Calculations

Calculations

• 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

• Runs joined across doors and outside walls moved to their middle

  Joins two runs on one line with a door between them into one wall, and moves a wall that has points on one side only half its thickness outward.

  c = (c₁ + c₂) ÷ 2; outside when the emptier side has < 15% of the other's points; c ← c ± thickness ÷ 2

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

  • BimCraft
  64-bit

• Wall ends snapped to corners

  Moves a wall's end onto the line of a perpendicular wall when it is within the snap distance.

  end ← c_other when |c_other − end| ≤ 350 mm

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

  • BimCraft
  64-bit

• Proposed wall coordinates

  Turns each wall back into the slice's own axes and writes its two ends.

  a, b = round(coordinate × 10) ÷ 10

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

  • BimCraft
  64-bit

• Proposed door offset

  The distance from a wall's start to the near edge of a door in it.

  offset = Math.round(max(0, along − width ÷ 2 − wall start))

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

  • BimCraft
  64-bit

• Rooms closed by the proposed walls

  The rooms the proposed walls close, each with its area and middle.

  area (m²) = round(area_mm² ÷ 1e6 × 10) ÷ 10

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

  • BimCraft
  64-bit

• Task duration

  A task's duration in days, counting its start and finish day.

  duration = finish − start + 1

  Construction schedule dates and critical path schedule-io.js

  • BimCraft
  Exact

• Date read from a project file

  Turns a date and time from a project XML file into a day number.

  day = date part of the text

  Construction schedule dates and critical path schedule-io.js

  • BimCraft
  Exact

• Link lag read from a project file

  Converts a dependency's lag from tenths of a minute to whole days.

  lag (days) = Math.round(LinkLag ÷ 10 ÷ minutes per day)

  Construction schedule dates and critical path schedule-io.js

  • BimCraft
  64-bit

• Offset of each dependency

  Turns each link type and lag into the least number of days between the two tasks' starts.

  FS: d = dur_pred + lag; SS: lag; FF: dur_pred + lag − dur_succ; SF: lag − dur_succ

  Construction schedule dates and critical path schedule-io.js

  • BimCraft
  Exact

• Early and late dates, float and the critical path

  Each task's earliest start and finish, latest start and finish, float, and whether it is critical.

  ES = max(own start, ES_pred + d); EF = ES + dur − 1; LS = min(finish − dur + 1, LS_succ − d); float = LS − ES

  Construction schedule dates and critical path schedule-io.js

  • BimCraft
  Exact

• Planes of a section cell

  The outward normal and a point of each plane that bounds a section cell, with tilted faces and extra planes.

  n = unit(n₀ + tan a × e_u + tan b × e_v); extra: n = (cos el cos az, cos el sin az, sin el)

  Section volumes in the 3D view section-volume.js

  • BimCraft
  32-bit, display only

• Corners and edges of a section cell

  The corners, faces and edges of the convex cell its planes bound, drawn as the cell's frame.

  corner = (d_a (n_b × n_c) + d_b (n_c × n_a) + d_c (n_a × n_b)) ÷ (n_a · (n_b × n_c))

  Section volumes in the 3D view section-volume.js

  • BimCraft
  32-bit, display only

• A plane through a point as an extra plane

  Turns a plane given by a normal and a point into the azimuth, elevation and offset a section cell keeps.

  az = atan2(u_y, u_x); el = asin(clamp(u_z, −1, 1)); off = u · (p − center)

  Section volumes in the 3D view section-volume.js

  • BimCraft
  32-bit, display only

• Longitude and latitude to local meters

  The position of a point in meters east and north of the address point.

  x = (lon − lon₀) × 111320 × cos(lat₀); y = (lat − lat₀) × 111320

  Site surroundings in local meters site-context.js

  • BimCraft
  • ModelCraft
  • CivilCraft
  64-bit

• Local meters back to longitude and latitude

  The longitude and latitude of a local point.

  lon = lon₀ + x ÷ (111320 × cos(lat₀)); lat = lat₀ + y ÷ 111320

  Site surroundings in local meters site-context.js

  • BimCraft
  • ModelCraft
  • CivilCraft
  64-bit

• Outlines and heights kept in the site file

  Converts each outline to local meters, thins and rounds it, and sets the item's height.

  ring = round(x × 100) ÷ 100, round(y × 100) ÷ 100; height = source height, else levels × 3

  Site surroundings in local meters site-context.js

  • BimCraft
  • ModelCraft
  • CivilCraft
  64-bit

• Thinning a long outline

  Reduces an outline of more than 400 points by keeping every n-th point.

  step = ⌈points ÷ 400⌉; keep indexes divisible by step

  Site surroundings in local meters site-context.js

  • BimCraft
  • ModelCraft
  • CivilCraft
  64-bit

• Surface areas and mean absorption of each pair

  The area of each pair of opposite surfaces and their mean absorption in a band.

  S_x = 2 L_y L_z; ᾱ_x = (α_west + α_east) ÷ 2; −ln(1 − ᾱ)

  Reverberation time of a box room stat.js

  • BimCraft
  64-bit

• Sabine, Eyring, Fitzroy and Arau-Puchades times

  The four reverberation times of the room in a band.

