Calculations

Calculations

• Cache key

  A short text that says whether the environment changed since a result was made.

  Environment: gravity, ambient pressure and temperature env/env.js

  • PartCraft
  64-bit

• Quantity and mass per row

  Counts the placed parts of each row and works out the mass of one and of all.

  mass each g = V mm³ × ρ g/cm³ ÷ 1000; total = each × quantity

  Manual parts list: quantities and mass illustrate/parts-list.js

  • PartCraft
  64-bit

• Same shape test

  Decides whether two parts with the same number or name are one row.

  |V₁ − V₂| ≤ 10⁻⁶ × max(V₁, 1) and |A₁ − A₂| ≤ 10⁻⁶ × max(A₁, 1)

  Manual parts list: quantities and mass illustrate/parts-list.js

  • PartCraft
  64-bit

• Mass and volume text

  The text of the mass and volume cells in the table and the CSV.

  volume: 3 decimals; mass ≥ 1000 g: kg with 3 decimals; otherwise g with 2 decimals

  Manual parts list: quantities and mass illustrate/parts-list.js

  • PartCraft
  64-bit

• Part geometry for the view

  Builds the triangles and feature lines of a part for drawing.

  Manual scene in the 3D view illustrate/scene3d.js

  • PartCraft
  32-bit, display only

• Cut faces lifted off the section plane

  Places the filled cut faces so they are not hidden by the plane that cut them.

  Manual scene in the 3D view illustrate/scene3d.js

  • PartCraft
  32-bit, display only

• Value of a number row

  The number handed to the app when a person changes a number box.

  v = min(max, max(min, typed value))

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit

• Rounding of a slider value

  Removes binary noise such as 0.30000000000000004 from a slider's value.

  v = round to (decimals of the step + 2) decimals, at most 8

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit

• Value of a slider row

  The number handed to the app while a slider is dragged or its box is changed.

  v = fix(clamp(value, min, max), step)

  Numbers typed into the property grid app-propgrid.js Every app
  64-bit

• Integer or float

  Decides how a number is written.

  Numbers sent between people editing together live-client.js Every app
  64-bit

• Writing a float

  Writes a number as 8 bytes.

  Numbers sent between people editing together live-client.js Every app
  64-bit

• Writing an integer

  Writes a whole number in the shortest integer form that holds it.

  Numbers sent between people editing together live-client.js Every app
  Exact

• Reading a float

  Reads a 4-byte or an 8-byte float from a message.

  Numbers sent between people editing together live-client.js Every app
  64-bit

• Reading a 64-bit integer

  Reads an unsigned or signed 64-bit integer.

  Numbers sent between people editing together live-client.js Every app
  Exact

• Cost of one call

  The cost of a call from its token counts and the model's prices.

  cost = (in × price in + out × price out) ÷ 1,000,000

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Spending today and this month

  The cost, tokens and number of calls for the current day and month, and the calls in the last hour.

  amount = Σ cost of the calls in the period

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Check before a call

  Refuses a call when the calls per hour, the day's or month's spending, or the day's tokens could pass a limit.

  refuse when spent + worst-case cost > limit; worst case = cost(estimated input, largest allowed output)

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Recorded cost and the token estimate

  Stores each call's cost and estimates the input tokens of the next request.

  estimated tokens = ⌈JSON length ÷ 3⌉ + 500

  Spending on a person's own AI model ai-byok.js Every app
  64-bit

• Flow through a passage

  Persons per second through a door or corridor of a given width.

  rate = max(0, Fsm × (width − 2 × boundary))

  People flow and evacuation time people.js Every app
  64-bit

• Speed and specific flow at a density

  Walking speed and flow per meter of width at a given density of people.

  S = k × (1 − 0.266 × D); Fs = S × D; k = 1.4 m/s

  People flow and evacuation time people.js Every app
  64-bit

• Rate and speed of each passage

  The flow rate and walking speed each passage gets, from its own values or the defaults for its kind.

  People flow and evacuation time people.js Every app
  64-bit

• Door service time and walking time

  How long a door takes per person, how long the passage takes to walk, and each room's distance to an exit in time.

  service = 1 ÷ rate; walk = length ÷ speed; to exit = least total walking time

  People flow and evacuation time people.js Every app
  64-bit

• Which way a room empties

  The next passage for people in a room: the one with the least remaining walking time to an exit.

  keep a hop when toExit(next) < toExit(room) − 1e-9; choose the least walk + toExit(next)

  People flow and evacuation time people.js Every app
  64-bit

• Evacuation results

  People evacuated, the time the last person reaches an exit, peak occupancy and density per room, and queues per door.

  time = latest arrival at any exit; density = peak people in a room ÷ its area

  People flow and evacuation time people.js Every app
  64-bit

• Joint frames at a pose

  Each joint's rotation and offset from its parent at the given joint values.

