Calculations

Calculations

• Subtitle timestamp

  A cue time as an SRT or WebVTT timestamp.

  ms = round(s × 1000); h, m, s, ms by integer division

  Narration cue times narration.js

  • BimCraft
  64-bit

• Stored size, roughness and bump

  The numbers saved with a photo material.

  x = round(clamp(x) × 100) ÷ 100

  Photo material settings photo-materials.js

  • BimCraft
  64-bit

• Width and height in pixels

  The pixel size of the picture.

  h = round(w × vh ÷ vw); k = min(1, MAX ÷ w, MAX ÷ h)

  Rendered picture size render-tools.js

  • BimCraft
  64-bit

• Value and time of one reading

  A single reading of a feed with its time.

  t = tt × 1000 if tt < 1e11, else tt

  Live feed values and times assets-bim-live.js

  • BimCraft
  64-bit

• Outside diameter handed to the router

  The pipe's outside diameter in millimeters for a route between two ports.

  od = od in × 25.4

  Pipe route clearance size addons/plant/main.js

  • BimCraft
  64-bit

• Mesh handed to the solid kernel

  Welds the mesh's corners and passes it to manifold-3d.

  weld grid = 10⁻⁶ × max(Δx, Δy, Δz); positions → Float32Array

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Boolean of two solids

  The difference, union or intersection of two element meshes.

  c = center of a's box; R = (a − c) OP (b − c); result = R + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Element minus all its openings

  Subtracts every opening from an element, one after another.

  A₀ = base − c; Aᵢ = Aᵢ₋₁ − (cutterᵢ − c); result = Aₙ + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Face planes of a convex cutter

  Finds the outward planes of a cutter and decides whether it is convex.

  n = (b − a) × (c − a) ÷ |…|; d = n · a; convex when n · p − d ≤ 10 ε for every corner p

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Polygon split by a plane

  Cuts a convex polygon into the part in front of a plane and the part behind it.

  t = dₐ ÷ (dₐ − d_b); x = a + (b − a) t

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Mesh clipped by a plane

  Keeps the part of a mesh on one side of a plane and closes the cut.

  dᵢ = (pᵢ − p) · n; ε = 10⁻⁹ × (d_max − d_min); cut point = a + (b − a) dₐ ÷ (dₐ − d_b)

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Cap of a cut

  Joins the cut segments into loops, sorts outer loops from holes and fills them.

  key = round(x ÷ tol), round(y ÷ tol), round(z ÷ tol); area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Half-space cut

  Removes the part of an element behind a plane, optionally only inside a polygon boundary.

  L = 4 × max(1, box diagonal) + |P₀ − box min|; prism height = 2 L

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Vertex data of one geometry

  Returns a geometry's positions and normals for drawing and for measuring.

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Placement matrix of each piece

  The matrix that takes a geometry's vertices to model space in meters, Y up.

  M = C × Y-up × scale(u) × placement

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Shift to the origin

  Finds the translation that brings the model near the origin.

  c = (box min + box max) ÷ 2 of the first element; C = translate(−(Y-up × scale(u) × placement × c))

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• File units to meters, Z up to Y up

  Scales a placement by the file's length unit and turns its axes.

  M′ = Y-up × scale(u) × M

  IFC geometry handed to the apps ifc/api.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Rounding to one and two decimals

  Rounds a value for a message or for a warning's stored fields.

  f1(x) = round(10 x) ÷ 10; f2(x) = round(100 x) ÷ 100

  MEP check messages: units and rounding mep/problems-mep.js

  • BimCraft
  64-bit

• Pipe flow and velocity in the message

  Shows a flow in gallons per minute or liters per second and a velocity in feet or meters per second.

  gpm = q ÷ 0.003785411784 × 60; L/s = 1000 q; ft/s = v ÷ 0.3048

  MEP check messages: units and rounding mep/problems-mep.js

  • BimCraft
  64-bit

• Stored velocity and pressure values

  Writes the required and found velocity and the pressure left at a fixture into each pipe warning.

  found = f2(V) m/s; required = f2(v_max) m/s; pressure = f1(kPa)

  MEP check messages: units and rounding mep/problems-mep.js

  • BimCraft
  64-bit

• Duct velocity, friction rate and aspect ratio

  Writes a duct's flow, velocity, needed round size and aspect ratio into its warning.

  fpm = round(V ÷ 0.00508); L/s = f1(1000 q); needed size = round(mm)

  MEP check messages: units and rounding mep/problems-mep.js

  • BimCraft
  64-bit

• Tube dimensions for a size

  The outside, wall and inside dimensions of one tube, in inches and millimeters.

  id = od − 2 × wall; odMm = round(od × 25.4 × 1000) ÷ 1000; wallMm = wall × 25.4

  Refrigeration copper tube sizes mep/tables-acr.js

  • BimCraft
  64-bit

• Filmic tone curve

  Maps scene brightness to screen brightness for the filmic view transform.

  h(x) = (x (0.15 x + 0.05) + 0.004) ÷ (x (0.15 x + 0.5) + 0.06) − 0.02 ÷ 0.3; output = h(2 c) ÷ h(11.2)

  Real-time view and render bench rt/rt-post.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Baked probe light

  Collects the bounce light at each probe and removes the sky's own part.

  shᵢ,ₖ = bakedᵢ,ₖ − skyₖ (k = 0…11)

  Real-time view and render bench rt/rt-gi.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Mean radiance per pixel

  Averages the accumulated samples of each pixel for the bench and the parity comparison.

  mean = Σ samples ÷ n

  Real-time view and render bench render/bench-kernels.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Scene for the standalone viewer

  Packs the drawn scene into the viewer's file.

  Real-time view and render bench rt/rt-export.js

  • BimCraft
  • ModelCraft
  32-bit, display only

• Placements from the modifier stack

  The list of placement matrices for the source, first the original.

  stepₖ = (hiₖ − loₖ) × relₖ + absₖ; Mᵢ = translate(i × step) × M

  Group modifiers: scale and array placements group-mods.js

  • ModelCraft
  64-bit

• Number of copies

  How many placements the enabled Array items make together.

  copies = Π countᵢ

  Group modifiers: scale and array placements group-mods.js

  • ModelCraft
  Exact

• Size of a loose piece

  Decides whether a separate piece is small enough to remove.

  max(Δx, Δy, Δz) < minSize

  3D-print mesh repair print-repair.js

  • ModelCraft
  64-bit

• Middle point of a filled hole

  The new vertex a hole's fan of triangles meets at.

  c = Σ pᵢ ÷ n

  3D-print mesh repair print-repair.js

  • ModelCraft
  64-bit

• Signed volume and inside-out pieces

  Finds closed pieces that face inward and turns them outward.

  V = Σ a · (b × c) ÷ 6; turned when V < 0 and the piece is not inside another

  3D-print mesh repair print-repair.js

  • ModelCraft
  64-bit

• Ray and triangle

  Where a ray meets a triangle, for the inside test.

  det = e₁ · (d × e₂); u = (s · h) ÷ det; v = (d · q) ÷ det; t = (e₂ · q) ÷ det

  3D-print mesh repair print-repair.js

  • ModelCraft
  64-bit

• Delaunay triangulation

  Triangles over a set of points in plan.

