the zone ÷ points in the parcel, on a 40 × 40 grid over the parcel's bounding box

  Address to site: parcel area, distances and shares site-sources.js

  • CivilCraft
  64-bit

• Ground mesh with elevation bands

  The triangles, normals and colors of a ground surface, cut at the elevation band levels.

  position = (x + dx, y + dy, (z − origin z) × exaggeration); normal = normalized sum of face normals

  3D site view scene site3d.js

  • CivilCraft
  32-bit, display only

• Map picture coordinates on the ground

  Where each ground vertex falls in the map picture draped over it.

  u = (x + origin x − min x) ÷ width; v = (y + origin y − min y) ÷ height

  3D site view scene site3d.js

  • CivilCraft
  32-bit, display only

• Road body mesh

  The lanes, shoulders, curbs and walks of a corridor as triangles between neighboring sections.

  3D site view scene site3d-landscape.js

  • CivilCraft
  32-bit, display only

• Rail mesh

  Each rail as a swept I-shaped outline along the track's sections.

  3D site view scene site3d-rail.js

  • CivilCraft
  32-bit, display only

• Local origin of the 3D scene

  The project point every 3D position is measured from.

  x, y = the ground surface's own origin; z = floor(lowest elevation)

  3D site export (GLB, OBJ, USD) and the 3D pointer readout site3d.js

  • CivilCraft
  64-bit

• Point under the pointer in 3D

  The object under the pointer and the project coordinates of the hit, shown in the 3D view's tooltip.

  X = x + origin x; Y = y + origin y; Z = z ÷ exaggeration + origin z

  3D site export (GLB, OBJ, USD) and the 3D pointer readout site3d.js

  • CivilCraft
  32-bit in part

• Tooltip coordinates in the 3D view

  The name of the object under the pointer with its easting, northing and elevation.

  E, N, Z to 2 decimals

  3D site export (GLB, OBJ, USD) and the 3D pointer readout site-view3d.js

  • CivilCraft
  32-bit in part

• Scene positions to meters, Y up

  Turns the scene's local positions into the coordinates written to GLB and OBJ files.

  x′ = x·k; y′ = (z ÷ exaggeration)·k; z′ = −y·k; k = 1200 ÷ 3937 (US survey feet) or 1

  3D site export (GLB, OBJ, USD) and the 3D pointer readout site3d-export.js

  • CivilCraft
  32-bit in part

• GLB position bounds

  The smallest and largest coordinate of each mesh, which a GLB file must state.

  min, max over the vertices, each passed through Math.fround

  3D site export (GLB, OBJ, USD) and the 3D pointer readout site3d-export.js

  • CivilCraft
  32-bit in part

• OBJ vertex text

  Writes the vertices, normals, faces, lines and points of the site as OBJ text.

  v x y z with 4 decimals (meters); vn with 5 decimals

  3D site export (GLB, OBJ, USD) and the 3D pointer readout site3d-export.js

  • CivilCraft
  32-bit in part

• USD points and the Site transform

  Writes the site's meshes, lines and survey points to USD in meters, with the Site's transform putting them at the project coordinates.

  point = (x·k, y·k, (z ÷ exaggeration)·k) as 32-bit; Site translation = origin × k as doubles

  3D site export (GLB, OBJ, USD) and the 3D pointer readout usd-civilcraft.js

  • CivilCraft
  32-bit in part

• Ground slope under a table

  The slope of the ground under one table, from a plane fitted through its sample points.

  least squares z = a + b·x + c·y on centered points; b = (Sxz·Syy − Syz·Sxy) ÷ d, c = (Syz·Sxx − Sxz·Sxy) ÷ d, d = Sxx·Syy − Sxy²

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• Table size and the shadow rule

  The width, slant length, plan depth and height of one table, and how fast the winter shadow drops behind a row.

