Calculations

Calculations

• 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

• 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

• Typed length to millimeters

  Reads a typed length in feet and inches, inches with a fraction, or any unit mark, as millimeters.

  mm = sign × (|feet| × 12 + inches + n ÷ d) × 25.4

  Typed lengths, angles and pitches model-units.js

  • BimCraft
  Exact

• Typed point, step or polar entry

  Reads a relative step, an absolute point, a length at an angle, or a bare length from the keyboard.

  Typed lengths, angles and pitches model-units.js

  • BimCraft
  Exact

• Typed roof pitch to degrees

  Reads a pitch typed as a rise over a run, or in degrees.

  degrees = atan(rise ÷ run) × 180 ÷ π

  Typed lengths, angles and pitches model-units.js

  • BimCraft
  64-bit

• Area as text

  Formats square millimeters as m² or ft² for labels.

  m² = round(mm² ÷ 10⁴) ÷ 100; ft² = round(mm² ÷ 304.8² × 10) ÷ 10

  Typed lengths, angles and pitches model-units.js

  • BimCraft
  64-bit

• Pitch as text

  Formats a pitch in degrees as a rise in 12, or as degrees.

  rise = round(tan(θ) × 12 × 4) ÷ 4

  Typed lengths, angles and pitches model-units.js

  • BimCraft
  64-bit

• Angle as text

  Formats an angle in degrees, wrapped to 0 to 360.

  a = round(((deg mod 360) + 360) mod 360 × 10) ÷ 10

  Typed lengths, angles and pitches model-units.js

  • BimCraft
  64-bit

• Next point from a typed entry

  The plan point for a typed absolute point, relative step, length at an angle, or length along the pointer's direction; and a door or window offset from a typed distance.

  relative: q = last + (dx, dy); polar: q = last + len × (cos θ, sin θ), θ = degrees × π ÷ 180; along the pointer: q = last + len × (to − last) ÷ |to − last|

  Typed points and door or window positions model-ui.js

  • BimCraft
  64-bit

• Door or window position from the pointer

  The wall under the pointer and the offset of an opening centered on it.

  s = (p − a)·u; offset = s − width ÷ 2, then (L − width) ÷ 2 near the middle, else round(offset ÷ step) × step

  Typed points and door or window positions model-ui.js

  • BimCraft
  64-bit

• Mode frequencies of a box room

  Every standing-wave frequency of a rigid box up to a top frequency, with its kind.

  f = c ÷ 2 × √((i ÷ L_x)² + (j ÷ L_y)² + (k ÷ L_z)²), c = 343 m/s

  Room modes and low-frequency wave solver modes.js

  • BimCraft
  64-bit

• Schroeder frequency

  The frequency below which the sound field is separate modes, from reverberation time and volume.

  f_S = 2000 × √(T ÷ V)

  Room modes and low-frequency wave solver modes.js

  • BimCraft
  64-bit

• Smallest gap between modes

  The smallest difference between neighboring mode frequencies below a limit.

  min(fᵢ − fᵢ₋₁)

  Room modes and low-frequency wave solver modes.js

  • BimCraft
  64-bit

• Wave simulation of a box room

  The pressure over time at a listener after a pulse at a source, and its spectrum.

  pⁿ⁺¹ = damp × (2pⁿ − pⁿ⁻¹) + Σ_axes (c·Δt ÷ Δ)² × (p₋ + p₊ − 2pⁿ); Δt = 0.9 × Δ_min ÷ (c √3)

  Room modes and low-frequency wave solver modes.js

  • BimCraft
  32-bit in part

• Resonance peaks of the spectrum

  The frequencies and sizes of the local maxima of the spectrum.

  offset = ½ (y₀ − y₂) ÷ (y₀ − 2y₁ + y₂); f = (i + offset) × Δf

  Room modes and low-frequency wave solver modes.js

  • BimCraft
  32-bit in part

• 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

• Page scale matrix

  The matrix that lets the rest of the page be written in millimeters.

  [K 0 0 K 0 0] with K written as num(K) = 2.8346

  Vector PDF output pdf.js

  • BimCraft
  • DetailCraft
  64-bit

• Page size in points

  The page box from the sheet size in millimeters.

  points = num(mm × K)

  Vector PDF output pdf.js

  • BimCraft
  • DetailCraft
  64-bit

• Circle as four curves

  A circle written as four cubic Bézier curves.

  control distance k = 0.5522847498 × r

  Vector PDF output pdf.js

  • BimCraft
  • DetailCraft
  64-bit

• Text position and matrix

  Where a text starts and how it is turned and sized.

  x = x₀ + dx·cos θ, y = y₀ + dx·sin θ; matrix = [h·cos θ, h·sin θ, −h·sin θ, h·cos θ, x, y]

  Vector PDF output pdf.js

  • BimCraft
  • DetailCraft
  64-bit

• Room grid

  Covers a room with square cells and marks the ones whose center is inside it.

  cell × 1.5 while (W ÷ cell + 1) × (H ÷ cell + 1) > 60000

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Distance field over a room

  The walked distance from one cell to every other free cell of a room.

  d(n) = min over 16 neighbors of d(c) + √(Δi² + Δj²) × cell

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Route between two places in a room

  The distance in meters between two points of a room and the path walked.

  straight: √(Δx² + Δy²) ÷ 1000; else Σ segment lengths of the string-pulled path ÷ 1000

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Distance to the goal from every opening

  The remaining walking distance to an exit, or to a room, from each side of each door and stair.

  d(far side of j) = min(d(i) + walk(j → i) + length of opening j)

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Travel distance of each room

  The farthest point of each room from an exit, in meters along the walls.

  max over cells and corners of min over openings (distance to opening + distance beyond it); rounded to 0.01 m

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Speed factor from crowd density

  How much the crowd in a room slows a walker.

  D = people ÷ max(area, 0.5); factor = 1 for D ≤ 0.54, else max(min factor, (1 − 0.266·D) ÷ (1 − 0.266 × 0.54))

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit