Calculations

Calculations

• 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

• Elements above, and the gap to each

  What sits over an element's footprint and how far above its top each one starts.

  gap = max(0, lowest Y of the other element − top Y of this element)

  Assistant answers: what is above an element ask-tools.js

  • BimCraft
  32-bit in part

• Placed triangles of an element

  Every triangle of an element in the file's Z-up coordinates and length unit.

  p = (x, −z, y) of (C⁻¹ · M · v) × (1000 ÷ unitMm)

  Element triangles for analysis ifc-util.js

  • BimCraft
  32-bit in part

• Body mesh in the item's own frame

  The item's 3D shape in millimeters, relative to its own placement.

  p_item = round(W⁻¹ · p × mm, 4 decimals)

  Library items from IFC types libitem-ifc.js

  • BimCraft
  32-bit in part

• Width, depth and height

  The item's overall size from its body.

  width = max x − min x; depth = max y − min y; height = max z − min z

  Library items from IFC types libitem-ifc.js

  • BimCraft
  32-bit in part

• Plan outline from the type's footprint

  The item's 2D plan symbol, from the type's FootPrint or Plan curves.

  (x, y) = round(coordinate × mm, 4 decimals)

  Library items from IFC types libitem-ifc.js

  • BimCraft
  64-bit

• Sizes from properties

  Width, depth and height from the type's properties when the body gave none.

  size = round(value × mm, 4 decimals) for a length measure

  Library items from IFC types libitem-ifc.js

  • BimCraft
  64-bit

• Mesh points of an element

  The vertices of each element as the USD file stores them.

  (x′, y′, z′) = P · (x, y, z, 1); stored as (x′, −z′, y′)

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  32-bit in part

• Inverse of a placement

  The matrix that undoes a model's placement.

  R⁻¹ = Rᵀ ÷ s², s² = m₀² + m₁² + m₂²; t⁻¹ = −R⁻¹ · t

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  64-bit

• Site transform back to the file's coordinates

  The transform on each Site that returns the exported points to the IFC file's own coordinates.

  toFile = A · (P · C)⁻¹ · A⁻¹

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  64-bit

• Storey elevation in meters

  Each storey's elevation as an attribute of the USD file.

  elevation in m = elevation × (mm per file unit ÷ 1000)

  USD export and render hand-off usd-bimcraft.js

  • BimCraft
  64-bit

• Inverse of a placement (hand-off)

  The matrix that undoes a model's placement, for the render hand-off.

  R⁻¹ = Rᵀ ÷ s²; t⁻¹ = −R⁻¹ · t

  USD export and render hand-off handoff-bim.js

  • BimCraft
  64-bit

• Viewer scene to the USD stage

  The transform that takes camera, sun and lamp positions from the viewer's scene to the exported file's world.

  toStage = A · (P · C)⁻¹; A alone when the model has no coordination matrix

  USD export and render hand-off handoff-bim.js

  • BimCraft
  64-bit

• Mesh handed to the solid kernel

  Welds the mesh's corners and passes it to manifold-3d.

  weld grid = 10⁻⁶ × max(Δx, Δy, Δz); positions → Float32Array

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Boolean of two solids

  The difference, union or intersection of two element meshes.

  c = center of a's box; R = (a − c) OP (b − c); result = R + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Element minus all its openings

  Subtracts every opening from an element, one after another.

  A₀ = base − c; Aᵢ = Aᵢ₋₁ − (cutterᵢ − c); result = Aₙ + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Face planes of a convex cutter

  Finds the outward planes of a cutter and decides whether it is convex.

  n = (b − a) × (c − a) ÷ |…|; d = n · a; convex when n · p − d ≤ 10 ε for every corner p

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Polygon split by a plane

  Cuts a convex polygon into the part in front of a plane and the part behind it.

  t = dₐ ÷ (dₐ − d_b); x = a + (b − a) t

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Mesh clipped by a plane

  Keeps the part of a mesh on one side of a plane and closes the cut.

  dᵢ = (pᵢ − p) · n; ε = 10⁻⁹ × (d_max − d_min); cut point = a + (b − a) dₐ ÷ (dₐ − d_b)

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Cap of a cut

  Joins the cut segments into loops, sorts outer loops from holes and fills them.

  key = round(x ÷ tol), round(y ÷ tol), round(z ÷ tol); area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Half-space cut

  Removes the part of an element behind a plane, optionally only inside a polygon boundary.

  L = 4 × max(1, box diagonal) + |P₀ − box min|; prism height = 2 L

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Vertex data of one geometry

  Returns a geometry's positions and normals for drawing and for measuring.

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Placement matrix of each piece

  The matrix that takes a geometry's vertices to model space in meters, Y up.

  M = C × Y-up × scale(u) × placement

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Shift to the origin

  Finds the translation that brings the model near the origin.

  c = (box min + box max) ÷ 2 of the first element; C = translate(−(Y-up × scale(u) × placement × c))

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• File units to meters, Z up to Y up

  Scales a placement by the file's length unit and turns its axes.

  M′ = Y-up × scale(u) × M

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Face points

  The new point in the middle of each face.

  F = Σ corners ÷ n

  Subdivision surfaces mesh/subdiv.js

  • ModelCraft
  64-bit

• Edge points

  The new point on each edge.

  m = (a + b) ÷ 2; e = (a + b + F₁ + F₂) ÷ 4; point = e + (m − e) × s for 0 ≤ s < 1

  Subdivision surfaces mesh/subdiv.js

  • ModelCraft
  32-bit in part

• Vertex points

  Where each old vertex moves to.

  smooth = (F̄ + 2 R̄ + (n − 3) V) ÷ n; crease = (6 V + a + b) ÷ 8; k = min(1, (sₐ + s_b) ÷ 2); point = smooth + (crease − smooth) × k

  Subdivision surfaces mesh/subdiv.js

  • ModelCraft
  32-bit in part

• Edge sharpness per level

  The sharpness each new edge inherits.

  s′ = max(0, s − 1); open edge: ∞; crease layer = min(1, s′ ÷ 4)

  Subdivision surfaces mesh/subdiv.js

  • ModelCraft
  32-bit in part

• Texture coordinates and other corner layers

  Interpolates per-corner values onto the new quads.

  corner: own value; edge: mean of two; face: mean of the face's corners

  Subdivision surfaces mesh/subdiv.js

  • ModelCraft
  64-bit

• Limit positions

  Where each vertex of an all-quad mesh lies on the limit surface.

  smooth: (n² V + 4 Σ E + Σ F) ÷ (n (n + 5)); crease or border: (4 V + a + b) ÷ 6

  Subdivision surfaces mesh/subdiv.js

  • ModelCraft
  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

• 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

• Clear spacing a bar asks for

  The least clear distance between parallel bars for a bar size and aggregate.

  max(25.4, d_b, 4/3 × aggregate) mm; BS bars: max(d_b, aggregate + 5, 20) mm

  Rebar congestion map of a footing congestion.js

  • DetailCraft
  64-bit

• Free gap at a point

  The length of the free stretch that contains a point, between the bars either side of it.

  gap = right − left; 0 inside a bar

  Rebar congestion map of a footing congestion.js

  • DetailCraft
  64-bit

• Need and grid size

  Sets what the concrete needs and how fine the map is.

  cell = max(5, given, or max(10, ⌈max(L, B) ÷ 160 ÷ 5⌉ × 5)); columns = round(L ÷ cell)

  Rebar congestion map of a footing congestion.js

  • DetailCraft
  64-bit

• Opening and ratio per cell, and the worst place

  Fills the map and finds the tightest opening and the number of cells that are too tight.

  opening = min of the gaps in each layer; ratio = need ÷ opening

  Rebar congestion map of a footing congestion.js

  • DetailCraft
  64-bit

• Share of the open area that is too tight

  The fraction of free cells whose ratio is over 1.

  share = cells with ratio > 1 ÷ cells with opening > 0

  Rebar congestion map of a footing congestion.js

  • DetailCraft
  32-bit in part

• The congestion problem

  The warning or error listed for a footing whose steel is too tight.

  Rebar congestion map of a footing congestion.js

  • DetailCraft
  32-bit in part

• Positions stored as offsets from the origin

  The kept points as 32-bit offsets from a whole-unit origin.

  pos = fround(x − floor(min))

  Point cloud positions and read-in values pointcloud.js

  • CadCraft
  • BimCraft
  32-bit in part