Calculations

Calculations

• 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

• 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

• 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

• 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

• Triangles of a referenced object

  The target's triangles in the modified mesh's space, for booleans and similar modifiers.

  q = (toLocal × placement) × p

  Modifier references and lattice cages mesh/mod-eval.js

  • ModelCraft
  64-bit

• Cage point displacements

  How far each cage point has been moved from its place on the even grid.

  rest = min + (max − min) × i ÷ (n − 1); disp = M × now − M × rest

  Modifier references and lattice cages mesh/mod-eval.js

  • ModelCraft
  64-bit

• Cage around a mesh

  A box of grid points around a mesh's bounds.

  d = pad × max side; min′ = min − d; max′ = max + d; p = min′ + (max′ − min′) × i ÷ (n − 1)

  Modifier references and lattice cages mesh/mod-eval.js

  • ModelCraft
  64-bit

• Multiplicity of a knot

  How many times a value occurs in a knot vector.

  count of |Uᵢ − u| ≤ tol × (U_last − U_first)

  Knot vectors nurbs/basis.js

  • ModelCraft
  • PartCraft
  64-bit

• Distinct knots

  The different knot values with their multiplicities.

  a knot joins the previous one when |x − u_prev| ≤ tol × range

  Knot vectors nurbs/basis.js

  • ModelCraft
  • PartCraft
  64-bit

• Clamped uniform knot vector

  A knot vector with evenly spaced interior knots.

  uᵢ = a + (b − a) × i ÷ (inner + 1)

  Knot vectors nurbs/basis.js

  • ModelCraft
  • PartCraft
  64-bit

• Knot vector check

  Checks a knot vector read from a file: count, order, clamping and multiplicities.

  Knot vectors nurbs/basis.js

  • ModelCraft
  • PartCraft
  64-bit

• Greville abscissae

  One parameter value per control point.

  gᵢ = (Uᵢ₊₁ + … + Uᵢ₊ₚ) ÷ p

  Knot vectors nurbs/basis.js

  • ModelCraft
  • PartCraft
  64-bit

• Binomial coefficients

  The number of ways to choose k of n.

  C(n, k) = C(n − 1, k − 1) + C(n − 1, k)

  Knot vectors nurbs/basis.js

  • ModelCraft
  • PartCraft
  Exact

• A number as IGES text

  Writes one real number into the file.

  whole numbers below 10¹⁵: digits and a point; otherwise String(x) with E → D

  IGES files of NURBS curves and surfaces nurbs/iges.js

  • ModelCraft
  • PartCraft
  64-bit

• Global section

  States the file's number sizes, unit, resolution and largest coordinate.

  unit flag 2 (MM); scale 1; resolution 10⁻⁶; largest coordinate = max |x| over all control points

  IGES files of NURBS curves and surfaces nurbs/iges.js

  • ModelCraft
  • PartCraft
  64-bit

• A number from IGES text

  Reads one real number from the file.

  IGES files of NURBS curves and surfaces nurbs/iges.js

  • ModelCraft
  • PartCraft
  64-bit

• Unit factors

  Millimeters per file unit, by the file's unit flag.

  1: 25.4; 2: 1; 3: 25.4 × 12; 4: 1609344; 5: 10⁶; 6: 1000; 7: 10⁶; 8: 10⁻³; 9: 10⁻³; 10: 10; 11: 25.4 × 10⁻⁶

  IGES files of NURBS curves and surfaces nurbs/iges.js

  • ModelCraft
  • PartCraft
  64-bit

• Control points in millimeters

  Scales a curve's control points by the file's unit as it is read.

  scale = UNITS[flag] (1 when unknown); p′ = p × scale

  IGES files of NURBS curves and surfaces nurbs/iges.js

  • ModelCraft
  • PartCraft
  64-bit

• Volume and box of each body

  The volume and bounding box the body list shows.

  volume = Σ volume of the body's solids; box = min and max over them

  Bodies: volume, move and scale brep-bodies.js

  • PartCraft
  64-bit

• Move matrix

  The matrix a Move body feature applies: by distances, point to point, about an axis, or plane to plane.

  points: T(to − from); align: rotate n_a onto ∓n_b about c, then t = n_b ((o_b − c) · n_b)

  Bodies: volume, move and scale brep-bodies.js

  • PartCraft
  64-bit

• Shape under a move or a uniform scale

  Applies the matrix or the scale to a solid in the kernel.

  Bodies: volume, move and scale brep-bodies.js

  • PartCraft
  64-bit

• Scale center and affine map

  Chooses the center of a scale and builds the map for unequal factors.

  c = picked point, or (box min + box max) × 0.5; A = diag(sₓ, s_y, s_z); t = c (1 − s)

  Bodies: volume, move and scale brep-bodies.js

  • PartCraft
  64-bit

• Scalar arithmetic and comparison

  Adds, subtracts, multiplies, divides and compares two plain numbers.

  a + b, a − b, a × b, a ÷ b, a < b, a = b

  CraftScript operators in the interpreter cs-vm.js

  • PartCraft
  64-bit

• Matrix multiply, divide and power

  The *, /, \ and ^ operators on matrices.

  A ÷ B = (solve(Bᵀ, Aᵀ))ᵀ; Aⁿ by repeated squaring; A⁻ⁿ = (A⁻¹)ⁿ

  CraftScript operators in the interpreter cs-vm.js

  • PartCraft
  64-bit

• Values of a counted loop

  The value the loop variable takes on each pass of for x = a:s:b.

  xₖ = a + k × s; last value = b when |xₖ − b| < 10⁻¹⁰ × max(1, |b|)

  CraftScript operators in the interpreter cs-vm.js

  • PartCraft
  64-bit

• Number text in the echo

  The text printed for a number when a statement has no semicolon.

  integer below 10¹⁵: all digits; otherwise 5 significant digits

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Matrix text in the echo

  The text printed for a vector or matrix.

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit

• Arrays read from a saved workspace

  Checks and copies a numeric array from a part file or a worker message.

  CraftScript values: storage, reading and number text cs-values.js

  • PartCraft
  64-bit