Calculations

Calculations

• Arcs as short lines

  Door swings and other arcs written as polylines.

  steps = max(8, ⌈|a₁ − a₀| ÷ (π ÷ 32)⌉)

  Plan as a vector PDF model-pdf.js

  • BimCraft
  64-bit

• Rounding of a stored value

  Rounds a number to a given count of decimals before it is written to the file.

  round(v, d) = Math.round(v × 10ᵈ) ÷ 10ᵈ, d = 6 by default

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Placement position and turn

  The origin and X direction of an element's placement from a point in millimeters and an angle in degrees.

  location = round(mm ÷ unit, 6); X direction = (round(cos θ, 12), round(sin θ, 12), 0), θ = degrees × π ÷ 180

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Profile and polyline points

  A 2D point of a profile, axis or outline as it is stored.

  (round(x ÷ unit, 6), round(y ÷ unit, 6))

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Extrusion base and depth

  The start height and depth of a swept solid.

  position z = round(z₀ ÷ unit, 6); depth = round(depth ÷ unit, 6)

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Sloped placement frame

  A placement with its own Z and X directions, used for sloped parts.

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Quantity values

  Converts a length, area or volume in millimeter units to the value stored in a quantity set.

  length = round(mm ÷ unit, 6); area = round(mm² ÷ 10⁶, 6); volume = round(mm³ ÷ 10⁹, 6)

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• World matrix in millimeters

  Converts a placement matrix from file units to millimeters.

  translation × unit in mm; rotation part unchanged

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Placement relative to a parent

  Where an element sits in the axes of its level or site.

  M = P⁻¹ × C

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Layers of a wall type at another thickness

  The layer thicknesses of a starter wall type made thicker or thinner.

  thickest layer = wanted thickness − Σ other layers

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Type key for a thickness

  Names the wall type that has a given total thickness.

  key = base@(Math.round(mm × 10) ÷ 10)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Total thickness of a type

  The sum of a wall type's layer thicknesses.

  t = Σ layer thickness

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Wall ends from the stored placement

  The start point, end point, length and thickness of a wall as read back from the file.

  a = (M₁₂, M₁₃); b = a + (M₀, M₁) ÷ |(M₀, M₁)| × chord; chord = chordFor(Length, Bulge)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Wall height

  A wall's height from the level its top follows, or its own fixed height.

  h = (top elevation + top offset) − (base elevation + base offset)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Walls cut by another level's plan

  Finds walls of other levels that pass through a level's plan cut height.

  base + 1 < level elevation + cut < top − 1 (mm)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• New wall: angle and stored sizes

  The placement angle and the Length, Thickness, Height and offsets stored for a new wall.

  angle = atan2(b_y − a_y, b_x − a_x) × 180 ÷ π; Length = arc length (chord when straight)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Moved wall: placement and length

  Rewrites a wall's start point, angle and Length after its ends move.

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Whether a wall's shape is out of date

  Compares the stored outline, depth and axis length with the ones just computed.

  |stored − computed| < 0.001 mm for depth, length and every outline point

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Outline in the wall's own axes

  Turns the plan outline into coordinates along and across the wall.

  x′ = (x − a_x)·cos θ + (y − a_y)·sin θ; y′ = −(x − a_x)·sin θ + (y − a_y)·cos θ

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Stored shape read back

  The outline, extrusion depth and axis length a wall's shape holds now.

  arc axis length = R × |Δangle|

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Wall quantities

  Footprint area, side areas and volumes of a wall, with its openings taken off the net values.

  footprint = |shoelace(outline)|; gross side = length × height; net side = max(0, gross side − Σ w·h); gross volume = footprint × height; net volume = max(0, gross volume − Σ w·h·t)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Outline area

  The signed area of the site outline.

  A = ½ Σ (xᵢ·yᵢ₊₁ − yᵢ·xᵢ₊₁)

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Site area and perimeter

  The GrossArea and GrossPerimeter stored for the site.

  A = |shoelace|; P = Σ √(Δx² + Δy²)

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Outline saved as text

  The site outline written to the CadCraft_Site Points property.

  x,y;x,y;… each rounded to 3 decimals of the file unit

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Building position and angle on the site

  Where the building sits on the site and how far it is turned.

  M = site⁻¹ × building; at = (M₁₂, M₁₃); angle = atan2(M₁, M₀) × 180 ÷ π

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Plan points to site axes

  Moves points drawn on a level's plan into the site's own axes.

  p′ = site⁻¹ × level × p

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Building placed on the site

  Writes the building's new position and turn relative to the site.