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Joint torques for a motion (inverse dynamics)

  The torque or force each joint needs for given positions, velocities and accelerations, with gravity, external loads and damping.

  outward: ω, α, a of each link; F = m × a_com; N = I α + ω × (I ω); inward: τᵢ = axis · n (revolute) or axis · f (prismatic) + damping × q̇ᵢ

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Mass matrix

  The joint-space mass matrix at a pose.

  column j = rnea(q, q̇ = 0, q̈ = unit vector j) with no gravity, damping or external loads

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Joint accelerations for given torques (forward dynamics)

  The acceleration of each joint under applied torques.

  M q̈ = τ − h

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Kinetic and potential energy

  The mechanism's kinetic, potential and total energy at a pose and velocity.

  KE = ½ q̇ᵀ M q̇; PE = −Σ m × (g · p_com)

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Simulated motion over time

  Joint positions and velocities at each time step under gravity and applied torques.

  RK4: y₊ = y + dt ÷ 6 × (k₁ + 2k₂ + 2k₃ + k₄); steps = round(T ÷ dt); t = step × dt

  Rigid-body dynamics of a mechanism dynamics.js Every app
  64-bit

• Courtyard of a footprint

  The rectangle around all pads, grown by a margin.

  courtyard = (min(x − w ÷ 2) − m, min(y − h ÷ 2) − m, max(x + w ÷ 2) + m, max(y + h ÷ 2) + m)

  Parametric PCB footprints footlib.js Every app
  64-bit

• Two-terminal chip

  Two pads at half the pitch either side of the center.

  x = ∓ pitch ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Dual-row surface-mount package

  Pads in two rows, numbered counter-clockwise from the top left.

  y = ((n ÷ 2 − 1) ÷ 2 − i) × pitch; x = ∓ row spacing ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Dual in-line through-hole package

  Drilled pads in two rows.

  y = ((n ÷ 2 − 1) ÷ 2 − i) × pitch; x = ∓ row spacing ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Pin header

  Drilled pads in one or two rows at a pitch.

  x = (r − (rows − 1) ÷ 2) × pitch; y = ((n − 1) ÷ 2 − i) × pitch

  Parametric PCB footprints footlib.js Every app
  64-bit

• Quad flat package

  Pads on four sides, numbered counter-clockwise from the top left.

  along a side: ((n − 1) ÷ 2 − i) × pitch; across: ± span ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Axial through-hole part

  Two drilled pads at half the lead pitch either side of the center.

  x = ∓ pitch ÷ 2

  Parametric PCB footprints footlib.js Every app
  64-bit

• Ray against boxes

  Calls back for every item whose box a ray passes through.

  t₀ = max(nearₐ), t₁ = min(farₐ); hit if t₀ ≤ t₁

  Box tree for picking and collisions m3d/bvh.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• Boxes of point lists

  The box of each item from its points, grown by a pad.

  Box tree for picking and collisions m3d/bvh.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• Material and band thicknesses

  The thickness of each library sheet and edge band in millimeters and in inches.

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  Exact

• Rules from the material picks

  The thicknesses, groove and band thicknesses that the construction rules use.

  groove = min(tback, 0.6 × tcarcass)

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Sheet size for a material

  The sheet width and height a material is cut from.

  in = round(mm ÷ 25.4 × 4) ÷ 4

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Hole positions in the drill XML

  The x and y of each hole as written in the drill file.

  x = round(x × 1000) ÷ 1000

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/export.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• G-code scale and thickness

  The unit scale and cut depth passed to the sheet G-code writer.

  thickness_mm = thickness × scale

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/export.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Relative difference

  The fraction by which a coarse result differs from the refined result.

  |a − b| ÷ |b|

  Spread between coarse and refined results study/live.js

  • CadCraft
  • BimCraft
  • DetailCraft
  • PartCraft
  64-bit

• Vertices and loose edges

  The point positions of a model definition and its loose edges.

  Model points written to USD usd/m3d.js

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

• Mesh arrays

  The point, normal, UV and color arrays of a mesh.

  Model points written to USD usd/m3d.js

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

• Number to text

  The text a number is written as, by type.

  f32: text = shortest s with fround(+s) = fround(x)

  Number text in USD files usd/usda-write.js

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

• Shortest digits

  A number to p significant digits without trailing zeros.

  Number text in USD files usd/usda-write.js

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

• Type name to number type

  Which number type a USD type name uses (32-bit float, half or 64-bit double).

  Number text in USD files usd/sdf.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact