Calculations

Calculations

• 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

• Ray against boxes

  Calls back for every item whose box a ray passes through.

  t₀ = max(nearₐ), t₁ = min(farₐ); hit if t₀ ≤ t₁

  Box tree for picking and collisions m3d/bvh.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• Boxes of point lists

  The box of each item from its points, grown by a pad.

  Box tree for picking and collisions m3d/bvh.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• 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

• 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

• 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

• Type name to number type

  Which number type a USD type name uses (32-bit float, half or 64-bit double).

  Number text in USD files usd/sdf.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Inline values

  A value that the file stores inside its 32-bit payload word.

  Floats read from USD files usd/usdc-read.js

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

• Raw arrays

  A packed array of numbers of one type.

  Floats read from USD files usd/usdc-read.js

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

• Compressed float arrays

  An array stored as whole numbers or as a lookup table and indexes.

  Floats read from USD files usd/usdc-read.js

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

• Float text rounding

  A float or half value read from .usda text.

  Floats read from USD files usd/usda-read.js

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

• Arrays from text

  A list of parsed numbers as a typed array of the right type.

  Floats read from USD files usd/usda-read.js

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

• Half to float

  The value of a 16-bit half float.

  v = ± (1 + m ÷ 1024) × 2^(e − 15)

  Half floats in USD usd/util.js

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

• Float to half

  The 16-bit half closest to a number.

  Half floats in USD usd/util.js

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

• Half to float

  The value of a 16-bit half float.

  v = ± (1 + m ÷ 1024) × 2^(e − 15)

  Half floats in EXR exr/util.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Float to half

  The 16-bit half closest to a number.

  Half floats in EXR exr/util.js

  • BimCraft
  • ModelCraft
  32-bit in part

• Measure to SI

  A property value in meters, square meters or cubic meters.

  area = v × L²; volume = v × L³

  IFC measures in SI for USD usd/ifc.js

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

• Start editing a key

  Saves the current points as the basis and shows the key at full strength.

  point = basis + offset

  Shape keys: offsets, editing and blending anim/shapes.js

  • ModelCraft
  32-bit in part

• Finish editing a key

  Turns the edited points into the key's offsets and puts the mesh back to its basis.

  offset = edited − basis; point = basis

  Shape keys: offsets, editing and blending anim/shapes.js

  • ModelCraft
  32-bit in part

• Key from imported positions

  Makes a key that moves the basis to a list of positions (glTF morph targets, USD blend shapes).

  offset = position − basis point

  Shape keys: offsets, editing and blending anim/shapes.js

  • ModelCraft
  32-bit in part

• Blend of the keys

  The points of a mesh with each key at its weight.

  pᵢ = basisᵢ + Σ wₖ × offsetₖ,ᵢ

  Shape keys: offsets, editing and blending anim/shapes.js

  • ModelCraft
  32-bit in part

• Deformed copy of a mesh

  The mesh moved by its shape keys and then its skin, which the view, picking and exports read.

  points = blend of keys; then skin applied to the same array

  Shape keys: offsets, editing and blending anim/deform.js

  • ModelCraft
  32-bit in part

• Bone data for the card

  Packs the bone matrices (or dual quaternions) for the kernel.

  Skinning on the graphics card anim/skin-gpu.js

  • ModelCraft
  32-bit, display only

• Skinned points read back

  Runs one skin on the card and reads the points back.

  Skinning on the graphics card anim/skin-gpu.js

  • ModelCraft
  32-bit, display only

• Key time of a baked frame

  The timeline time given to each baked frame.

  t = round((from + f ÷ fps) × 1000) ÷ 1000

  Baked physics key times anim/bake.js

  • ModelCraft
  64-bit

• Time of day to seconds

  Turns HH:MM text into seconds.

  seconds = h × 3600 + m × 60

  Shift calendar working time addons/flow/lib/calendar.js

  • ModelCraft
  Exact

• Weekly on-intervals

  The merged list of on-intervals in a week, with windows that pass midnight wrapped.

  length = to − from (+ one day if the end is not after the start)

  Shift calendar working time addons/flow/lib/calendar.js

  • ModelCraft
  Exact

• On time between two instants

  The total seconds the calendar is on between two times.

  Σ (off − on) over the on-intervals inside [a, b]

  Shift calendar working time addons/flow/lib/calendar.js

  • ModelCraft
  64-bit

• Factor from text

  A factor from a plain number, a percent of the size, or a percent change.

  f = n; n ÷ 100; 1 ± n ÷ 100

  Typed scale factors and shrinkage allowance scale-factors.js

  • ModelCraft
  • PartCraft
  64-bit

• Shrinkage allowance

  The pattern factor for a casting that shrinks by a percentage.

  add: 1 + s ÷ 100; exact: 1 ÷ (1 − s ÷ 100)

  Typed scale factors and shrinkage allowance scale-factors.js

  • ModelCraft
  • PartCraft
  64-bit

• Meters per file unit

  The conversion factor for each unit system a 3DM file can name.

  meters = file value × factor

  Units and tolerance read from a 3DM file io/3dm/read.js

  • ModelCraft
  • PartCraft
  64-bit

• Units and tolerance from the file settings

  Reads the unit system, custom meters-per-unit and the tolerance from a file's settings record.

  Units and tolerance read from a 3DM file io/3dm/read.js

  • ModelCraft
  • PartCraft
  64-bit

• Box and cylinder

  A 20 mm cube and a 20 mm cylinder, standing on z = 0 and centered on the origin.

  S = 0.02; R = S ÷ 2; box: S × S square pulled up by S; cylinder: 32-sided polygon of radius R pulled up by S

  Beginner shapes, align and drop to ground beginner.js

  • ModelCraft
  64-bit