Calculations

Calculations

• Model bounds in the section frame

  The bounds of every drawn vertex in the turned section frame.

  box = min and max of turned vertex positions

  3D view drawing viewer3d.js

  • BimCraft
  32-bit, display only

• Polygon clipped at a station or an offset

  Cuts a wall outline at an opening's edge or at a layer boundary.

  t = (at − a) ÷ (b − a); new point has the clip coordinate exactly

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Layer bands across a wall in plan

  The band of each wall layer across the wall, from the exterior face inward.

  off₀ = ±t ÷ 2; offᵢ₊₁ = offᵢ ∓ tᵢ

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Layer thicknesses against the wall thickness

  Checks that a wall's layers add up to its thickness before any layer is drawn.

  |Σ tᵢ − t| ≤ 0.005 mm

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Curved wall outlines as chords

  Maps a path from the wall's frame back to the plan, adding points along a curved wall so the chords stay close to the arc.

  step = 2 acos(max(−1, 1 − 0.002 ÷ radius)); n = ⌈|Δstation| ÷ R ÷ step⌉

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Boundary lines between layers

  Finds the stretches of a layer boundary that lie inside the wall's outline.

  x = x_a + (x_b − x_a) × (offset − y_a) ÷ (y_b − y_a)

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Outline of joined wall pieces

  Finds the outer edges of wall pieces that touch, so shared edges inside a joint are not drawn.

  t = cross(c − a, v) ÷ cross(d, v); parallel when |cross(d, v)| < 1e-12 × |d| × |v|

  Wall layers drawn in plans and sections wall-plan-graphics.js

  • BimCraft
  64-bit

• Building width on an elevation

  The overall width of the building's walls across a view direction, for the width note on an elevation.

  x = p · right ± |n · right| × t ÷ 2 over every wall end

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Wall and opening edges for an elevation

  The edges of a straight wall's two faces, its ends and its openings, handed to the hidden-line view.

  P(s, t, h) = a + u s + n t at height h

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Walls of every level in one level's axes

  Moves every wall and opening into one level's plan and height, for a section through several levels.

  T = inverse(level) × level_wall; a′ = T a; z = T₁₄ + base offset

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Where a section cuts a wall

  The station along a wall at which the section plane cuts it, when the cut is square to the wall.

  s = ((o − a) · dir) ÷ (u · dir)

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Layer bands in a section cut

  The rectangle of each wall layer in a section, between the heights the openings leave.

  x = c + off × (n · right); offᵢ₊₁ = offᵢ ∓ tᵢ

  Wall layers drawn in plans and sections wall-section-graphics.js

  • BimCraft
  64-bit

• Solid of revolution

  Turns a profile of radius and height points into a closed triangle mesh about the vertical axis.

  vertex = (r × cos(2π i ÷ 24), r × sin(2π i ÷ 24), z), i = 0 … 23

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Elliptical head profile

  The outline of a 2:1 elliptical vessel head from the tangent line to the pole.

  (r × cos a, z₀ ± (r ÷ 2) × sin a), a = (π ÷ 2) × i ÷ 6

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Vessel capacity

  The capacity in cubic meters of a vessel or column: a cylinder and two 2:1 elliptical heads.

  V = (π (d ÷ 2)² L + (4 ÷ 3) π (d ÷ 2)² (d ÷ 4)) ÷ 10⁹

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Tank capacity

  The capacity in cubic meters of an atmospheric tank.

  V = π r² h ÷ 10⁹

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Signed volume of a mesh

  The volume enclosed by a triangle mesh in cubic millimeters, positive when the triangles face outward.

  V = Σ p · (q × r) ÷ 6 over the triangles

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Dimensions accepted for a piece of equipment

  Takes the dimensions a person typed, builds the solids and returns their bounding box, nozzles and capacity.

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Equipment moved and turned

  Moves a piece of equipment to a point and turns it about the vertical axis by an angle in degrees.

  (x', y') = (x₀ + x cos a − y sin a, y₀ + x sin a + y cos a), a = rot × π ÷ 180

  Plant equipment solids, capacity and placement addons/plant/lib/equip.js

  • BimCraft
  64-bit

• Zone solid in millimeters

  Turns a hazard or consequence zone given in meters into a closed solid in millimeters for the model.

  vertex (mm) = vertex (m) × 1000

  Plant equipment solids, capacity and placement addons/plant/lib/engineering.js

  • BimCraft
  64-bit

• Pipe run handed to the pipe stress input

  Takes the model's pipe run with the most points and gives its points and total length to the pipe stress calculator.

  length = Σ √(Δx² + Δy² + Δz²) over the legs

  Plant equipment solids, capacity and placement addons/plant/lib/engineering.js

  • BimCraft
  64-bit

• Nozzle port size

  The outside diameter in millimeters stored on a nozzle's port, from its nominal pipe size.

  size = round(od (in) × 25.4 × 10) ÷ 10

  Plant equipment solids, capacity and placement addons/plant/lib/place.js

  • BimCraft
  64-bit

• Capacity property in the model

  The capacity in cubic meters written to the CadCraft_Plant property set of the placed equipment.

  CapacityM3 = round(V × 1000) ÷ 1000

  Plant equipment solids, capacity and placement addons/plant/lib/place.js

  • BimCraft
  64-bit

• Number written to the file

  Formats a coordinate, direction component or property value as STEP text.

  num(v) = round(v × 10⁴) ÷ 10⁴

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Placement of an item

  The position and the turn about the vertical axis of a piece of equipment in the file.

