Calculations

Calculations

• Attribute value to its storage type

  Converts a list of numbers to the number type its USD attribute type calls for.

  USD mesh coordinates in saved and exported files usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Mesh points and extent

  Stores the points of a mesh and its bounding box in the scene.

  extent = [min x, min y, min z, max x, max y, max z] of the points

  USD mesh coordinates in saved and exported files usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Lamp intensity

  Converts a lamp's lumens to the intensity a renderer reads.

  intensity = lumens ÷ (683 × area × π)

  USD mesh coordinates in saved and exported files usd/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit, display only

• Single values in the binary file

  Writes one number, tuple or matrix into the binary USD file.

  USD mesh coordinates in saved and exported files usd/usdc-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arrays in the binary file

  Writes an array of numbers into the binary USD file.

  USD mesh coordinates in saved and exported files usd/usdc-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Reading a mesh

  The points, faces and attached values of a mesh read from a USD scene.

  USD mesh coordinates in saved and exported files usd/geom.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Built-in shapes as meshes

  A cube, sphere, cylinder, cone, capsule or plane of a USD scene as a mesh.

  ring point = (r·cos θ, r·sin θ, z), θ = 2π·j ÷ 24

  USD mesh coordinates in saved and exported files usd/geom.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Elevation grid from a surface

  The elevation at the center of every grid cell, row by row from the north.

  x₀ = ⌊minX ÷ cell⌋·cell; y₀ = ⌈maxY ÷ cell⌉·cell; center = (x₀ + (c + 0.5)·cell, y₀ − (r + 0.5)·cell)

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  32-bit in part

• Elevations written to the file

  The tiles or strips of elevation values as they go into the TIFF.

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  32-bit in part

• Grid origin and cell size in the file

  The pixel scale and the tie point that place the grid.

  pixel scale = (cell, cell, 0); tie point = pixel (0, 0) at (x₀, y₀)

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  64-bit

• Default cell size

  The mean plan length of the surface's triangle edges, offered as the cell size.

  Σ |edge| ÷ number of edges

  Surface exported as a GeoTIFF elevation grid geotiff-write.js

  • CivilCraft
  64-bit

• Gravity and the foot

  The constants the simulation uses.

  g = 9.80665 m/s²; 1 ft = 0.3048 m

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  Exact

• Grid from the surface

  Samples the ground surface into square cells in meters.

  n_x = round(W ÷ c), n_y = round(H ÷ c); c = max(W ÷ n_x, H ÷ n_y); z (m) = elevation × meters per unit

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Low spots and what they hold

  Finds each depression, its area, the volume it holds before it spills, its greatest depth and its sill level.

  filled = max(ground, lowest way out); depth = filled − ground; volume = Σ depth × cell²

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Rain depth of a storm

  The total depth of rain over the storm's duration.

  depth (mm) = Σ i × Δt ÷ 60

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Design storm by alternating blocks

  Builds a storm from an intensity-duration curve with the heaviest block in the middle.

  depth_k = idf(k·Δt) × k·Δt ÷ 60 − depth_(k−1); i_k = depth_k × 60 ÷ Δt

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Time step

  The length of each simulation step.

  dt = min(dt_max, α × Δx ÷ √(g × max(h_max, 0.01)))

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Flow across a cell face

  The unit flow between two neighboring cells for one time step.

  q = (q − g·h_f·dt·Δη ÷ Δx) ÷ (1 + g·dt·n²·|q| ÷ h_f^(7/3)); |q| ≤ h_f·√(g·h_f)

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Flow leaving at an open edge

  The unit flow out of the grid at an open edge or beside a hole in the ground.

  q = h^(5/3) × √S ÷ n, S = max(edge slope, bed slope to the cell behind); q ≤ h·√(g·h)

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Keeping depths from going negative

  Scales the outflows of a cell so it cannot give away more water than it has.

  when Σ out × dt ÷ Δx > available: out ← out × available ÷ (Σ out × dt ÷ Δx)

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• New depth, deepest water, fastest flow and first-wet time

  Updates each cell's depth and records its greatest depth, greatest speed and the time it first got wet.

  h ← h + rain − losses + (dt ÷ Δx) × (q_W − q_E + q_S − q_N); speed = |q| ÷ h

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  32-bit in part

• Where the records are kept

  Sets up the arrays that hold the per-cell maximum depth, maximum speed and first-wet time.

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  32-bit in part

• Drains

  Takes water out of a drain's cell up to its capacity each step.

  take = min(capacity × dt, depth × cell area)

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Volumes of rain, loss and outflow

  Adds each step's rain, losses and outflow to the running totals.

  out += Σ q × Δx × dt; rain += Σ depth of rain × cell area

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Mass balance and the results

  The stored volume, the mass balance error, the pond volumes at the end and the peak outflow.

  error = (rain − loss − out − drained − stored) ÷ rain

  Rain on the ground: overland flow, ponding and outflow rain.js

  • CivilCraft
  64-bit

• Least-cost search

  Searches the grid for the cheapest allowed path and returns its points and total cost.

  grade = |z₂ − z₁| ÷ length ≤ limit; cost = length × unit cost × factor × (1 + w·(grade ÷ limit)²) + area × length × earth cost

  Best route across the terrain route.js

  • CivilCraft
  32-bit in part

• Path points and their elevations

  Turns the chain of grid cells into the route's points, with the two ends at the picked points and collinear points removed.

  x = minX + (i + 0.5) × cell; collinear when |cross product| < 1e-9 × cell²

  Best route across the terrain route.js

  • CivilCraft
  32-bit in part

• Route length, steepest grade and earthwork

  The length, steepest grade, cut and fill along a finished route.

  length = Σ √(Δx² + Δy²); grade = |Δz| ÷ l; s = |z_left − z_right| ÷ width; area = width²·s ÷ 4 ÷ max(0.05, 1 − sideSlope·s); volume += area × l ÷ n

  Best route across the terrain route.js

  • CivilCraft
  64-bit

• Curve radius at each bend

  The turn angle and the radius implied at each bend of the route.

  turn = atan2 of the leg after − atan2 of the leg before, wrapped to (−π, π]; radius = (l₁ + l₂) ÷ (2|turn|)

  Best route across the terrain route.js

  • CivilCraft
  64-bit

• Route profile

  Distance along the route against elevation, for the profile drawing and the point table.

  dᵢ = dᵢ₋₁ + √(Δx² + Δy²)

  Best route across the terrain route.js

  • CivilCraft
  64-bit

• 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

• 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

• Received power at each grid cell

  The received power at every cell around the transmitter and the share of cells at or above the receiver's sensitivity.

  Pr = Pt + Gt + Gr − (FSPL + J(v_max) + other); covered = cells with Pr ≥ sensitivity ÷ known cells

  Radio coverage over the terrain telecom.js

  • CivilCraft
  32-bit in part

• Diffraction parameter

  The parameter that measures how far an obstruction rises into the path, used for the knife-edge loss.

  v = h × √(2(d₁ + d₂) ÷ (λ·d₁·d₂))

  Radio coverage over the terrain telecom.js

  • CivilCraft
  64-bit

• Registered position of a point

  One point in the registered frame: its stored position plus the scan's origin, moved by the scan's matrix.

  p = M × (pos + origin)

  Registered scans written as LAS and E57 scan-export.js

  • CadCraft
  • BimCraft
  32-bit in part

• Bounds of the registered cloud

  The minimum and maximum x, y, z over every moved point, and the point count.

  Registered scans written as LAS and E57 scan-export.js

  • CadCraft
  • BimCraft
  32-bit in part