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Levels at given elevations

  Adds levels at heights above the building's base.

  z = base + e; height = next e − e, at least 1000 mm

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Height split into equal levels

  Divides a building height into a number of equal levels.

  h = T ÷ n; zᵢ = base + i × h

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Footprint of a site-study mass

  The outline of a mass in world millimeters, read from its extruded profile.

  p = world matrix × (profile point × unit)

  Site outline, building placement and levels model-site-mass.js

  • BimCraft
  64-bit

• A point inside the footprint

  Finds a point inside a possibly concave outline, used as the seed for the floor.

  x = aₓ + (y − a_y) ÷ (b_y − a_y) × (bₓ − aₓ); seed = middle of the widest span

  Site outline, building placement and levels model-site-mass.js

  • BimCraft
  64-bit

• Walls round the footprint

  Makes a wall along every edge of the mass footprint on each of its levels.

  Site outline, building placement and levels model-site-mass.js

  • BimCraft
  64-bit

• Room quantities

  Height, perimeters, floor areas and volume of a room.

  h = elevation above − elevation; gross area = |shoelace(outline)|; volume = net area × h

  Room, floor and ceiling quantities model-slabs.js

  • BimCraft
  64-bit

• Floor slab quantities

  Thickness, perimeter, areas and volume of a floor slab.

  net area = |A(outline)| − Σ |A(hole)|; volume = net area × thickness; solid from offset − thickness, depth = thickness

  Room, floor and ceiling quantities model-slabs.js

  • BimCraft
  64-bit

• Ceiling quantities

  Thickness and areas of a ceiling.

  net area = |A(outline)| − Σ |A(hole)|

  Room, floor and ceiling quantities model-slabs.js

  • BimCraft
  64-bit

• Change key of a shape

  A short key of what a shape was made from, used to decide whether to write it again.

  numbers rounded to 0.01 mm → text → 32-bit FNV-1a hash + text length

  Room, floor and ceiling quantities model-slabs.js

  • BimCraft
  64-bit

• Height a roof sits at

  The top of the tallest wall under a roof.

  top = max(base offset + height) over the walls, else the level's height

  Room, floor and ceiling quantities model-slabs.js

  • BimCraft
  64-bit

• Default roof sizes

  The pitch, overhang and thickness a new roof gets when none are given.

  pitch = 26.565°; overhang = 12 × 25.4 mm; thickness = 8 × 25.4 mm

  Room, floor and ceiling quantities model-slabs.js

  • BimCraft
  64-bit

• Drawing units to millimeters

  The factor that turns drawing units into millimeters, by the drawing's INSUNITS code.

  1 → 25.4, 2 → 304.8, 4 → 1, 5 → 10, 6 → 1000, 10 → 914.4

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  Exact

• Extents of a block

  The bounding box of a block's lines, polylines, circles, arcs and nested blocks.

  arc: its two ends and every quarter point k × π ÷ 2 inside the sweep

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Box of a placed block

  The box of a block reference in plan millimeters.

  corner = (insert + R(rotation) · (scale · block corner)) × unit; box = min and max of the four corners

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Joining lines into chains

  Links line segments that share an end point into chains.

  key = round(x ÷ tol), round(y ÷ tol)

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Chain offset to the wall's center line

  Moves a chain of face lines sideways by half the wall thickness, with mitred corners.

  n = (−Δy, Δx) ÷ L × d; corner = axisMeet of neighboring offset lines

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Walls from pairs of parallel lines

  Pairs two parallel lines as the faces of a wall and gives its center line and thickness.

  d = (q.a − p.a)·n; overlap = [max(0, min(s₀, s₁)), min(L, max(s₀, s₁))]; center line = p + (d ÷ 2)·n over the overlap; t = |d|

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Closing traced corners

  Runs a wall end that stops short of another wall to that wall's center line.

  gap = |end − meeting point| ≤ 0.75 × max(t₁, t₂) + 1 mm

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Doors and windows from blocks

  Places a door or window on the wall nearest a block's box, with its offset and width along the wall.

  s = (c − a)·u; width = |Δx·uₓ| + |Δy·u_y| of the box, between 400 mm and L − 50 mm; offset = s − width ÷ 2

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Wall type for a traced thickness

  Chooses the wall type for a traced wall from its measured thickness.

  |t − t₀| > 1 mm → type at Math.round(t) mm, else the chosen type

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Underlay line points

  The points of the reference drawing stored with the level.

  round(mm ÷ unit, 6)

  Walls and openings traced from a drawing model-trace.js

  • BimCraft
  64-bit

• Number format in the file

  Turns a number into the text written in the PDF.

  toFixed(4), trailing zeros removed; |v| < 5e-5 → 0

  Vector PDF output pdf.js

  • BimCraft
  • DetailCraft
  64-bit

• Millimeters to points

  The factor between millimeters and PDF points.

  K = 72 ÷ 25.4

  Vector PDF output pdf.js

  • BimCraft
  • DetailCraft
  Exact