Calculations

Calculations

• Smallest rectangle round a wall's plan points

  The minimum-area bounding rectangle of a set of plan points.

  for each hull edge direction u: area = (max u − min u) × (max v − min v); keep the smallest

  Wall faces and plan frames from element meshes ifc-place.js

  • BimCraft
  64-bit

• Snapping an item to the nearest wall face

  The position and rotation that put an item's back against the nearest wall face.

  t = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); q = a + t (b − a); position = q + n × maxY; rot = atan2(−n_y, −n_x) − 90°

  Wall faces and plan frames from element meshes ifc-place.js

  • BimCraft
  32-bit in part

• Plan frame of copied elements

  The turn of the first copied element and the box of all copied meshes measured in those turned axes.

  rot = atan2(W[1], W[0]) in degrees, rounded to 6 decimals; box from orientedBox

  Wall faces and plan frames from element meshes ifc-place.js

  • BimCraft
  32-bit in part

• Box of points in turned plan axes

  The bounds of a point list in plan axes turned by an angle, and the box center in model millimeters.

  u = x cos r + y sin r; v = −x sin r + y cos r; center = ((u₀ + u₁) ÷ 2, (v₀ + v₁) ÷ 2) turned back

  Wall faces and plan frames from element meshes ifc-place.js

  • BimCraft
  64-bit

• Reading WAV samples

  The first channel of a WAV file as numbers between −1 and 1.

  x = sample ÷ 2^(bits − 1)

  Room acoustic measures from an impulse response metrics.js

  • BimCraft
  32-bit in part

• Decay time from a line fit

  A decay time from the slope of the least-squares line through part of the decay curve.

  slope = (m Σ t d − Σ t Σ d) ÷ (m Σ t² − (Σ t)²); T = 60 ÷ −slope

  Room acoustic measures from an impulse response metrics.js

  • BimCraft
  64-bit

• Decay curve, clarity, definition and center time

  The energy decay curve and the measures read from it.

  curve = 10 lg(∫ₜ p² ÷ ∫₀ p²); C = 10 lg(early ÷ late); D50 = early ÷ total; Ts = Σ t p² ÷ Σ p²

  Room acoustic measures from an impulse response metrics.js

  • BimCraft
  64-bit

• Predicted against measured

  The difference between a predicted and a measured value in each band, against the just-noticeable difference.

  within when |predicted − measured| ≤ JND

  Room acoustic measures from an impulse response metrics.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

• 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

• Site position and time zone

  The latitude, longitude, north direction and time zone used for the sun.

  time zone = round(longitude ÷ 15) unless given

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Model triangles in millimeters

  Every placed triangle of the model that can shade or carry modules.

  mm = mesh position × unit in mm

  Solar arrays on the model pv-calc.js

  • BimCraft
  32-bit in part

• Array tilt and power

  The tilt, azimuth and peak power recorded for a planned array.

  tilt = acos(clamp(n_z, −1, 1)) × 180 ÷ π; kWp = modules × Wp ÷ 1000

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Array definition stored in the file

  The text that records an array's plane, module size and module centers.

  normal, u, v: round to 1e-6; module centers and table corners: round to 0.1 mm

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Arrays read back from the file

  Rebuilds each array's modules and corners from its stored definition.

  corner = c ± u × across ÷ 2 ± v × along ÷ 2

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Module frames in the level's axes

  Turns module centers and the array's directions from model axes into the level's own axes for the stored solids.

  point′ = S⁻¹ · p; direction′ = S⁻¹ · d − S⁻¹ · 0

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Shade fraction of an array

  The shaded share of each array for every month and hour.

  fraction = Σ (table fraction × table samples) ÷ Σ samples

  Solar arrays on the model pv-calc.js

  • BimCraft
  64-bit

• Millimeters per survey unit

  The factor from a survey file's length unit to millimeters.

  m = 1000; ft = 304.8; US survey ft = 1200 ÷ 3937 × 1000

  Ground read from a survey file res-ui.js

  • BimCraft
  Exact

• Ground points from a LAS or LAZ cloud

  Takes the ground-class points of a cloud and thins them to the lowest point in each 1 m cell.

  x = pos[3i] + origin_x; cell = 1000 ÷ (mm per unit)

  Ground read from a survey file res-ui.js

  • BimCraft
  32-bit in part

• Thinning an elevation grid

  Chooses every how many cells of a GeoTIFF or ASCII grid to read so that about 15000 points remain.

  step = max(1, ⌈√(width × height ÷ 15000)⌉)

  Ground read from a survey file res-ui.js

  • BimCraft
  64-bit

• Unit, offset and datum of an imported ground

  Sets the unit factor, moves far-off coordinates to the building and picks the datum so the ground near the building sits 200 mm under the first floor.

  datum = median(z near the building) + 200 ÷ k

  Ground read from a survey file res-ui.js

  • BimCraft
  64-bit

• Model triangles in plan millimeters

  Collects every element's triangles from the loaded model and converts them from viewer meters to plan millimeters.

  p′ = M × (x, y, z, 1)

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  32-bit in part

• Projection and section cut

  Projects each triangle into view coordinates and finds where the section plane cuts it.

  x = p · right; y = z; depth = p · dir; cut point = a + (b − a) × (c₀ − d_a) ÷ (d_b − d_a)

