Calculations

Calculations

• Line ends and their directions

  The two end points of a line and the direction in which the line leaves each.

  a = atan2(end − neighbor)

  P&ID line geometry and connections addons/pid/lib/lines.js

  • CadCraft
  64-bit

• Move, rotate, scale or mirror a line

  The line's points, symbol size and text height after a transform.

  x′ = m₀x + m₂y + m₄; y′ = m₁x + m₃y + m₅; s = √|m₀m₃ − m₁m₂|

  P&ID line geometry and connections addons/pid/lib/lines.js

  • CadCraft
  64-bit

• Symbol connection points in the drawing

  Turns a point of a symbol's own frame into drawing coordinates using the symbol's position, rotation and scale.

  x′ = x₀ + (x·sx)·cos θ − (y·sy)·sin θ; y′ = y₀ + (x·sx)·sin θ + (y·sy)·cos θ

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Connection tolerance

  How close a line end must be to a connection point, a line end or a line for the two to count as joined.

  tol = 0.04 × max(size a, size b, 1e-6); joined when √(Δx² + Δy²) ≤ tol

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Candidate search grid

  Limits which symbol connections and lines are tested against each line end.

  cell = max(tol of the largest size, 1e-9); index = floor(v ÷ cell)

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Line end on the body of another line

  Decides whether a line end lands on another line between its ends, which makes it a branch.

  u = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); hit when |p − (a + u (b − a))| ≤ tol

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Connection points of a symbol

  Where lines attach to a placed symbol, in the symbol's own frame.

  x = x_unit × l; y = y_unit × l

  P&ID line geometry and connections addons/pid/lib/symbols.js

  • CadCraft
  64-bit

• Symbol drawn at its size

  Scales the unit-size symbol shapes to the placed symbol's length.

  v′ = v × k

  P&ID line geometry and connections addons/pid/lib/symbols.js

  • CadCraft
  64-bit

• Symbol turned and moved

  Rotates symbol entities about the origin and moves them to a point.

  x′ = pₓ + x cos θ − y sin θ; y′ = p_y + x sin θ + y cos θ

  P&ID line geometry and connections addons/pid/lib/symbols.js

  • CadCraft
  64-bit

• Drawing units to millimeters on export

  Converts every exported symbol position, line vertex and symbol size to millimeters.

  mm = round(v × mmPerUnit, 3 decimals)

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

  • CadCraft
  • BimCraft
  64-bit

• Drawing extent on export

  The width and height stated for the exported drawing.

  w = ceil(mm(max x) + 50); h = ceil(mm(max y) + 50)

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

  • CadCraft
  • BimCraft
  64-bit

• Symbol position and size on import

  Places an imported plant item in the drawing at the file's position and size.

  x = x_file × perMm; l = SymbolSize × perMm

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

  • CadCraft
  • BimCraft
  64-bit

• Line ends moved onto connections on import

  Moves an imported line end onto the nearest symbol connection when it is close enough.

  moved when distance ≤ 0.6 × symbol size

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

  • CadCraft
  • BimCraft
  64-bit

• Numbers read from DEXPI attributes

  Turns an attribute's text into a number.

  DEXPI and PCF plant exchange files addons/pid/lib/interop/dexpi.js

  • CadCraft
  • BimCraft
  64-bit

• Position and rotation of a plant item

  The location of an item and its rotation in the plane, read from its Position element.

  rotation = atan2(Reference.Y, Reference.X)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/dexpi.js

  • CadCraft
  • BimCraft
  64-bit

• Position and direction written to DEXPI

  Writes an item's location and its direction vector.

  Reference = (round(cos θ, 9 decimals), round(sin θ, 9 decimals), 0)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/dexpi.js

  • CadCraft
  • BimCraft
  64-bit

• Numbers written to PCF

  How a coordinate or a bore is written in a PCF file.

  text = round(n, 4 decimals)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• End point lines read from PCF

  Reads a component's end point: three coordinates, a bore and an end type.

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• PCF units to millimeters

  Converts coordinates and bores from the units named in the file header to millimeters.

  x_mm = x × factor; factors: inch 25.4, foot 304.8, meter 1000, cm 10

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• Bend angle read from PCF

  Reads a component's angle in degrees.

  angle = value ÷ 100

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• Geometry checks on a PCF file

  Flags pipes with no length, elbows whose center is not equally far from both ends, and straight parts that change bore.

  |r₀ − r₁| > 0.01 × max(r₀, r₁, 1)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• Length of a PCF component

  The straight distance between a component's two end points, in millimeters.

  length = √(Δx² + Δy² + Δz²)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• Which PCF components meet

  Finds end points and branch points that coincide, and the ends left open.

  joined when √(Δx² + Δy² + Δz²) ≤ tol

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• Point lines written to PCF

  Writes an end point, branch point or center point line.

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
  • BimCraft
  64-bit

• Size units per drawing unit

  How many inches or millimeters one drawing unit is.

  factor = (meters per drawing unit) ÷ 0.0254 or ÷ 0.001

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Feet per drawing unit

  The factor that turns drawing units into feet for the takeoff export.

  feet = (meters per drawing unit) ÷ 0.3048

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Segments of a run

  Each straight stretch of a run with its length, unit direction, left normal and distance from the start.

  t = (b − a) ÷ |b − a|; n = (−t_y, t_x); s₀ = Σ earlier lengths

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Point at a distance along a run

  The point a given distance along the centerline.

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Nearest point on a run

  The point of a run's centerline closest to a given point.

  at = clamp((p − a)·t, 0, length)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Turn between two directions

  The signed angle from one direction to the next.

  turn = atan2(t₁ × t₂, t₁ · t₂)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Bend at a corner

  Where an elbow starts and ends, its center and its angles.

  T = R × tan(θ ÷ 2); p₁ = V − t_in T; p₂ = V + t_out T; c = p₁ + n_in R

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Cross-section outline

  The points of a rectangular, round or flat-oval section used to build the 3D solid.

  round: (r cos a, r + r sin a), a = −¾π + 2πj ÷ N

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Signed volume of a closed mesh

  The volume enclosed by a set of polygons, positive when the faces point outward.

  V = Σ a · (b × c) ÷ 6 over the fan triangles of each face

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Solid through a row of sections

  One closed solid from the cross-sections along a run, with its two ends capped.

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Numbers in CSV exports

  How a number cell is written in a CSV file.

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Takeoff mark coordinates

  Rounds the points of each takeoff mark before they are stored in the takeoff project.

  v′ = round(v × 10⁶) ÷ 10⁶

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Scale of the takeoff sheet

  Feet per PDF point for the sheet the takeoff is measured on, and the mapping of drawing points to PDF points.

  K = 72 ÷ 25.4; feet per point = (feet per drawing unit) ÷ (m₀ × K)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

  • CadCraft
  64-bit

• Cleaning a run's data

  Checks a run's points, sizes, elevation, slope and valves before the run is stored.

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Move, rotate, scale or mirror a run

  The run's points, scale, elevation, symbol size and valve positions after a transform.

  s = √|m₀m₃ − m₁m₂|; k′ = k ÷ s; z′ = z × s

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Elevation along a run

  The centerline elevation a given plan distance along the run.

  z(s) = z₀ − slope × s

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Branches onto other runs

  Finds where a run's end sits on another run and works out the tee or wye, its angle and how far the branch is cut back.

  sin φ = |t_main × t_branch|; cut = (OD_main ÷ 2) ÷ sin φ; gap = OD_branch ÷ sin φ

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Elbows, reducers and trimmed pieces

  Places an elbow at each turn and a reducer at each size change, and trims the straight pieces to fit.

  T = R × tan(θ ÷ 2); reducer length = 1.5 × max(OD₁, OD₂)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Sections for the 3D pipe

  The cross-sections along the centerline that the 3D solid is built from.

  elbow steps = max(2, ceil(θ ÷ 15°)); z = z₀ − slope × s − OD ÷ 2

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Drawing units to feet or meters, and the slope factor

  Converts a plan length to feet or meters and corrects it for the run's slope.

  ft = du × k ÷ 12; m = du × k × 25.4 ÷ 1000; factor = √(1 + slope²)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Pipe length by size

  The length of pipe of each size in a run, in plan and along the slope.

  len = Σ lenOut(segment) × √(1 + slope²)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Schedule totals

  Pipe length and steel weight by material and size, fitting counts, and the totals.

  weight = (weight per length) × length; total = Σ rows

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Slope label

  The slope written on the drawing and in the schedule: a fraction of an inch per foot, or a percentage.

  in/ft = slope × 12; % = slope × 100

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Plan of a run

  The lines and arcs drawn for a run: a single centerline, or two side lines with elbow arcs and reducers.

  side line = centerline ± n × OD ÷ 2; elbow arcs at R ± OD ÷ 2

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Size label

  The size written beside a pipe: NPS, DN, or a tube size with its outside diameter in millimeters.

  mm = OD (in) × 25.4

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

  • CadCraft
  64-bit

• Typed pipe size

  Matches what a person types (2, 1-1/2, 1.5, DN50) to a size of the pipe table.

  Pipe runs: layout, 3D solid and schedule addons/piping/main.js

  • CadCraft
  64-bit