Calculations

Calculations

• Quadrature nodes and weights

  The eight points and weights used to integrate the path's speed.

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Length of the path

  The arc length of the path and the running length at each piece boundary.

  piece length = h Σ wᵢ |C′(m + h xᵢ)|, h = (b − a) ÷ 2, m = (a + b) ÷ 2; L = Σ pieces

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Parameter at an arc length

  Finds the curve parameter that lies a given length along the path.

  tₙ₊₁ = tₙ − (s(tₙ) − s) ÷ |C′(tₙ)|, kept inside the bracket by bisection

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Path point nearest the seed

  The arc length of the path point closest to the center of what is copied.

  root of (C(s) − p) · C′(s) = 0 by bisection, beside the nearest of 8 samples per piece

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Turn of each copy

  Rotates each copy so it follows the path's direction without twisting.

  R ← rot(t_prev → t) × R, in n = ⌈distance ÷ (L ÷ 2000)⌉ steps between stations

  Pattern along a path brep-bodies.js

  • PartCraft
  64-bit

• Modal coordinate word

  Decides whether an address word such as X or Z is written on a line, and writes its value.

  written when round(v × 1000) ≠ round(last × 1000); text = letter + v to 3 decimals

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Numbers in a line template

  Fills the {variable} holes of a raw, comment or word template with values.

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Whole-number filter

  The int filter a post can put on a value, for example a spindle speed.

  int(s) = round(number(s))

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Arc center offsets I and J

  The center of an arc move, written relative to the start point.

  I = round₃(cₓ − round₃(X_last)); J = round₃(c_y − round₃(Y_last))

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Equality in post conditions

  The == and != tests a post definition can make on two values.

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Stock size variables

  The stock's diameter, side lengths and corners that a post can print in its header.

  sx = maxₓ − minₓ; d = 2 × r

  G-code written by text post definitions cam-postdef.js

  • PartCraft
  64-bit

• Scalar arithmetic and comparison

  Adds, subtracts, multiplies, divides and compares two plain numbers.

  a + b, a − b, a × b, a ÷ b, a < b, a = b

  CraftScript operators in the interpreter cs-vm.js

  • PartCraft
  64-bit

• Matrix multiply, divide and power

  The *, /, \ and ^ operators on matrices.

  A ÷ B = (solve(Bᵀ, Aᵀ))ᵀ; Aⁿ by repeated squaring; A⁻ⁿ = (A⁻¹)ⁿ

  CraftScript operators in the interpreter cs-vm.js

  • PartCraft
  64-bit

• Values of a counted loop

  The value the loop variable takes on each pass of for x = a:s:b.

  xₖ = a + k × s; last value = b when |xₖ − b| < 10⁻¹⁰ × max(1, |b|)

  CraftScript operators in the interpreter cs-vm.js

  • PartCraft
  64-bit

• Number text in the echo

  The text printed for a number when a statement has no semicolon.

  integer below 10¹⁵: all digits; otherwise 5 significant digits

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Matrix text in the echo

  The text printed for a vector or matrix.

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Arrays read from a saved workspace

  Checks and copies a numeric array from a part file or a worker message.

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Minimum and maximum of a variable

  The range shown for each variable in the Variables panel.

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Numeric data as 64-bit

  Gives builtins a Float64Array of any numeric value.

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Number and position text

  How a number and a position are turned into text for the script.

  number → 12 significant digits; position → 9 decimals, then 12 significant digits

  Numbers in a PartCraft script file script.js

  • PartCraft
  64-bit

• Sketch geometry and dimensions

  Writes a sketch's points, circles, relations and dimension values.

  Numbers in a PartCraft script file script.js

  • PartCraft
  64-bit

• A feature value read from a script

  Reads a setting such as a depth, given as a number or as an expression.

  Numbers in a PartCraft script file script.js

  • PartCraft
  64-bit

• Vertex placement and unit scale

  Moves every mesh vertex to where the file places it and converts it to the part's unit.

  p′ = (M · p) ÷ w × s; s = meters per file unit × 1000

  3DM mesh import: placement and units mesh3dm.js

  • PartCraft
  64-bit

• Combined block placement

  Multiplies the placement of a block by the placement of the block inside it.

  (A · B)ᵢⱼ = Σₖ Aᵢₖ × Bₖⱼ

  3DM mesh import: placement and units mesh3dm.js

  • PartCraft
  64-bit

• Scaled triangles packed for export

  Turns the scaled triangles back into a mesh for the file writers.

  Scaled mesh for printing print-export.js

  • PartCraft
  32-bit in part

• Triangles of the part's mesh

  Reads the part's mesh as a list of triangles for the scaling and splitting code.

  Scaled mesh for printing print-export.js

  • PartCraft
  64-bit

• Scaled STL or 3MF file

  Builds the file a person downloads from the Scale for printing dialog.

  Scaled mesh for printing print-export.js

  • PartCraft
  32-bit in part

• Mesh points in meters, Z up

  Converts the part's mesh vertices for the USD file.

  (x, y, z) mm → (x, −z, y) ÷ 1000 m

  USD export of a part or assembly usd-partcraft.js

  • PartCraft
  64-bit

• Instance placement

  Turns an assembly instance's placement matrix from millimeters, Y up, to meters, Z up.

  M′ = A · M · A⁻¹; translation ÷ 1000

  USD export of a part or assembly usd-partcraft.js

  • PartCraft
  64-bit

• Volume and mass attributes

  The volume in cubic meters and the mass in kilograms written on each part.

  volume m³ = V mm³ × 10⁻⁹; mass kg = V mm³ × ρ g/cm³ × 10⁻⁶

  USD export of a part or assembly usd-partcraft.js

  • PartCraft
  64-bit

• Parameter values per variant

  The value each driving parameter ends up with in each variant.

  value = parameter to 12 significant digits

  Variant pack: parameter table, sizes and library bodies variants.js

  • PartCraft
  64-bit

• Numbers in variants.csv

  How a table value is written into the CSV file.

  Variant pack: parameter table, sizes and library bodies variants.js

  • PartCraft
  64-bit

• Size of a variant

  The width, depth and height of each variant written to variants.json.

  size = max − min per axis, to 4 decimals

  Variant pack: parameter table, sizes and library bodies variants.js

  • PartCraft
  64-bit

• Volume written per variant

  The volume_mm3 figure of each variant in variants.json.

  volume to 9 significant digits

  Variant pack: parameter table, sizes and library bodies variants.js

  • PartCraft
  64-bit

• Variant body in library coordinates

  Turns a variant's mesh to Z up, anchors it at the back middle bottom and rounds it for the library item.

  (x, y, z) → (x, −z, y), shifted to the anchor, rounded to d decimals

  Variant pack: parameter table, sizes and library bodies variants-item.js

  • PartCraft
  64-bit

• Rounding helper

  Rounds a value to a number of decimals for the library item.

  r(v, d) = round(v × 10ᵈ) ÷ 10ᵈ

  Variant pack: parameter table, sizes and library bodies variants-item.js

  • PartCraft
  64-bit

• Readout rounding and flux units

  The text of each number in the results panel.

  text = v to p significant digits (p = 4 by default); flux in mWb when |Φ| ≥ 10⁻³ Wb, else µWb

  Magnetics add-on: readouts in the panel addons/magnetics/main.js

  • PartCraft
  64-bit

• Air box size

  The width and height of the air box shown under the setup.

  margin = max(width, height) × pad; box = extent + 2 × margin

  Magnetics add-on: readouts in the panel addons/magnetics/main.js

  • PartCraft
  64-bit

• Body, volume and area from a field

  The mesh that to_body returns, with its volume, area and triangle count.

  Field builtins for scripts engineer/cs-lib-field.js

  • PartCraft
  32-bit in part

• Volume of a field

  The number field_volume returns to the script.

  Field builtins for scripts engineer/cs-lib-field.js

  • PartCraft
  32-bit in part

• Density map for a graded size

  Turns a 0 to 1 density array into a profile that drives a cell size or wall thickness.

  d = clamp(D, 0, 1), stored in 32 bits; size = v₀ + (v₁ − v₀) × d

  Field builtins for scripts engineer/cs-lib-field.js

  • PartCraft
  32-bit in part

• Distance at points

  The signed distance of a field at each row of a points matrix.

  Field builtins for scripts engineer/cs-lib-field.js

  • PartCraft
  64-bit

• Inside or outside on a box grid

  Marks each cell of a box as inside (−1) or outside (0) the field.

  nᵢ = round((maxᵢ − minᵢ) ÷ h); sample at min + (i + ½) × h

  Field builtins for scripts engineer/cs-lib-field.js

  • PartCraft
  64-bit

• Overhang reported by the manufacturing check

  The overhang problem mfg_check adds, with its area and locations.

  reported when area > 4 × h²

  Field builtins for scripts engineer/cs-lib-field.js

  • PartCraft
  64-bit

• Preset figures

  The gravity, pressure and temperature each world starts from.

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

  • PartCraft
  64-bit

• Gravity in solver units

  Gravity in mm/s² for a gravity load.

  g mm/s² = g m/s² × 1000

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

  • PartCraft
  64-bit

• Ambient pressure in MPa

  The ambient pressure in the solvers' unit.

  p MPa = p Pa ÷ 10⁶

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

  • PartCraft
  64-bit

• Gauge pressure

  The pressure that loads the wall of a sealed volume.

  gauge = absolute − ambient

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

  • PartCraft
  64-bit

• Weight of a mass

  Weight in newtons from a mass in kilograms.

  W = m × g

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

  • PartCraft
  64-bit

• Loads filled in from the environment

  Gives a solver job its gravity, gauge pressures and ambient temperatures.

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

  • PartCraft
  64-bit