Calculations

Calculations

• Deepest water

  The deepest water anywhere in the run, as shown in the facts list.

  deepest = max over cells of maxDepth, converted to mm or in

  Rainfall run read-outs: deepest water and depth scale rain-ui.js

  • CivilCraft
  32-bit in part

• Depth scale of the picture

  The depth at which the picture reaches its deepest color, printed in the legend.

  top = max(0.02, 99.5th percentile of wet maxDepth cells)

  Rainfall run read-outs: deepest water and depth scale rain-ui.js

  • CivilCraft
  32-bit in part

• Assistant rounding to 3 decimals

  Rounds a result to 3 decimals before the assistant is given it.

  round(v × 1000) ÷ 1000

  Assistant and window read-outs of radio link and coverage geo-agent.js

  • CivilCraft
  64-bit

• Radio link figures

  The distance, loss, received power, fade margin and availability the assistant reports for a radio link.

  annual unavailability = round(U × 1e6 × 1000) ÷ 1000 ÷ 1e6

  Assistant and window read-outs of radio link and coverage geo-agent.js

  • CivilCraft
  64-bit

• Coverage share and map

  The share of the area covered, the farthest covered point and a coarse map of received power.

  map cell = r3(p) when p ≥ sensitivity, else null

  Assistant and window read-outs of radio link and coverage geo-agent.js

  • CivilCraft
  32-bit in part

• Coverage read-out in the window

  The share covered, the farthest covered distance and the cell count shown for a coverage item.

  covered % = covered × 100; farthest = distance as returned

  Assistant and window read-outs of radio link and coverage geo-ui.js

  • CivilCraft
  32-bit in part

• Array position from the coordinate system

  The latitude and longitude of the middle of the array's region.

  c = mean of corners; (lon, lat) = toLonLat(c); rounded to 1e-5°

  Solar array site and saved summary solar-run.js

  • CivilCraft
  64-bit

• Saved plan summary

  The counts, kWp and yearly kWh the file keeps for an array.

  kWh = round(annual AC kWh)

  Solar array site and saved summary solar-run.js

  • CivilCraft
  64-bit

• Area read-out

  Prints an area in the project's area unit.

  text = round to 0 decimals, grouped

  Massing window read-outs and typed height massing-ui.js

  • CivilCraft
  64-bit

• Typed height to floors

  Turns a height the person types into a whole number of floors.

  floors = clamp(round(H ÷ floor height), 1, max floors)

  Massing window read-outs and typed height massing-ui.js

  • CivilCraft
  64-bit

• Zoning coverage percent

  Turns the percent a person types for building coverage into the stored fraction.

  coverage = n ÷ 100

  Massing window read-outs and typed height massing-ui.js

  • CivilCraft
  64-bit

• Bench rim line segments

  Segment pairs for the rim of each bench.

  Pit and solar table meshes in the 3D view site3d-pit.js

  • CivilCraft
  32-bit, display only

• Haul ramp ribbon

  A road-wide ribbon on the pit walls for the haul ramp.

  offset = (−dy, dx) ÷ length × width ÷ 2; lift = 0.02 × width

  Pit and solar table meshes in the 3D view site3d-pit.js

  • CivilCraft
  32-bit, display only

• Solar table triangle normal

  A flat-shaded triangle with its normal.

  n = (b − a) × (c − a) ÷ |…|

  Pit and solar table meshes in the 3D view site3d-solar.js

  • CivilCraft
  32-bit, display only

• Pit scene in project units

  Converts a pit's ramp and bench outlines from meters back to project units for the 3D view.

  coordinate ÷ k, where k is meters per project unit

  Pit and solar table meshes in the 3D view pit-view.js

  • CivilCraft
  32-bit, display only

• Finding the sheet

  The four corners of the paper in the photo.

  corners = the pixels of the largest bright region with the smallest and largest x + y and x − y; photo position = (pixel + 0.5) × reduction factor

  Sketch photo to drawing: sheet, perspective and scale photosketch/photosketch.js

  • ModelCraft
  • CivilCraft
  64-bit

• Perspective transform from four points

  The 3 × 3 matrix that takes four points to four others.

  8 equations in h₁…h₈ with h₉ = 1, solved by Gauss–Jordan elimination

  Sketch photo to drawing: sheet, perspective and scale photosketch/photosketch.js

  • ModelCraft
  • CivilCraft
  64-bit

• Applying the perspective transform

  A point taken through the 3 × 3 matrix.

  w = h₆x + h₇y + h₈; x′ = (h₀x + h₁y + h₂) ÷ w; y′ = (h₃x + h₄y + h₅) ÷ w

  Sketch photo to drawing: sheet, perspective and scale photosketch/photosketch.js

  • ModelCraft
  • CivilCraft
  64-bit

• Sheet proportions

  The long-to-short ratio of the straightened sheet.

  w = mean of top and bottom lengths, h = mean of left and right; r = max ÷ min; replaced by the named paper's ratio, or by the nearest standard ratio within 8 %

  Sketch photo to drawing: sheet, perspective and scale photosketch/photosketch.js

  • ModelCraft
  • CivilCraft
  64-bit

• Drawing units per pixel

  The size of one pixel of the straightened sheet in drawing units, and the mapping from pixels to drawing coordinates.

  mm per px = long side in mm ÷ long side in px; units per px = mm per px × scale ÷ unit in mm; x = origin_x + px·k, y = origin_y + (height − py)·k

  Sketch photo to drawing: sheet, perspective and scale photosketch/photosketch.js

  • ModelCraft
  • CivilCraft
  64-bit

• Arcs and circles into the drawing

  Converts each traced arc to drawing units as a circle or as an arc through its start, middle and end.

  r = r_px × units per px; circle when a₁ − a₀ ≥ 2π − 1e-6; else arc through start, middle (at (a₀ + a₁) ÷ 2) and end

  Sketch photo to drawing: sheet, perspective and scale photosketch/photosketch.js

  • ModelCraft
  • CivilCraft
  64-bit

• Arc through three points

  The center, radius and end angles of the arc through three points.

  d = 2·(a_x(b_y − c_y) + b_x(c_y − a_y) + c_x(a_y − b_y)); center from the sums of |p|²·(differences) ÷ d; r = |a − center|

  Sketch photo to drawing: sheet, perspective and scale photosketch/paper.js

  • ModelCraft
  • CivilCraft
  64-bit

• Significand width of a number

  How many bits of a number this device keeps.

  bits = the first n where 1 + 2⁻ⁿ = 1

  Device number check accuracy.js Every app
  Exact

• Digits of a graphics float

  The number of significant digits stated for the graphics processor's float type.

  bits < 23: digits = max(1, ⌊(bits + 1) × log₁₀ 2⌋); bits ≥ 23: the fixed text "about 7"

  Device number check accuracy.js Every app
  64-bit

• Size and position text

  A dimension, port size or port position as text in millimeters.

  text = round(x × 10⁴) ÷ 10⁴

  Library configurator sizes library-configurator.js Every app
  64-bit

• Option value used for matching

  The text an option value is compared by when the page picks the variant that matches the selected options.

  numbers: round(v × 10⁴) ÷ 10⁴ as text; other values: trimmed text

  Library configurator sizes library-configurator.js Every app
  64-bit

• Mesh buffers

  The item's box or mesh as geometry for drawing, turned from z up to y up.

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Camera position

  Where the camera sits as the view is turned and zoomed.

  position = target + dist × (sin φ sin θ, cos φ, sin φ cos θ)

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Variant body buffers

  The chosen variant's box or mesh as geometry for drawing.

