Calculations

Calculations

• 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

• Turning a picture

  The new angle after a turn about the picture's center.

  angle′ = r6(((angle + deg) mod 360 + 360) mod 360)

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Fit in a box

  Centers an unscaled picture in the view at 90 % of the box.

  k = min(box width ÷ w, box height ÷ h) × 0.9

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Corners in 3D

  The picture's corners in level coordinates, for a level or a vertical plane.

  p = origin + u·û + v·v̂

  Picture backgrounds: scale, placement and print picture.js

  • BimCraft
  64-bit

• Vertical picture in an elevation or section

  Decides whether a standing picture shows in a view and gives its matrix there.

  shown when |û·dir| ≤ sin(2°) and, in a section, |(a − o)·dir| ≤ 100 mm; x = a·right ± picture x, y = level difference + picture y

  Picture backgrounds: scale, placement and print picture-sheet.js

  • BimCraft
  64-bit

• Number format for picture matrices

  Turns a matrix entry or opacity into the text written in the PDF.

  toFixed(6), trailing zeros removed; |v| < 5e-7 → 0

  Picture backgrounds: scale, placement and print picture-pdf.js

  • BimCraft
  64-bit

• Pixels to print a picture at

  The pixel size a picture is drawn at on a sheet, limited by dots per inch and total pixels.

  paper mm per pixel = scale ÷ ratio; dpi = 25.4 ÷ that; k = min(1, max dpi ÷ dpi, √(max pixels ÷ (w·h)))

  Picture backgrounds: scale, placement and print picture-pdf.js

  • BimCraft
  64-bit

• Matrix for the image's unit square

  Turns the pixel-to-plan matrix into the one PDF needs for an image drawn on a unit square.

  [a·w, b·w, −c·h, −d·h, e + c·h, f + d·h]

  Picture backgrounds: scale, placement and print picture-pdf.js

  • BimCraft
  64-bit

• Scale from two points and a distance

  How many millimeters one page unit is, from two picked points and the true distance between them.

  scale = distance in mm ÷ √(Δx² + Δy²)

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Circle through three points

  The center and radius of the circle through three points.

  d = 2(p_x(q_y − r_y) + q_x(r_y − p_y) + r_x(p_y − q_y)); center from the squared lengths ÷ d

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Arc from a Bézier curve

  Recognizes a cubic curve that is a circular arc and gives its center, radius, start angle and sweep.

  circle through P(0), P(0.5), P(1); accepted when |dist(P(t), center) − r| ≤ 0.012 r at t = 0.25 and 0.75

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Page lines and arcs in millimeters

  Scales a PDF page's line segments and arcs to millimeters and finds their bounds.

  x_mm = x_pt × mm per point

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Scan lines and arcs in millimeters

  Scales a traced scan from pixels to millimeters and turns its y axis up.

  x = px × k; y = (height in px − py) × k

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Joining lines cut at a tee

  Merges lines of one straight run that are split by a joining wall.

  merged when |cos angle| ≥ cos 1.2°, both ends within 35 mm of the first line, and the gap ≤ 350 mm

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Hatching detection

  Finds bundles of short parallel lines so they are not taken for walls.

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Merged wall line and thickness

  The center line and thickness of a wall made of collinear pieces with openings between them.

  t = Σ tᵢ·Lᵢ ÷ Σ Lᵢ; offset = Σ offsetᵢ·Lᵢ ÷ Σ Lᵢ; A, B = base + u·s + n·offset

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Squaring a scanned page

  Decides whether a scan is turned back before it is traced.

  turned by the found angle when |angle| > 0.15° and confidence > 1.6

  Walls and openings from PDF pages and scans plan-pages.js

  • BimCraft
  64-bit

• Stored position and angle

  The X, Y and Angle written for a symbol.

  X, Y = round(mm ÷ unit, 6); Angle = round(radians × 180 ÷ π, 4)

  Plan symbol positions plan-symbols.js

  • BimCraft
  64-bit

• Point on a wall face

  The point on a wall's face at a distance along the wall, and the direction the face looks.

  at = a + s·u + side × (t ÷ 2)·n; face angle = atan2(side·n_y, side·nₓ)

  Plan symbol positions plan-symbols.js

  • BimCraft
  64-bit

• Symbols following a wall

  Moves a symbol to where its stored side and distance are on the wall now.

  turn = atan2(sin Δ, cos Δ), Δ = new face angle − stored face angle

  Plan symbol positions plan-symbols.js

  • BimCraft
  64-bit

• Program totals

  The net and gross floor area and the number of rooms in the program.

  net = Σ count × area; gross = net ÷ efficiency

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• Rectangle inside the envelope

  Tests whether a turned rectangle lies inside the envelope.

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• Rectangle of a wanted area

  The rectangle of a given proportion and area nearest the middle of the envelope.

  short = √(area ÷ ratio); long = short × ratio

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• L and U shapes of a wanted area

  An L-shaped or U-shaped footprint scaled to the wanted area and placed in the envelope.

  k = √(wanted area ÷ template area)

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• Rooms stacked on floors

  Assigns rooms to floors up to each floor's usable area.

  placed when floor net + room area ≤ usable area + 1e-6

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• Areas reported for an option

  Footprint, gross area, required area, surplus and coverage of one massing option.

  footprint = |shoelace|; gross = footprint × floors ÷ 10⁶; surplus = gross − required; coverage = footprint ÷ envelope area

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• Option handed to the site study

  The option's points and floor height in the project's units.

  x = mm × unit per mm

  Massing options from a room program program-mass.js

  • BimCraft
  64-bit

• Normal of a tilted plane

  The unit normal of a plane from its tilt and compass bearing.

  n = (h_x·sin β, h_y·sin β, cos β), h = north·cos az + east·sin az

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Tilt and azimuth of a normal

  The tilt from horizontal and the compass bearing a plane faces.

  tilt = acos(clamp(n_z, −1, 1)); azimuth = (atan2(n·east, n·north) + 360) mod 360

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Axes of a plane from its normal

  The along-eave and up-slope directions of a roof face.

  u = (−n_y, nₓ, 0) ÷ √(nₓ² + n_y²); v = n × u

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Roof faces from triangles

  Groups upward triangles into planes and gives each plane's normal, tilt, azimuth, area and centroid.

  n = (B − A) × (C − A) ÷ |…|; area = |…| ÷ 2; face normal = unit(Σ area·n); centroid = Σ area·mid ÷ Σ area

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Point inside the face's triangles

  Tests whether a point in the face's own axes lies in any of its triangles.

  barycentric l₁, l₂, l₃ ≥ −eps ÷ √|d|

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit

• Modules fitted in a roof face

  The positions and corners of the modules that fit inside a face with a setback.

  position = (s₀ + col × (across + gap), t₀ + row × (along + gap)); corner = centroid + s·u + t·v

  Solar array layout on roofs and ground pv.js

  • BimCraft
  • CivilCraft
  64-bit