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Triangle clipped at a depth

  Keeps the part of a triangle behind the section plane, or in front of the far limit.

  f = (d₀ − d_a) ÷ (d_b − d_a); new vertex = a + (b − a) × f

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Depth buffer and the visibility test

  Rasterizes every triangle's depth onto a pixel grid and tests whether an edge sample is covered.

  s = 1600 ÷ max(W, H); visible when d ≤ nearest depth in 3 × 3 pixels + tol; tol = max(3, 0.002 × depth range, 4 ÷ s)

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Triangle depth on the pixel grid

  Writes a triangle's depth into each pixel whose center it covers, keeping the nearest.

  d = w₀ d_a + w₁ d_b + w₂ d_c at the pixel center, barycentric weights

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  32-bit, display only

• Visible runs of an edge

  Samples each feature edge and keeps the stretches that are visible as drawn lines.

  n = max(1, ⌈edge length in pixels ÷ 0.75⌉); samples at a + (b − a) × k ÷ n

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Boundary and crease edges

  Finds the edges of an element's triangles that are open boundaries or creases sharper than 25 degrees.

  crease when |n₁ · n₂| < cos 25°; vertices matched by round(2 × coordinate)

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Cut segments joined into loops

  Joins the segments where the section plane cuts an element into the closed outlines that are filled.

  ends matched by round(2 × coordinate)

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Line cut to the view's frame

  Cuts a drawn line to the view's box.

  Liang–Barsky: t₀, t₁ from q ÷ p on each side

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Cut outline cut to the view's frame

  Cuts a filled section outline to the view's box.

  Sutherland–Hodgman against the four sides

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Collinear pieces joined

  Joins touching pieces of the same element's lines that run in the same direction into one line.

  join when ends ≤ 0.5 mm apart and cos(angle) ≥ 0.99999

  Elevations and sections with hidden lines removed res-views.js

  • BimCraft
  64-bit

• Scan points into the model's space

  Moves every scan point through the cloud's placement matrix into the model's space.

  p′ = M × (x, y, z, 1), stored in a Float32Array

  Scan compared with the model scan-progress.js

  • BimCraft
  32-bit in part

• Signed distance of a point from a box

  The distance from a scan point to an element's box surface, positive outside and negative inside, and the running sums for the mean and RMS.

  outside: d = √Σ gapₖ²; inside: d = −min distance to a face

  Scan compared with the model scan-progress.js

  • BimCraft
  32-bit in part

• Coverage, state and deviation of an element

  An element's covered share, its state, and the mean offset and RMS of the scan from its surface.

  coverage = max over large faces of covered cells ÷ cells; mean = Σd ÷ n; rms = √(Σd² ÷ n)

  Scan compared with the model scan-progress.js

  • BimCraft
  32-bit in part

• Percent complete

  The share of judged elements that are built, by count and by box volume.

  pct = round(1000 × built ÷ judged) ÷ 10; by volume: round(1000 × V_built ÷ V_judged) ÷ 10

  Scan compared with the model scan-progress.js

  • BimCraft
  64-bit

• Progress report as CSV

  Writes one row per element with its state, coverage, mean offset, RMS, point count and volume.

  coverage: 3 decimals; mean, rms, volume: 4 decimals

  Scan compared with the model scan-progress.js

  • BimCraft
  32-bit in part

• Slice turned square

  Turns the slice's points by the walls' angle so that every wall runs along one of two axes.

  u = x cos(−α) − y sin(−α); v = x sin(−α) + y cos(−α)

  Walls, doors and rooms proposed from a scan scan-walls.js

  • BimCraft
  64-bit

• Wall line from a histogram peak

  Finds where a wall lies across its direction: a peak in the histogram of the points, then the mean of the points in that peak.

  peak: h_b ≥ h_b₋₁, h_b > h_b₊₁, three-cell sum ≥ 2 × minimum points; position = mean of the points in the three cells

  Walls, doors and rooms proposed from a scan scan-walls.js

  • BimCraft
  64-bit

• Wall runs and their ends

  Splits the points on a wall line into runs and keeps the runs that are long, thin and denser than what lies beside them.

  split at gaps > 450 mm; keep when length ≥ 800 mm, min(side counts) ≤ 0.25 × count, core density ≥ 3 × side density

  Walls, doors and rooms proposed from a scan scan-walls.js

  • BimCraft
  64-bit

• Door gaps

  Finds a door where two wall runs on one line are a door's width apart.

  gap = second.from − first.to; door when 600 ≤ gap ≤ 1300; width = Math.round(gap)

  Walls, doors and rooms proposed from a scan scan-walls.js

  • BimCraft
  64-bit

• Plan slice of a scanned mesh

  Finds where a horizontal plane cuts each triangle of a mesh and samples points along the cut.

  f = (z_cut − z_a) ÷ (z_b − z_a); samples every 20 mm along each cut segment

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  64-bit

• Plan slice of a point cloud

  Takes the cloud's points in a band above the floor as the plan slice, in millimeters from the cloud's origin.

  k = 304.8 for feet, 304.8006 for US survey feet, 1000 otherwise

  Walls, doors and rooms proposed from a scan scan-propose.js

  • BimCraft
  32-bit in part