  Library 3D preview library-configurator.js Every app
  32-bit, display only

• Required and found values as text

  A limit or a measured value in words, such as ≤ 196.85 mm or 863.6–965.2 mm.

  text = round(x × 100) ÷ 100, then the unit

  Check report values problems.js Every app
  64-bit

• Built-in unit factors

  The factor from each built-in unit of mass, time, force, pressure, energy, power, current, voltage and volume to SI.

  lb = 0.45359237 kg; lbf = 4.4482216152605 N; psi = 6894.757293168 Pa; psf = 47.88025898 Pa

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Constants and fallback lengths

  pi, e, standard gravity g0, and the length units used when no unit table is given.

  g0 = 9.80665 m/s²; in = 0.0254 m; ft = 0.3048 m; yd = 0.9144 m

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Unit lookup

  The SI factor and dimension of a unit name.

  deg = π ÷ 180; rad = 1

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Dimension comparison

  Whether two values have the same dimensions, so they can be added, compared or converted.

  |aᵢ − bᵢ| < 1e-9 for each of the five exponents

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Power

  a ^ b for a value with units.

  value = aᵇ; dimensions × b

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Conversion with to

  M to kN m: checks the dimension and records the unit to show the answer in.

  shown = value ÷ factor of the target unit

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Shown amount

  The number and unit a row displays, and the amount passed to other modules.

  amount = value ÷ factor

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Square root and absolute value

  sqrt(a) and abs(a) for a value with units.

  √a halves the dimensions

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Rounding to a step

  round, floor and ceil, with an optional step such as round(x, 5 mm).

  round(a ÷ s) × s

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Minimum, maximum, sum and average

  min, max, sum and avg of values of one kind.

  sum = Σ aᵢ in order; avg = sum ÷ n

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Trigonometry, logarithms and exponent

  sin, cos, tan, their inverses, atan2, ln, log10, exp and pow.

  sin, cos, tan of radians; asin, acos need |x| ≤ 1; ln, log10 need x > 0

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Reading an app parameter

  @Name: the app's parameter as a value in SI.

  value = parameter value × factor of its unit

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Values written to driven parameters

  What each drive would set in the app: the row's answer in the parameter's unit.

  value = row value ÷ factor of the unit; change when |current − value| > 1e-9 × max(1, |value|)

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Time-weighted average

  The average of a value that changes at events: queue length, units busy, work in process.

  average = (Σ vᵢ × Δtᵢ) ÷ (t − t₀)

  Flow simulation (discrete events) engine.js Every app
  64-bit

• Mean, deviation and percentiles of observations

  Waiting time, service time and time in system: mean, standard deviation, minimum, maximum, P50 and P95.

  m ← m + (x − m) ÷ n; s ← s + (x − m_old)(x − m_new); sd = √(s ÷ (n − 1)); P = sorted[⌊p × k⌋]

  Flow simulation (discrete events) engine.js Every app
  64-bit

• Event time

  When a scheduled event happens.

  t_event = t_now + delay

  Flow simulation (discrete events) engine.js Every app
  64-bit

• Conveyor slots and timing

  How many items fit on a belt, the gap between items and the travel time.

  slots = max(1, ⌊length ÷ pitch + 1e-9⌋); headway = pitch ÷ speed; travel = length ÷ speed

  Flow simulation (discrete events) engine.js Every app
  64-bit

• Shift edges

  When a server goes on and off shift.

  x = t − ⌊t ÷ period⌋ × period; on shift when a ≤ x < b

  Flow simulation (discrete events) engine.js Every app
  64-bit

• Server utilization

  The share of time a server's units were busy, blocked, down and idle.

  utilization = average busy units ÷ units; idle = max(0, 1 − busy − blocked − down)

  Flow simulation (discrete events) engine.js Every app
  64-bit

• Throughput

  Finished entities per unit of time at a sink.

  throughput = count ÷ (t − t₀)

  Flow simulation (discrete events) engine.js Every app
  64-bit