  D = 2 (aₓ(b_y − c_y) + bₓ(c_y − a_y) + cₓ(a_y − b_y)); center = (Σ |p|² × Δ) ÷ D; inside when |p − center|² < r² (1 − 10⁻¹²)

  Terrain from contours and terrain grids terrain.js

  • ModelCraft
  64-bit

• Terrain from contour edges

  Collects the contour points, merges close ones and triangulates them.

  key = round(100 x), round(100 y); thinning step = n ÷ 8000

  Terrain from contours and terrain grids terrain.js

  • ModelCraft
  64-bit

• Terrain grid

  A flat grid of triangles of a given width, depth and spacing.

  nₓ = round(width ÷ spacing), 1…200; x = x₀ + width × i ÷ nₓ

  Terrain from contours and terrain grids terrain.js

  • ModelCraft
  64-bit

• Entourage parts into the model

  Converts each part's triangles from millimeters to meters.

  p (m) = p (mm) ÷ 1000

  Starter library: plants and entourage sizes starter.js

  • ModelCraft
  64-bit

• Plant scaled to its listed size

  The scale that makes a plant model as wide and tall as the species' data says.

  s_xy = 1000 × spread ÷ max(Δx, Δy, 1); s_z = 1000 × height ÷ max(z_max, 1)

  Starter library: plants and entourage sizes starter.js

  • ModelCraft
  64-bit

• Unit factor

  Chooses the factor that turns the file's unit into meters.

  k = meters per file unit, or 0.001 when that is missing, zero or not finite

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Mesh points in meters

  Scales a mesh's points and builds the model's mesh from them.

  p′ = p × k

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Block placement matrix

  Turns a block reference's matrix into the model's placement.

  m[c × 4 + r] = x[r × 4 + c]; translation × k

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Curve points in meters

  Scales each curve's points and drops segments of no length.

  a′ = a × k; kept when a′ ≠ b′

  3DM import: units, placements and mesh points io/3dm-import.js

  • ModelCraft
  • PartCraft
  64-bit

• Mesh record: 32-bit and 64-bit points

  Reads a mesh's points from the file and chooses between its 32-bit and 64-bit copies.

  use the 64-bit points when |aᵢ − vᵢ| ≤ |vᵢ| × 10⁻⁶ + 10⁻⁶ × max(1, |aᵢ|) for every coordinate

  3DM import: units, placements and mesh points io/3dm/objects.js

  • ModelCraft
  • PartCraft
  64-bit

• Orientation of three points

  Twice the signed area of a triangle: which way it turns.

  (b − a) × (c − a) = (bₓ − aₓ)(c_y − a_y) − (b_y − a_y)(cₓ − aₓ)

  Triangles inside a trimmed face io/3dm/cdt.js

  • ModelCraft
  • PartCraft
  64-bit

• Point inside a circumcircle

  Whether a fourth point lies inside the circle through three others.

  determinant of the rows (pₓ − dₓ, p_y − d_y, |p − d|²) for p = a, b, c; inside when it is positive

  Triangles inside a trimmed face io/3dm/cdt.js

  • ModelCraft
  • PartCraft
  64-bit

• Triangle that holds a point

  Walks from the last triangle toward the point, then searches all triangles if the walk fails.

  Triangles inside a trimmed face io/3dm/cdt.js

  • ModelCraft
  • PartCraft
  64-bit

• Point insertion

  Splits the triangle a new point falls in, or the side it falls on.

  ε = 10⁻⁶ × orient(a, b, c); on a side when a sub-area ≤ ε

  Triangles inside a trimmed face io/3dm/cdt.js

  • ModelCraft
  • PartCraft
  64-bit

• Edge flip

  Flips an edge while the opposite corner lies inside the circumcircle.

  Triangles inside a trimmed face io/3dm/cdt.js

  • ModelCraft
  • PartCraft
  64-bit

• Flips with no new points

  Makes an existing triangulation Delaunay by flipping edges.

  Triangles inside a trimmed face io/3dm/cdt.js

  • ModelCraft
  • PartCraft
  64-bit

• Welded corners in meters

  Merges corners that coincide and converts them from millimeters to meters.

  key = round(x ÷ q), round(y ÷ q), round(z ÷ q); p (m) = p (mm) × 0.001

  STEP import: welding and meters io/step-import.js

  • ModelCraft
  64-bit

• Single values by type

  Reads one property value with the width the file states.

  FBX reader: number types as stored io/fbx-parse.js

  • ModelCraft
  64-bit