Calculations

Calculations

• Where two face lines meet

  The point where two lines, each given by a point and a direction, cross.

  s = ((p₂ − p₁) × d₂) ÷ (d₁ × d₂); point = p₁ + s·d₁

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Nodes and tees

  Groups wall ends that meet and finds ends that land on another wall's side.

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Corner points at a node

  The mitre or corner point between each pair of neighboring walls at a node.

  c = left face of A ∩ right face of B; kept when |c − node| ≤ 4 × max(h_A, h_B) + tol

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Faces of curved walls

  Where a straight face meets a circular face, or two circular faces meet, nearest a given point.

  line and circle: t = −b ± √(b² − c); two circles: x = (d² + r₁² − r₂²) ÷ 2d, y = √(r₁² − x²)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Curved wall outline

  The outline of a curved wall with each arc edge kept as a bulge.

  bulge = tan(sweep ÷ 4)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Removing repeated and collinear points

  Drops outline points that repeat or lie on a straight run.

  collinear when |ab × bc| ≤ 1e-6 × (|ab|·|bc| + 1e-12) and ab·bc ≥ 0

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Signed outline area

  The signed area of an outline, used for the footprint and to check its direction.

  A = ½ Σ (xᵢ·yᵢ₊₁ − yᵢ·xᵢ₊₁)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Outline validity test

  Decides whether an outline is anticlockwise and does not cross itself.

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Location line offset

  How far a wall's location line is from its center line for each justification.

  face: ± t ÷ 2; core: ± (t ÷ 2 − layer thickness up to the core face or core middle)

  Wall joins and plan outlines model-walls.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

• Point along a snapped direction

  The point at an orthogonal or stepped angle from the last point, stopping at a wall it crosses or at a rounded length.

  θ = round(θ ÷ step) × step; l = len × cos(θ₀ − θ); p = from + l × (cos θ, sin θ)

  Drawn points: angle, length and wall-face paths model-tools.js

  • BimCraft
  64-bit

• Nearest point on a wall line or face

  The point on a wall's center line or face nearest the pointer.

  s = clamp((p − a)·u, 0, L); q = a + s·u

  Drawn points: angle, length and wall-face paths model-tools.js

  • BimCraft
  64-bit

• Signed area of a drawn loop

  The signed area of a closed chain of points, used to tell which side is outside.

  A = ½ Σ (xᵢ·yᵢ₊₁ − yᵢ·xᵢ₊₁)

  Drawn points: angle, length and wall-face paths model-tools.js

  • BimCraft
  64-bit

• Center lines for a path drawn on a wall face

  Offsets a drawn path by half the wall thickness and mitres the corners.

  offset = ± t ÷ 2 along the left normal; corner = intersection of neighboring offset lines

  Drawn points: angle, length and wall-face paths model-tools.js

  • BimCraft
  64-bit

• Where two center lines meet

  The meeting point of line a→b and line c→d, with its position along each.

  den = r × s; t = ((c − a) × s) ÷ den; u = ((c − a) × r) ÷ den; p = a + t·r

  Trim, extend and corner walls model-trim.js

  • BimCraft
  64-bit

• New ends of a trimmed wall

  Which part of the wall stays and where its moved end goes.

  inside when 0.5 ÷ L < t < 1 − 0.5 ÷ L; click side by t_c = (click − a)·(b − a) ÷ L²

  Trim, extend and corner walls model-trim.js

  • BimCraft
  64-bit

• Trim or extend to a wall

  A wall's new ends when it is trimmed or extended to another wall.

  allowed when −slack ≤ u ≤ 1 + slack, slack = (t_edge ÷ 2) ÷ L_edge

  Trim, extend and corner walls model-trim.js

  • BimCraft
  64-bit

• Corner two walls

  Both walls' new ends at the point their center lines meet.

  Trim, extend and corner walls model-trim.js

  • BimCraft
  64-bit

• Whether a trim cuts through an opening

  Checks each door and window on the wall against the wall's new extent.

  s₀ = offset − shift, s₁ = s₀ + width; cut when the opening is not wholly outside and s₀ < −0.5 or s₁ > L + 0.5

  Trim, extend and corner walls model-trim.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