  Sabine: 0.161 V ÷ (S ᾱ + A_air); Eyring: 0.161 V ÷ (−S ln(1 − ᾱ) + A_air); Fitzroy: 0.161 V ÷ S² × Σ Sᵢ ÷ (−ln(1 − ᾱᵢ)); Arau: Π [0.161 V ÷ (−S ln(1 − ᾱᵢ) + A_air)]^(Sᵢ ÷ S)

  Reverberation time of a box room stat.js

  • BimCraft
  64-bit

• Local origin and merging of points

  Moves every point to a local origin and makes points that fall on the same spot one vertex.

  origin = ⌊min x⌋, ⌊min y⌋; key = round(x ÷ 1e-4), round(y ÷ 1e-4)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Coordinates handed to the triangulator

  Packs the local coordinates for Delaunator and runs the Delaunay triangulation.

  coords = (x, −y) per vertex

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Boundary clipped to the data and given elevations

  Clips the outer boundary to the convex hull of the data and takes each corner's elevation from a first surface built without it.

  z_corner = elevationAt(x, y) with a 1e-6 edge tolerance

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Triangles kept inside the boundary

  Drops the triangles whose center lies outside the boundary.

  keep when the centroid (Σx ÷ 3, Σy ÷ 3) is inside the boundary polygon

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Surface from given triangles

  Builds a surface from vertices and faces read from a file, keeping every triangle counter-clockwise.

  o = (x_b − x_a)(y_c − y_a) − (y_b − y_a)(x_c − x_a); swap b, c when o < 0

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Crossing of two breakline segments

  Finds where two segments properly cross, as a fraction along each.

  t = cross(c − a, s) ÷ cross(r, s); u = cross(c − a, r) ÷ cross(r, s)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Vertex at a breakline crossing

  Places a new vertex where two breaklines cross and gives it an elevation.

  x = x_a + (x_b − x_a) t; z from the first breakline

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Side of a breakline a vertex is on

  Decides whether a vertex lies left of, right of, or on the line of a breakline being forced in.

  on the line when |orient| ÷ L < 1e-7 × (1 + L)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Whether a diagonal can be flipped

  Tests that the two triangles on an edge form a strictly convex quadrilateral.

  orient(c, d, a) and orient(c, d, b) have opposite signs

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  Exact

• Whether an edge crosses a breakline

  Tests whether two segments properly cross during the flips that force a breakline in.

  each segment's ends lie on opposite sides of the other

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  Exact

• Long outer triangles removed

  Removes triangles on the outside whose outer edge is longer than a limit, working inward.

  remove when outer edge length > maxEdge

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Contour lines

  The contour lines of the surface at every multiple of an interval.

  level = base + k × interval; t = (L − zᵢ) ÷ (zⱼ − zᵢ); point = pᵢ + (pⱼ − pᵢ) t

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Triangle clipped at an elevation

  Keeps the part of a triangle above or below a level, for the elevation bands.

  t = f_p ÷ (f_p − f_q); new point = p + (q − p) t at z = L

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Convex hull

  The convex hull of a set of points, counter-clockwise.

  monotone chain; pop while cross(o, a, b) ≤ 0

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Polygon area

  The signed area of a polygon.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Point inside a polygon

  Tests whether a point is inside a polygon.

  count crossings of a ray to the right; odd = inside

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Polygon clipped by a convex polygon

  Clips a polygon to a convex polygon, used to keep a boundary inside the data's hull.

  inside when cross(b − a, p − a) ≥ −1e-9; t = cross(a − p, e) ÷ cross(d, e)

  Ground surface triangulation and contours tin.js

  • BimCraft
  • CivilCraft
  64-bit

• Corners and edges an element offers to Measure

  Collects an element's feature edges and corners in world space for the pointer to snap to.

  p_world = M × p_local; corners merged by round(coordinate × 1e4)

  Points and faces picked for 3D measuring viewer3d.js

  • BimCraft
  32-bit in part

• Area of the face under the pointer

  The area of the flat face the pointer is on, in world units.

  area = region area × |det M|^(2 ÷ 3)

  Points and faces picked for 3D measuring viewer3d.js

  • BimCraft
  32-bit in part

• Bounding box of each element

  The world-space box of each element, over every loaded model.

  box = M × (min, max of the element's vertices)

  Points and faces picked for 3D measuring viewer3d.js

  • BimCraft
  32-bit in part

• Clipping planes of a section box

  Turns each section cell's planes into the viewer's clipping planes and draws the cell's frame a hair inside it.

  viewer normal = turn(−n_x, −n_z, n_y); frame inset = Σ sizes × 1e-5 + 1e-4

  3D view drawing viewer3d.js

  • BimCraft
  32-bit, display only

• Section frame turned with the building

  Rotates a viewer point about the vertical through the model's center into the section frame.

  x′ = c_x + x cos a + z sin a; z′ = c_z − x sin a + z cos a

  3D view drawing viewer3d.js

  • BimCraft
  32-bit, display only