Calculations

Calculations

• 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

• Flow rate of an opening

  How many people per second a door or stair lets through.

  rate = flow per meter × max(0.2, width ÷ 1000 − 2 × boundary)

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Walking step

  How far a walker moves in one time step and the distance added to their total.

  Δs = v₀ × factor × Δt; walked += min(Δs, remaining length of the leg)

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Passing an opening

  The moment each queued person passes a door or stair, and their wait.

  pass = max(next free, arrival, t) + counter-flow penalty; next free = pass + 1 ÷ rate; wait = pass − arrival

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Reported times and distances

  Total time, median and 90th percentile times, walked distances and waits.

  percentile p = times[ceil(n·p) − 1]; times rounded to 0.1 s, distances to 0.01 m

  People movement and travel distance people-sim.js

  • BimCraft
  64-bit

• Stair length

  The walked length of a stair from its plan walk line and its height.

  length = √(plan length² + height²)

  People movement and travel distance people-model.js

  • BimCraft
  64-bit

• People per room

  How many people each room holds before a run.

  count = floor(area in m² ÷ m² per person)

  People movement and travel distance people-model.js

  • BimCraft
  64-bit

• Resampling the chosen part of the photo

  Averages the chosen part of the photo down, or interpolates it up, to the tile size.

  Material maps and statistics from a photo photo-material.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Normal map from the height estimate

  The surface direction at each pixel of the tile.

  v = (−Δh_x × S, −Δh_y × S, 1) ÷ |v|, S = 4 × bump; stored as (v ÷ 2 + ½) × 255

  Material maps and statistics from a photo photo-material.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Seam ratio

  How big the jump across the tile's join is compared with the usual jump between neighboring pixels.

  ratio = mean |jump across the join| ÷ max(mean |jump between neighbors|, 1e-6)

  Material maps and statistics from a photo photo-material.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Statistics returned with the maps

  The crop, seam ratios, mean color, height spread and mean roughness reported for the material.

  σ = √(Σ band² ÷ n); seam and σ rounded to 0.01, mean roughness to 0.001, crop to 0.001

  Material maps and statistics from a photo photo-material.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Rounding of stored picture values

  Rounds a position, scale or angle to 6 decimals.

  r6(v) = Math.round(v × 10⁶) ÷ 10⁶

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• New picture record

  The cleaned numbers of a picture, with defaults.

  default scale = r6(20000 ÷ width in pixels); angle = r6(((a mod 360) + 360) mod 360)

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Scale by two points and a distance

  The new scale and center that make two picked points a given distance apart.

  k = mm ÷ |b − a|; scale′ = r6(scale × k); center′ = r6(a + (center − a) × k)

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Corners of a placed picture

  The four corners of the picture in plan millimeters.

  corner = center + R(θ) · (± w·scale ÷ 2, ± h·scale ÷ 2), θ = angle × π ÷ 180

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Pixel to plan matrix

  The transform from picture pixels to plan millimeters.

  [k·c, k·s, k·s, −k·c, x + k(−w/2·c − h/2·s), y + k(−w/2·s + h/2·c)]

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Plan point to picture pixel

  The pixel of the picture under a plan point.

  (u, v) = (R(−θ)·(q − center)) ÷ scale; pixel = (u + w ÷ 2, h ÷ 2 − v)

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Picture on a vertical plane

  Puts a picture on the plane standing over a line, as wide as the line.

  k = L ÷ w; center = (L ÷ 2, h·k ÷ 2)

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Picture width typed

  The scale that makes the picture a typed width.

  scale = r6(mm ÷ w)

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit