Calculations

Calculations

• Points in a slice

  The points that lie within a thickness of a plane.

  |pos − (at − origin)| ≤ thick ÷ 2

  Point cloud positions and read-in values pointcloud.js

  • CadCraft
  • BimCraft
  32-bit in part

• Intensities scaled to 0 to 65535

  The intensity of each kept point on a common 16-bit scale.

  out = round((v − lo) ÷ (hi − lo) × 65535)

  Point cloud positions and read-in values pointcloud.js

  • CadCraft
  • BimCraft
  32-bit in part

• LAS record decoder

  The x, y, z of each LAS point from its stored integers.

  x = Int32 × scale + offset

  Point cloud positions and read-in values pointcloud.js

  • CadCraft
  • BimCraft
  64-bit

• Size of the cloud

  The extent of the cloud in each axis shown in the summary.

  size = max − min

  Point cloud positions and read-in values pointcloud.js

  • CadCraft
  • BimCraft
  64-bit

• Round a box edge outward to 32-bit

  A 32-bit number that is never above (down) or never below (up) the 64-bit value.

  Ray hits against 32-bit triangle records compute/bvh-core.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Ray and triangle

  Whether a ray meets a triangle and at what distance t and barycentric u, v.

  t = (e2 · (s × e1)) ÷ (e1 · (d × e2))

  Ray hits against 32-bit triangle records compute/bvh-core.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Ray and box slab test

  The distance at which a ray enters a box, or Infinity.

  t = (box − o) ÷ d, max of the near, min of the far

  Ray hits against 32-bit triangle records compute/bvh-core.js

  • BimCraft
  • ModelCraft
  64-bit

• Instance inverse matrix

  The world-to-object matrix of an instance as 12 numbers.

  M⁻¹ = adj(M) ÷ det(M), translation = −M⁻¹ t

  Ray hits against 32-bit triangle records compute/bvh-scene.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Ray into object space of an instance

  The ray origin and direction in an instance frame, and the triangle test that follows.

  Ray hits against 32-bit triangle records compute/bvh-scene.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Triangle records from world triangles

  The 12-number triangle records the scatter ray tests use.

  e1 = v1 − v0; e2 = v2 − v0

  Ray hits against 32-bit triangle records rt/rt-scatter-ui.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Accumulation buffer read back

  The per-pixel sums of red, green, blue and sample count.

  Path-traced picture sums and the saved file render/pt-gpu.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Sum of an exact range of samples

  The sum of samples s0 to s0 + spp − 1 for every pixel.

  Path-traced picture sums and the saved file render/pt-gpu.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Render elements read back

  The per-pixel render elements and light-group sums.

  Path-traced picture sums and the saved file render/pt-gpu.js

  • BimCraft
  • ModelCraft
  32-bit in part

• EXR channels from the sums

  The mean (or raw sum) of each channel for the EXR and render file.

  mean = Σ ÷ max(samples, 1)

  Path-traced picture sums and the saved file render/pt-output.js

  • BimCraft
  • ModelCraft
  32-bit in part

• 16-bit PNG

  The picture as 16 bits per channel.

  v₁₆ = round(clamp(v, 0, 1) × 65535)

  Path-traced picture sums and the saved file render/pt-output.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Reopening a render file

  The sums and counts read back from the layers file.

  Path-traced picture sums and the saved file render/pt-output.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Save as 16-bit PNG

  Chooses the 32-bit or the 8-bit path to write the 16-bit PNG.

  Path-traced picture sums and the saved file render/render-ui.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Span text to millimeters

  A listed span, as a number or as feet-inches text, in millimeters.

  mm = ft × 304.8 + (in + n ÷ d) × 25.4

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Table units to millimeters

  Depth, spacing and bearing of the loaded table in millimeters.

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Spacing match

  Whether a requested on-center spacing is served by a listed column.

  0.98 × listed ≤ want ≤ 1.005 × listed

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Smallest depth that reaches the span

  The joist size for a span, spacing and load case.

  first candidate with max + 10⁻⁶ ≥ span

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Listed maximum span for a size

  The listed span of a named framing size at a spacing and case.

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Depth written on the drawing

  The depth text used in the size label.

  in = round(mm ÷ 25.4 × 1000) ÷ 1000

  Joist depth from a span table the person loads tji-table.js

  • BimCraft
  64-bit

• Summed K of a list of fittings

  The total loss coefficient of the fittings on one link at its own Reynolds number and diameter.

  K = Σ nᵢ × Kᵢ(Re, D)

  Fitting losses summed from a pack process/equip/fittingk.js

  • CadCraft
  • BimCraft
  64-bit

• Head loss of a fitting

  The head loss in meters from K and the velocity.

  h = K × v² ÷ (2g)

  Fitting losses summed from a pack process/equip/fittingk.js

  • CadCraft
  • BimCraft
  64-bit

• Pressure thrust

  The axial force on a blind end or an unbalanced joint.

  F = P × π × Di² ÷ 4

  Pipe stress support helpers process/equip/pipestress2.js

  • CadCraft
  • BimCraft
  64-bit

• Variable spring selection

  The spring sizes that carry the hot load and travel within the allowed load variation.

  variation = |travel| × rate ÷ hot load

  Pipe stress support helpers process/equip/pipestress2.js

  • CadCraft
  • BimCraft
  64-bit

• Stop clearance check

  Whether the thermal displacement closes a gap or stop.

  Pipe stress support helpers process/equip/pipestress2.js

  • CadCraft
  • BimCraft
  64-bit

• Fall along a run

  The corner points with the slope applied to the heights.

  zᵢ = zᵢ − slope × Σ √(Δx² + Δy²)

  Pipe run points with fall applied addons/plant/lib/runs.js

  • BimCraft
  64-bit

• Outside diameter of a run

  The pipe outside diameter in millimeters from the size table.

  od = in × 25.4

  Pipe run points with fall applied addons/plant/lib/runs.js

  • BimCraft
  64-bit

• Meets the limit

  True, false or null for a found value against a rule.

  min − e ≤ found ≤ max + e

  Pass or fail against a regulation limit addons/regs/lib/rows.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Material and band thicknesses

  The thickness of each library sheet and edge band in millimeters and in inches.

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  Exact

• Rules from the material picks

  The thicknesses, groove and band thicknesses that the construction rules use.

  groove = min(tback, 0.6 × tcarcass)

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Sheet size for a material

  The sheet width and height a material is cut from.

  in = round(mm ÷ 25.4 × 4) ÷ 4

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/materials.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Hole positions in the drill XML

  The x and y of each hole as written in the drill file.

  x = round(x × 1000) ÷ 1000

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/export.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• G-code scale and thickness

  The unit scale and cut depth passed to the sheet G-code writer.

  thickness_mm = thickness × scale

  Cabinet material sizes, grooves and drill files addons/cabinetcraft/lib/export.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Relative difference

  The fraction by which a coarse result differs from the refined result.

  |a − b| ÷ |b|

  Spread between coarse and refined results study/live.js

  • CadCraft
  • BimCraft
  • DetailCraft
  • PartCraft
  64-bit

• Ring orientation

  The signed area that decides if a ring runs counter-clockwise.

  A = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Polygon triangulation by ear clipping ifc/geo-tri.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Cross product and inside test

  Which side of a line a point lies on and whether a point is inside a triangle.

  cross = (bx−ax)(cy−ay) − (by−ay)(cx−ax)

  Polygon triangulation by ear clipping ifc/geo-tri.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Hole bridge

  The vertex of the outer ring a hole is joined to.

  Polygon triangulation by ear clipping ifc/geo-tri.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Ear test

  Whether a corner can be cut off as a triangle.

  Polygon triangulation by ear clipping ifc/geo-tri.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Triangulate rings on a plane

  The triangles of 3D rings that lie on one plane.

  Polygon triangulation by ear clipping ifc/geo-tri.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Run point to viewer frame

  A run point in the viewer frame in meters.

  p = Lm · C · (storey · p ÷ 1000)

  MEP openings and clearances shown and exported mep/structure-ui.js

  • BimCraft
  64-bit

• Opening rows in the CSV

  The insulation, size, X, Y, Z and through length of an opening as written in the CSV.

  v = round(mm)

  MEP openings and clearances shown and exported mep/structure-ui.js

  • BimCraft
  64-bit

• Opening text in the BCF

  The insulation, gap and position written into the BCF description.

  MEP openings and clearances shown and exported mep/structure-ui.js

  • BimCraft
  64-bit

• Gap and need shown for a soft clash

  The gap and the needed clearance shown in the list in the display unit.

  MEP openings and clearances shown and exported mep/structure-ui.js

  • BimCraft
  64-bit

• Vertices and loose edges

  The point positions of a model definition and its loose edges.

  Model points written to USD usd/m3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Mesh arrays

  The point, normal, UV and color arrays of a mesh.

  Model points written to USD usd/m3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Number to text

  The text a number is written as, by type.

  f32: text = shortest s with fround(+s) = fround(x)

  Number text in USD files usd/usda-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  32-bit in part

• Shortest digits

  A number to p significant digits without trailing zeros.

  Number text in USD files usd/usda-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit