Calculations

Calculations

• Quaternion to rotation matrix

  The rotation matrix of an orientation stored as a quaternion.

  q ÷ |q|; R₀₀ = 1 − 2(y² + z²), R₀₁ = 2(xy + wz), …

  USD transforms and placement usd/geom.js

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

• Value at a time

  An animated value at a given time, between its stored samples.

  v = a + (b − a) × (t − t₀) ÷ (t₁ − t₀)

  USD transforms and placement usd/geom.js

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

• An object's own transform

  Builds the transform of one object from its list of translate, rotate, scale and matrix operations.

  M = op₁ × op₂ × … in the listed order; an inverted operation uses its inverse

  USD transforms and placement usd/geom.js

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

• World transform

  The transform of an object in the scene, through all its parents.

  W = M_root × … × M_parent × M_own

  USD transforms and placement usd/geom.js

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

• Scene units and up axis

  The transform from the scene's own units and up axis to meters with Z up.

  scale by metersPerUnit; Y-up scenes: rotate 90° about X

  USD transforms and placement usd/geom.js

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

• Placement of instanced copies

  The transform of each copy of a point instancer from its position, orientation and scale.

  M = translate(p) × rotate(q) × scale(s)

  USD transforms and placement usd/scene.js

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

• Writing an object's transform

  Stores an object's placement in the exported scene.

  USD transforms and placement usd/build.js

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

• 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

• 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-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

• Drawer boxes of a face-frame cabinet

  The sides, ends and bottom of each drawer box behind a face frame.

  box h = min(front h − clearance, opening h − 20 mm); end = bw − 2t; bottom = (bw − 2t + 2g) × (slide − 2t + 2g); bw = opening w − 2 × slide gap

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Dowels of a corner cabinet

  The number of dowels a corner cabinet's drilling needs.

  dowels = dowel holes ÷ 2

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Curved cabinet outline in the cell's own axes

  The outline points of a made-to-order curved cabinet, measured from the cell's origin along its two axes.

  (x′, y′) = ((q − o) · u, (q − o) · n)

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Closing panel of an angled corner

  The height of the panel that closes a corner which is not a right angle.

  height = cabinet h − plinth height

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

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Picked room corner

  A corner of the room outline picked on the plan, snapped to the grid.

  p = round(x ÷ g) × g; g = 50 (mm job) or 2 (inch job)

  CabinetCraft room picking and dry-run units addons/cabinetcraft/main.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Direction of the picked outline

  Whether the corners were picked clockwise, which decides the sign of each arc's sweep.

  Σ (xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ) < 0 means clockwise

  CabinetCraft room picking and dry-run units addons/cabinetcraft/main.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Sheet size in the program's units

  The sheet size, thickness and rapid rate the dry run checks a G-code program against.

  k = (1 ÷ 25.4 or 1) × (25.4 or 1); sheet = job sheet × k; rapid (inch program) = rapid ÷ 25.4

  CabinetCraft room picking and dry-run units addons/cabinetcraft/main.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Numbers on labels and the maker review

  Writes a number with at most 2 decimals.

  text = round(v × 100) ÷ 100

  CabinetCraft room picking and dry-run units addons/cabinetcraft/main.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Job converted to the other unit

  Every size in the job converted from millimeters to inches or back when the job's unit is changed.

  to inches: round(v × (1 ÷ 25.4) × 16) ÷ 16; to millimeters: round(v × 25.4)

  Cabinet job edits that change sizes addons/cabinetcraft/lib/edit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Gap at a door or window

  The width of the gap put in a run's floor row so that the cabinets after it clear an opening.

  width = ⌈(at + w + clear − start) × 10⌉ ÷ 10

  Cabinet job edits that change sizes addons/cabinetcraft/lib/edit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Filler for a leftover

  Adds a filler as wide as the space a row leaves on its wall.

  filler width = rest, when 0.5 < rest ≤ 75 mm

  Cabinet job edits that change sizes addons/cabinetcraft/lib/edit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Notch of a new L or U room

  The first size of the notch when a rectangular room is made L or U shaped.

  notch width = round(W ÷ 3); notch depth = round(D ÷ 2)

  Cabinet job edits that change sizes addons/cabinetcraft/lib/edit.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Drilling distances in inches

  The 32 mm system's drilling and hardware distances for the inch rule set.

  value = round(mm × (1 ÷ 25.4) × 10⁴) ÷ 10⁴

  Cabinet parts from a box and construction rules addons/cabinetcraft/lib/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Box sizes

  The box height without the plinth, the inside width and the depth the back takes.

  boxH = h − kick; iw = w − 2t; backDepth = backSetback + backT

  Cabinet parts from a box and construction rules addons/cabinetcraft/lib/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Door and drawer front sizes

  The size and position of every door and drawer front in the cabinet's front view.

  one door: (w − reveal) × (boxH − reveal); a pair: each (w − 2·reveal) ÷ 2 wide; n drawer fronts: each (boxH − n·reveal) ÷ n high

  Cabinet parts from a box and construction rules addons/cabinetcraft/lib/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Longest drawer slide that fits

  Picks the drawer slide length from the rule's list for the cabinet's inside depth.

  room = panel depth − backDepth − drawerBackClear; the longest listed L with L ≤ room + 1e-9

  Cabinet parts from a box and construction rules addons/cabinetcraft/lib/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Part list of one cabinet

  Every part of a cabinet with its length, width, thickness, material, quantity and banded edges.

  back in grooves: (iw + 2·groove) × (boxH − n·t + n·groove); shelf: (iw − 2·shelfClear) × (inside depth − shelfFront); drawer end: iw − 2·slideGap − 2·drawerT

  Cabinet parts from a box and construction rules addons/cabinetcraft/lib/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Size checks on a cabinet

  Reports a cabinet that is too narrow, too low or too shallow for its parts, or whose drawers do not fit.

  iw ≤ 0; boxH ≤ 2t; inside depth ≤ shelfFront; Σ fronts + n·reveal > boxH + 1e-9

  Cabinet parts from a box and construction rules addons/cabinetcraft/lib/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Linear stock to buy

  The number of pieces and the total length of each hardwood section in the job.

  length = Σ qty × length; pieces = Σ qty

  Cabinet job totals: linear stock and sheet count addons/cabinetcraft/lib/sheets.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Sheets used by a nested job

  The total number of sheets over all materials, with each material's own count and efficiency.

  sheets = Σ sheets per material

  Cabinet job totals: linear stock and sheet count addons/cabinetcraft/lib/sheets.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  Exact

• Label position on the sheet

  Where each label is printed on the page, so that it lands on the die-cut label.

  x = left + col × (label width + gap x); y = top + row × (label height + gap y)

  Part labels on label sheets addons/cabinetcraft/lib/cutlist/labels.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Bar code module width

  The width of the narrowest bar of a label's Code 128 bar code, fitted to the space beside the id text.

  module = min(0.33 mm, room ÷ (code width + 20))

  Part labels on label sheets addons/cabinetcraft/lib/cutlist/labels.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Pieces from quantities

  One entry per piece to cut, from rows with a quantity.

  Cutting profile pieces from stock bars addons/windows/lib/cutlist/bars.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit