Calculations

Calculations

• Grid placement

  The point where two grid axes meet, with their offsets, as a placement.

  t = ((pB − pA) × dB) ÷ (dA × dB); point = pA + dA t

  IFC units and placements ifc/geo-ctx.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Map conversion

  The matrix that takes model coordinates to map coordinates, with its rotation and scale.

  map = (E, N, H) + R(θ) · S · model; θ = atan2(ordinate, abscissa)

  IFC units and placements ifc/geo-ctx.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Matrix product

  The product of two 4 × 4 matrices.

  IFC units and placements ifc/geo-math.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Point through a matrix

  Transforms a point by a matrix.

  p' = M · (x, y, z, 1)

  IFC units and placements ifc/geo-math.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Matrix inverse

  The inverse of a 4 × 4 matrix, or null when it has none.

  M⁻¹ = adjugate ÷ determinant

  IFC units and placements ifc/geo-math.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Rotation about an axis

  The matrix that turns by an angle about an axis through the origin.

  R = c I + s [a]× + (1 − c) a aᵀ

  IFC units and placements ifc/geo-math.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Polygon normal

  The normal of a 3D polygon, with a length of twice its area.

  n = Σ ((yₐ − y_b)(zₐ + z_b), (zₐ − z_b)(xₐ + x_b), (xₐ − x_b)(yₐ + y_b))

  IFC units and placements ifc/geo-math.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Signed area of a 2D polygon

  The area of a profile outline, positive when counter-clockwise; used to orient outlines and holes.

  A = Σ (xₐ y_b − x_b yₐ) ÷ 2

  IFC units and placements ifc/geo-math.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Position and direction of a port

  Where a port is, in millimeters, and the way it faces.

  p = M · (0, 0, 0) × mm; z = normalize(M · (0, 0, 1) direction)

  Piping in an IFC file as PCF components ifc/pipes.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Ends and bore from the extruded body

  The two ends of a pipe segment and its bore from its extruded solid.

  a = T · 0; b = T · (direction × depth); bore = 2 × radius × mm

  Piping in an IFC file as PCF components ifc/pipes.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Turn angle of a fitting

  The angle a two-port fitting turns the pipe through.

  turn = 180 − acos(p · q) × 180 ÷ π, rounded to 2 decimals

  Piping in an IFC file as PCF components ifc/pipes.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Center point of a bend

  The corner where the axes of a bend's two ports meet.

  s = (b e − c d) ÷ (a c − b²), t = (a e − b d) ÷ (a c − b²); center = midpoint of the two closest points

  Piping in an IFC file as PCF components ifc/pipes.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Bore of a component

  The bore written for a pipe section.

  bore = nominal diameter for the pipe size, else outside diameter to 1 decimal

  PCF piping files from and to pipe runs mep/pcf-bim.js

  • BimCraft
  64-bit

• Corner and angle of a bend

  The corner point and turn angle written for an elbow or bend.

  corner = p₀ + d₁ × R tan(θ ÷ 2); angle = θ × 180 ÷ π to 2 decimals

  PCF piping files from and to pipe runs mep/pcf-bim.js

  • BimCraft
  64-bit

• Where two legs meet

  The corner of an imported elbow from the legs before and after it.

  s = (b e − c d) ÷ (a c − b²), t = (a e − b d) ÷ (a c − b²); corner = midpoint of the two closest points

  PCF piping files from and to pipe runs mep/pcf-bim.js

  • BimCraft
  64-bit

• Position of a valve along a run

  The distance along an imported run to the point nearest a valve.

  s = Σ earlier leg lengths + clamp((p − a) · d, 0, L), rounded to 1 decimal

  PCF piping files from and to pipe runs mep/pcf-bim.js

  • BimCraft
  64-bit

• Pipe size for an imported bore

  The standard nominal diameter nearest to a bore that is not a standard size.

  nearest = table value with the least |value − bore|

  PCF piping files from and to pipe runs mep/pcf-bim.js

  • BimCraft
  Exact

• Distance of a point along the run

  How far along the run's drawn line a point lies, measured from the first point.

  s = Σ earlier leg lengths + clamp((p − a)·d, 0, L)

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Each part's place and center-line length

  The two ends of every pipe, bend and tee along the run, and the part's own center-line length.

  bend: R × θ; tee: 2 × m; straight: |b − a|

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Where the run is cut and where spools break

  The cut positions inside straight pipe and the breaks between spools, from the field welds and the longest spool length.

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Spool length

  The parts of each spool and the spool's total center-line length.

  length = Σ part lengths, in run order

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Cut length of a straight piece

  The length of each straight pipe piece on the spool sheet's cut list.

  length = |b − a|

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Bend angle on the fitting list

  The angle shown for each elbow and the count of like fittings.

  angle = round(θ × 180 ÷ π)

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Pipe length and weight on the bill of materials

  The total cut length of pipe in a spool and its steel weight.

  kg = (kg per m) × Σ cut lengths ÷ 1000

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Duct cut list

  How many stock-length duct pieces each straight duct needs, and the length left over.

  full = floor((L + 0.5) ÷ piece); rest = L − full × piece

  Pipe spools, cut lists and spool sheets mep/spools.js

  • BimCraft
  64-bit

• Lengths and weights printed on the spool sheet

  The spool length, cut lengths, pipe length and weight as they appear in the PDF.

  printed kg = round(kg × 10) ÷ 10

  Pipe spools, cut lists and spool sheets mep/spool-sheet.js

  • BimCraft
  64-bit

• Spool sheet CSV rows

  The cut lengths, quantities and pipe weight exported as CSV.

  exported kg = round(kg × 100) ÷ 100

  Pipe spools, cut lists and spool sheets mep/spool-sheet.js

  • BimCraft
  64-bit

• Axis placement

  The origin and three unit axes of an AXIS2_PLACEMENT_3D.

  z = axis ÷ |axis|; x = (ref − z (ref·z)) ÷ |…|; y = z × x

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Circle

  The point at an angle on a circle, and the angle of a point.

  P(t) = o + r cos t · x + r sin t · y; t = atan2(l_y, l_x)

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Polyline

  The point at a parameter along a polyline, and the parameter nearest a point.

  P(t) = (1 − f) Pᵢ + f Pᵢ₊₁, i = ⌊t⌋, f = t − i

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Knot span

  Which knot interval a B-spline parameter falls in.

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  Exact

• B-spline basis functions

  The p + 1 basis functions that are not zero at a parameter.

  N_{i,0} = 1; N_{i,j} built from (t − u) ÷ (u_b − u_a) terms in the Cox–de Boor triangular table

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• B-spline curve point

  The point on a B-spline or rational B-spline curve at a parameter.

  C(t) = Σ Nᵢ wᵢ Pᵢ ÷ Σ Nᵢ wᵢ

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Is a B-spline curve closed

  Decides whether a B-spline curve's two ends meet, so it can be treated as periodic.

  |C(t₀) − C(t₁)| < 1e-9 × max(1, max |Pᵢ|)

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• B-spline surface point

  The point on a B-spline or rational B-spline surface at (u, v).

  S(u, v) = Σ Σ Nᵢ(u) Nⱼ(v) wᵢⱼ Pᵢⱼ ÷ Σ Σ Nᵢ(u) Nⱼ(v) wᵢⱼ

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Seams and poles of a B-spline surface

  Decides which direction of a B-spline surface closes on itself and which boundary rows collapse to a point.

  two points are the same when |a − b| < 1e-7 × max(1, |a|)

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Cylinder

  The point at (angle, height) on a cylinder, and the angle and height of a point.

  S(u, v) = o + r cos u · x + r sin u · y + v · z

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Cone

  The point at (angle, distance along the axis) on a cone, and the inverse.

  r(v) = R + v tan α; v = ((ρ − R) tan α + l_z) ÷ (tan² α + 1)

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Sphere

  The point at (longitude, latitude) on a sphere, and the inverse.

  S(u, v) = o + r cos v cos u · x + r cos v sin u · y + r sin v · z

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Torus

  The point at two angles on a torus, and the inverse.

  c = R + r cos v; S(u, v) = o + c cos u · x + c sin u · y + r sin v · z

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Surface of revolution

  The point of a profile curve turned about an axis by an angle, and the inverse.

  S(u, v) = o + h z + rr cos u + (z × rr) sin u, h = (C(v) − o)·z, rr = (C(v) − o) − h z

  STEP curves and surfaces: points from parameters step/geom.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Length and angle units

  The file's length unit in millimeters and its plane-angle unit in radians.

  mm = prefix × 1000 for a meter; a conversion-based unit = its value × its base unit

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Point coordinates

  A CARTESIAN_POINT in millimeters.

  (x, y, z) × unit in mm

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Radii and cone angles

  The radius of a cylinder, cone, sphere or torus in millimeters and a cone's half angle in radians.

  r × unit in mm; α × angle unit, accepted when 0 < |α| < π ÷ 2

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Knot vectors

  The full knot vector of a B-spline from the file's knots and multiplicities, or the one a uniform, quasi-uniform or Bézier form implies.

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  Exact

• Model size and chord tolerance

  The size of the model and the distance a triangle may stray from a curved face.

  size = diagonal of the box around every point; tol = max(4e-4 × size, 1e-4 mm)

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Closing a loop of edges

  Drops the last point of an edge loop when it repeats the first.

  |first − last| ≤ 0.01 × tol

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Placement matrices

  A placement as a 4 × 4 matrix, the product of two and the inverse of one.

  M⁻¹ = [Rᵀ, −Rᵀ t]

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• A component placed in its assembly

  The transform that carries a component's coordinates into the assembly that uses it.

  T = M(A₂) × M(A₁)⁻¹

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Placed vertex positions

  Every vertex of a solid moved to its place and stored for the app.

  p′ = R p + t

  STEP import: units, points and assembly placement step/read.js

  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit