Calculations

Calculations

• Gap that separates parts

  The distance below which two objects count as one part.

  gap = max(Δx, Δy, 1e-9) × 0.04

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Size of a part's viewport at a scale

  The paper width and height a part needs at a scale 1:n, with padding and a caption band.

  w = Δx × s + 2 × 4 mm × k; h = Δy × s + 2 × 4 mm × k + 7 mm × k; k = 1 ÷ mm per paper unit

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Shelf packing

  Places boxes in rows inside the free zone and returns each box's lower-left corner, or nothing when they do not fit.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Scale and place for every part on one paper

  Chooses the scale or scales and the position of each viewport on a given paper.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Scale on automatic paper

  With no scale given and automatic paper, the scale the largest part gets on the default paper.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Viewport placed for a part

  The viewport stored for each part: paper size and center, model center and scale.

  h = packed h − 7 mm × k; paper center = (x + w ÷ 2, y + 7 mm × k + h ÷ 2); model center = midpoint of the window

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Point coordinates

  The x, y and z of one point record.

  x = X × scaleₓ + offsetₓ (and the same for y and z)

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Scale, offset and bounds from the header

  Reads the header's scale, offset, minimum and maximum and refuses a scale that cannot be used.

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• 64-bit counts and offsets

  Reads an unsigned 64-bit integer (LAS 1.4 point count, extended record positions and lengths).

  value = hi × 2³² + lo

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Points the file really holds

  The number of whole point records between the first point and the end of the point data.

  available = ⌊(end − offset to points) ÷ record length⌋, at most the header's count

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  Exact

• 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

• LAS scale and offset

  Chooses the scale and offset the LAS file stores its integer coordinates with.

  scale = first of 0.0001, 0.001, 0.01, 0.1, 1 with extent ÷ scale < 2e9; offset = ⌊min ÷ 100⌋ × 100

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

  • CadCraft
  • BimCraft
  64-bit

• LAS point record

  Stores one point's x, y, z as integers in the LAS file.

  X = round((p − offset) ÷ scale)

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

  • CadCraft
  • BimCraft
  32-bit in part

• E57 point record

  Stores one point's x, y, z in an E57 data packet and widens the scan's bounds.

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

  • CadCraft
  • BimCraft
  32-bit in part

• Numbers written as text in the E57 header

  Writes a bound or a time stamp as text in the E57 XML section.

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

  • CadCraft
  • BimCraft
  64-bit

• Parameter values in dependency order

  Evaluates every parameter after the ones it uses and reports cycles and missing values.

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Equation results written to their targets

  Evaluates each equation and writes the result into the dimension or feature value it drives.

  written when |current − v| > 1e-12 × max(1, |v|)

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Limits on a driven value

  Checks a value against its target's kind: whole number, minimum, maximum.

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Backward solve for a driving parameter

  Finds the parameter value that makes an equation give the value a person typed.

  secant: c = b − f(b) × (b − a) ÷ (f(b) − f(a)); stop when |f| ≤ 1e-10 × max(1, |target|, |x₀|)

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Rounding of the solved value

  Replaces the solved value by the roundest number near it that still solves the equation.

  first of round(x, d decimals) for d = 0…10, then x to 12 significant digits, that keeps |f| within tolerance; else x

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Edited dimension written back to a parameter

  When a driven value is edited, changes the driving parameter behind its equation, or rewrites a constant equation to the new number.

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Value typed for a parameter

  Sets a driving parameter to a typed value, or solves the driving parameter behind a driven one.

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Removing a parameter and writing its value in

  Removes a parameter and, when asked, writes its current value into every expression that used it.

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Design table row made permanent

  Writes a set of override values into the parameters.

  Parameters and equations params.js

  • CadCraft
  • PartCraft
  64-bit

• Frame a sheet maps onto

  The drawing area a redline sheet is mapped onto: a given box, or the extents of everything drawn.

  Redline items placed in the drawing redline.js

  • CadCraft
  64-bit

• Item geometry in drawing units

  An item's box, points and center in drawing coordinates.

  x = x0 + fx × (x1 − x0); y = y0 + fy × (y1 − y0); center = midpoint of the box

  Redline items placed in the drawing redline.js

  • CadCraft
  64-bit

• Cloud arc length and margin

  The arc length of a revision cloud, the margin round the item and the text height of the revision mark.

  base = text height × dimension scale; arc = 4 × base; margin = arc; text = 1.4 × base

  Redline items placed in the drawing redline.js

  • CadCraft
  64-bit

• Revision cloud outline

  The rectangle a revision cloud is drawn round: the item's box grown by the margin.

  x0 − margin, y0 − margin, x1 + margin, y1 + margin

  Redline items placed in the drawing redline.js

  • CadCraft
  64-bit

• Picture scale

  Drawing units per pixel of a pasted picture.

  units per pixel = W ÷ pixel width

  Pasted picture size pastepic.js

  • CadCraft
  64-bit

• Drawing units per millimeter

  The factor that turns a size in millimeters into the drawing's units.

  units per mm = units per point × 72 ÷ 25.4

  Pasted picture size pastepic.js

  • CadCraft
  64-bit

• Size of a copied area

  The width and height a copied area takes in the drawing, on paper or at its real size.

  size = size in mm × units per mm

  Pasted picture size pastepic.js

  • CadCraft
  64-bit

• Region size, enclosing triangle and tolerances

  Measures the region and sets the tolerances every later test uses.

  D = max(Δx, Δy); eps = 1e-13 × D; epsA = 1e-13 × D²

  Triangulation of solid faces acis/cdt.js

  • CadCraft
  • ModelCraft
  64-bit

• Orientation of three points

  Twice the signed area of the triangle a, b, c: positive when anticlockwise.

  (x_b − x_a) × (y_c − y_a) − (y_b − y_a) × (x_c − x_a)

  Triangulation of solid faces acis/cdt.js

  • CadCraft
  • ModelCraft
  64-bit

• In-circle test

  Whether point d lies inside the circle through a, b and c.

  det of rows (a − d, |a − d|²), (b − d, |b − d|²), (c − d, |c − d|²) > 0

  Triangulation of solid faces acis/cdt.js

  • CadCraft
  • ModelCraft
  64-bit

• Triangle that holds a point

  Walks from the last triangle to the one a new point falls in.

  Triangulation of solid faces acis/cdt.js

  • CadCraft
  • ModelCraft
  64-bit

• Inserting a point

  Adds one point: merged into a corner it coincides with, splitting an edge it lies on, or splitting the triangle it is inside.

  Triangulation of solid faces acis/cdt.js

  • CadCraft
  • ModelCraft
  64-bit

• Do two segments cross

  Whether edge c–d properly crosses boundary segment a–b.

  Triangulation of solid faces acis/cdt.js

  • CadCraft
  • ModelCraft
  64-bit

• Face corners in model units

  The corners of an add-on's solid in the 3D model's units, and where the solid is placed.

  local = (q − o) × k; translation = o × k

  Add-on solids placed on the 3D tab addons/cadcraft-api.js

  • CadCraft
  64-bit

• Rule read into the library

  Checks a rule from a file or from storage and sets the base size's move to zero.

  Grade rule library addons/apparel/lib/rules.js

  • CadCraft
  64-bit

• Rule applied to a piece

  A library rule as moves for a piece's own size range and units.

  move = round to 6 decimals of (m − base) × k; k = 1, 25.4 or 1 ÷ 25.4

  Grade rule library addons/apparel/lib/rules.js

  • CadCraft
  64-bit

• Rules read from a RUL file

  Turns a RUL file's rules into library entries measured from the sample size.

  move = value for the size − value for the sample size

  Grade rule library addons/apparel/lib/rules.js

  • CadCraft
  64-bit

• Rules written to a RUL file

  Writes the library's rules as the delta lines of a RUL file.

  Grade rule library addons/apparel/lib/rules.js

  • CadCraft
  64-bit

• Face-frame default sizes

  The stile and rail width, overlay and door gap a job uses when it sets none.

  stile = rail = 38 mm; overlay = 12 mm; gap = 3 mm; inch job: round(mm ÷ 25.4 × 16) ÷ 16

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Carcass depth behind a face frame

  The depth the carcass is built with when a face frame takes part of the cabinet's depth.

  d = max(1, d − frame thickness)

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Face-frame openings and overlay fronts

  The rails, the openings between them and the doors or drawer fronts that cover each opening.

  opening h = (box h − (2 + mids) × rail) ÷ (mids + 1); front h = opening h + lap below + lap above; pair door w = (opening w + 2 × overlay − gap) ÷ 2

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Door and blind panel of a blind corner

  The door over the open part of a blind corner cabinet and the panel over the blind part.

  door w = (w − blind) − reveal; panel w = blind − reveal; h = box h − reveal

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Part size stored in the cut list

  Adds one part with its length, width, thickness and material.

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Frame rail length and counts

  The length of the frame's rails and how many rails and mid rails a cabinet needs.

  rail length = w − 2 × stile − blind

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Doors and drawer fronts counted by size

  Groups equal fronts into one cut-list line with a quantity.

  CabinetCraft parts, fronts and face frames addons/cabinetcraft/lib/build.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  Exact