  D = Ls·cos β; H = Ls·sin β; shadow drop per meter = tan(α) ÷ max(0.2, cos Δ)

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• One table on its piles

  Tests a table position: inside the region, off kept-out ground, not too steep, and how high its lower edge must stand.

  z₀ = max over samples of (z_ground − dq·tan β + clearance); pile = z₀ − z_ground at the lower edge; slope = atan(|gradient|)

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• Row spacing on the ground

  Steps back from each placed table to the first position where its shadow no longer reaches the next table's lower edge.

  accept when q ≥ q_top + 0.02 and z₀ ≥ z_top − (q − q_top)·tanE − 1e-6; otherwise q += step

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• Module count and installed power

  The number of modules and the installed power of the array.

  modules = tables × per row × stacked; kWp = round(modules × Wp ÷ 10) ÷ 100

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• Terrain horizon

  The highest angle of the terrain seen from a point, in each 5 degrees of bearing.

  elevation angle = max over d of atan2(z(d) − (z₀ + observer height), d)

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• Hours hidden by the horizon

  Marks the hours of the year when the sun is below the terrain horizon as fully shaded before the yield is computed.

  shaded when sun altitude < horizon elevation at round(azimuth ÷ 5) × 5 degrees

  Ground-mounted solar arrays on terrain solar.js

  • CivilCraft
  64-bit

• Sun directions through a day

  The direction to the sun at the middle of each time step of a local day, and the hours it is above the horizon.

  minute = (k + 0.5) × step; day length = samples above the horizon × step ÷ 60

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  64-bit

• Terrain raster for shadows

  The ground elevations on a square grid, used to test whether the ground blocks the sun.

  z[i, j] = elevation at (minX + i·cell, minY + j·cell)

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  32-bit in part

• Ray against a building mass

  Whether the ray from a point toward the sun passes through a mass.

  t range from the mass's bottom and top; slab test on the footprint box; crossings of the sun's line with each footprint edge, inside between every other pair

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  64-bit

• Ray against the ground

  Whether a point sees the sun: no mass in the way and no ground rising above the ray.

  march one cell at a time: x += dx, y += dy, z += rise; blocked when ground > z + 0.001

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  64-bit

• Hours of sun per ground cell and wall point

  Adds one time step to every ground cell and wall point that is lit at each sun sample, then averages over the days.

  hours += step for each lit sample; mean = hours ÷ days; max = largest ground mean

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  32-bit in part

• Mean hours per floor and per wall

  The mean hours of sun on each floor of each wall and on the wall as a whole.

  floor mean = Σ point hours ÷ points; wall mean = Σ floor means ÷ floors

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  64-bit

• Combining runs over different days

  Joins the results of several runs of the same site into one, weighting each by its number of days.

  hours = Σ (hoursᵢ × daysᵢ) ÷ Σ daysᵢ

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  32-bit in part

• Ground hours as CSV

  Writes each ground cell's center and its hours of sun a day.

  x, y to 3 decimals; hours to 2 decimals

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  32-bit in part

• Wall hours as CSV

  Writes each wall's facing direction and the hours of sun a day on each floor.

  facing = round((90 − normal·180 ÷ π) mod 360); hours to 2 decimals

  Hours of direct sun on the ground and on walls sunhours.js

  • CivilCraft
  64-bit

• Turn angle at a point

  The signed turn of the line at a point of intersection.

  Δ = atan2 of the leg after − atan2 of the leg before, wrapped to (−π, π]

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Tangent length of each curve

  The turn and the tangent length each curve takes on either side of its point.

  T = r × tan(|Δ| ÷ 2)

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Largest radius that fits

  The largest radius at a point that fits between its neighbors' curves as they are.

  room = min(d_before − T_before, d_after − T_after); r_max = room ÷ tan(|Δ| ÷ 2)

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Overlapping curves and the fixes offered

  Finds neighboring curves whose tangents overlap and offers radii that fit.

  overlap when Tₐ + T_b > L + 1e-9; both scaled by f = L ÷ (Tₐ + T_b); offered radius = floor(r × 100 + 1e-9) ÷ 100

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Vertical curves that do not fit

  Finds vertical curves longer than the room between their neighbors and offers the longest length that fits.

  A = (g₂ − g₁) × 100; L = K × |A| when given by K; room = 2 × min(back, forward); offered L = floor(room × 100 + 1e-9) ÷ 100; K = L ÷ |A|

  Why a curve does not fit, and the radius or length that would solve-why.js

  • CivilCraft
  64-bit

• Stations to stake

  Every multiple of the step between two stations, both ends, and the alignment's own curve points in between.

  sta = k × step for whole k; neighbors closer than 1e-6 merged

  Staking reports staking.js

  • CivilCraft
  64-bit

• Stake position

  The coordinates of a stake at a station and an offset to the right or left.

  x = xₚ + off × sin(dir); y = yₚ − off × cos(dir)

  Staking reports staking.js

  • CivilCraft
  64-bit

• Stake rows with cut or fill

  One row per station and offset with design elevation, ground elevation and cut or fill.

  cf = ground − design (positive = cut)

  Staking reports staking.js

  • CivilCraft
  64-bit

• Survey points against the alignment

  Each survey point's station and offset on the alignment, the design there and the cut or fill to the point's own elevation.

  cf = point elevation − design

  Staking reports staking.js

  • CivilCraft
  64-bit

• Staking table as CSV

  Writes the stake rows to a CSV file.

  northing, easting, design, ground and cut or fill to 3 decimals; offset and the C/F column to 2 decimals

  Staking reports staking.js

  • CivilCraft
  64-bit

• Millimeters per project unit

  The factor from project feet or meters to millimeters.

  m: 1000; ft: 1,200,000 ÷ 3937 (US survey foot)

  Drainage structure types and their library items structs.js

  • CivilCraft
  Exact

• Inside and outside size of a structure

  The inside and outside width and length, the wall and the frame of a structure in project units.

  inside = size ÷ P; outside = inside + 2 × wall ÷ P; P = 12 (inches per foot) or 1000 (mm per m)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Plan shapes of a type

  The outside wall, inside wall and frame opening of a type as plan shapes in millimeters.

  r = round₆((size × M) ÷ 2); M = 25.4 (inch) or 1 (mm)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Round outline as a polygon

  The outline of a round structure's body as points on a circle.

  pᵢ = (r·cos(2π·i ÷ n), r·sin(2π·i ÷ n)), n = 48

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Library item of a type

  The library item for a type: its body from the underside of the floor slab to the rim, its sizes, and every parameter in millimeters.

  H = depth × U + base × M; body = outline from −H to 0; parameters as text of (value × factor)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Type read back from a library item

  Turns a library item's millimeter parameters back into a type in the project's units.

  value = millimeters ÷ M (sizes) or ÷ U (sump, depth)

  Drainage structure types and their library items structs.js

  • CivilCraft
  64-bit

• Follower behind a leader (tractrix)

  Where a rear axle ends up when the point that pulls it moves along a straight piece.

  α₁ = 2·atan(tan(α₀ ÷ 2) × e^(−d ÷ L)); follower = B + L × (−w turned by α₁)

  Vehicle swept paths swept.js

  • CivilCraft
  64-bit

• Steady-state turning radii

  The radius each rear axle and hitch runs on when the front axle follows a circle for ever.

  r = √(max(0, R² − L²)); hitch = √(r² + c²)

  Vehicle swept paths swept.js

  • CivilCraft
  64-bit

• Stepping along the path

  Cuts the path into steps no longer than the step length, with a point and travel direction on every line and arc.

  step = max(0.001, shortest wheelbase ÷ 40); k = ceil(L ÷ step); s = s₀ + L·j ÷ k

  Vehicle swept paths swept.js

  • CivilCraft
  64-bit