  X direction = (cos a, sin a, 0), a = rot × π ÷ 180

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Reference direction of a nozzle port

  A unit vector square to a nozzle's outward direction, used as the X axis of the port's placement.

  x = (d × a) ÷ |d × a|, a = (1, 0, 0) or (0, 1, 0)

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Capacity property

  The capacity in cubic meters written to the CadCraft_Plant property set.

  CapacityM3 = round(V × 1000) ÷ 1000

  Plant equipment written as an IFC file addons/plant/lib/ifc-out.js

  • BimCraft
  64-bit

• Isometric projection

  The position on the drawing of a 3D point, before fitting to the sheet.

  u = (x − y) × cos 30°; v = z + (x + y) × 0.5

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Length text

  Turns a length in millimeters into the text on the drawing: whole millimeters, or feet and inches to 1/8 inch.

  mm: round(L); inches: round(L ÷ 25.4 × 8) eighths

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Point at a distance along a run

  The 3D point and direction at a given distance along a pipe run, used to place valves and spool balloons.

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Bill of materials quantities

  Pipe length per size and spec, the count of elbows by angle, valves and welds.

  pipe = Σ leg lengths; elbow angle = round(acos(u · v ÷ (|u| |v|)) × 180 ÷ π); welds = 2 × bends + 2 × valves

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Fit to the sheet

  The single scale and offset that place the projected runs inside the drawing area of the sheet.

  scale = min(availW ÷ bw, availH ÷ bh)

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Leg dimension

  The dimension line beside each leg and the number on it.

  real = √(Δx² + Δy² + Δz²) of the leg's 3D ends

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Coordinates in the DXF file

  Formats paper coordinates, text heights and text angles for the DXF output.

  num(v) = v rounded to 4 decimals

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Coordinates in the SVG file

  Formats paper coordinates for the SVG output and flips Y to run downward.

  f(n) = n to 2 decimals; Y = paper height − y

  Piping isometric drawing and its bill of materials addons/plant/lib/iso.js

  • BimCraft
  64-bit

• Corners of an item

  The four corners in plan of an item of given width, depth, position and turn.

  corner = (x₀ + x cos a − y sin a, y₀ + x sin a + y cos a), a = rot × π ÷ 180

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Access strips

  The strips beside each side of an item that must stay free, as turned rectangles.

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Overlap of two convex polygons

  Whether two items, or an item and an access strip or obstacle, overlap by more than a sliver.

  separated if maxA ≤ minB + tol or maxB ≤ minA + tol on any edge normal; tol = 1

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Distance from a point to a segment

  The shortest distance from a corner of one item to an edge of another.

  t = clamp(((p − a) · (b − a)) ÷ |b − a|², 0, 1); d = |p − (a + t (b − a))|

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Gap between two items

  The least distance between two items that do not overlap, compared with the minimum aisle width.

  gap = min over corners and edges of the point-to-segment distance

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Floor load of an item

  The weight of an item divided by its footprint area, compared with the floor load limit.

  load = weight ÷ (area ÷ 10⁶) in kg per m²; area = |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)| ÷ 2

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Footprint of Plant equipment

  The width, depth, height and center of a piece of Plant equipment for the layout, from its bounding box.

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Flow path length

  The length of the path through a sequence of items, measured center to center along X then Y.

  L = Σ (|Δx| + |Δy|)

  Factory layout checks addons/plant/lib/layout.js

  • BimCraft
  64-bit

• Legs of a route

  The straight legs of a route with their axis and length.

  axis = first of x, y, z with |Δ| > 10⁻⁶; length = |Δ| on that axis

  Orthogonal pipe router addons/plant/lib/route.js

  • BimCraft
  64-bit

• Route against obstacles

  Whether the center line of a route comes within a clearance of any obstacle box.

  Orthogonal pipe router addons/plant/lib/route.js

  • BimCraft
  64-bit

• Grid lines of the search

  The X, Y and Z coordinates at which a route may turn.

  lines = nozzle and lead coordinates, obstacle faces ± clearance, levels, two outer lines, and the midpoint of each neighboring pair

  Orthogonal pipe router addons/plant/lib/route.js

  • BimCraft
  64-bit

• Search state and the minimum leg

  The key that identifies a search state: grid node, direction and the length of the current leg.

  cap = round(minLeg); key = ((node × 6 + direction) × (cap + 1)) + min(cap, round(run))

  Orthogonal pipe router addons/plant/lib/route.js

  • BimCraft
  64-bit

• Cost of a step

  The cost added for moving to the next grid node.

  cost = g + step × (1 + climbCost if vertical, else 1) + (bendCost if the direction changes)

  Orthogonal pipe router addons/plant/lib/route.js

  • BimCraft
  64-bit

• Route points and length

  The final corner points of the route with collinear points removed, its length, bends and climbs.

  length = Σ leg lengths; bends = legs − 1

  Orthogonal pipe router addons/plant/lib/route.js

  • BimCraft
  64-bit

• Openings and walls on a room's edge

  Finds the doors, windows and walls that lie on the outline of a room.

  t = clamp(((p − a) · (b − a)) ÷ |b − a|², 0, 1); d = |p − a − t (b − a)|; on the edge if d ≤ tolerance

  Rooms handed to add-ons with their doors, windows and walls addons/bimcraft-api.js

  • BimCraft
  64-bit