Calculations

Calculations

• Fairness measures

  Inflection count, largest curvature, roughness, curvature jumps at knots and length.

  R = ∫(dκ/ds)² ds ≈ (du ÷ 3) × Σ wᵢ gᵢ, gᵢ = ((κᵢ₊₁ − κᵢ₋₁) ÷ ds)² × |C′|ᵢ

  Hull lines: fairness measures and fairing hull/fair.js

  • PartCraft
  64-bit

• Fairing a curve

  The rebuild with the fewest control points that stays within tolerance and adds no inflection.

  Hull lines: fairness measures and fairing hull/fair.js

  • PartCraft
  64-bit

• Fairness problems

  Reports curves that have an inflection or a curvature jump.

  Hull lines: fairness measures and fairing hull/fair.js

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  64-bit

• Sampling a patch

  The parameter values at which each surface is evaluated.

  uᵢ = u₀ + (u₁ − u₀) × i ÷ N, N from 2 to 200

  Hull surfaces to a closed solid and its volume hull/solid.js

  • PartCraft
  64-bit

• Mirror half

  The other half of a hull drawn to the centerline.

  p′ = 2 × at − p on the mirror axis

  Hull surfaces to a closed solid and its volume hull/solid.js

  • PartCraft
  64-bit

• Welding corners

  Merges corners of neighboring patches that lie within the weld distance.

  merge when √(Δx² + Δy² + Δz²) ≤ eps

  Hull surfaces to a closed solid and its volume hull/solid.js

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• Planar opening test

  Decides whether an opening lies in a plane and can be capped.

  n by Newell's sums; deviation = max |(p − centroid)·n|; cap when deviation ≤ max(4 eps, 2e-4 × size)

  Hull surfaces to a closed solid and its volume hull/solid.js

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• Volume of the closed mesh

  The volume enclosed by the hull mesh.

  V = Σ a·(b × c) ÷ 6

  Hull surfaces to a closed solid and its volume hull/solid.js

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  64-bit

• Anchor point as assembled

  Where an annotation's anchor sits when the parts are assembled.

  Manual annotations: measured lengths, angles and radii illustrate/annotate.js

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  64-bit

• Circle through three points

  The center and radius of the circle through three points.

  n = ab × ac; c = a + ((n × ab)|ac|² + (ac × n)|ab|²) ÷ (2|n|²); r = |c − a|

  Manual annotations: measured lengths, angles and radii illustrate/annotate.js

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• Measured value

  The length, angle or radius an annotation shows.

  length = |P₁ − P₀|; angle = acos(û·ŵ) × 180 ÷ π; radius from the circle through three points

  Manual annotations: measured lengths, angles and radii illustrate/annotate.js

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• Unit vector

  A vector scaled to length 1.

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Point under a matrix

  A point moved by a 4 × 4 matrix.

  p′ = M₃ₓ₃ p + t

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Matrix product

  The product of two 4 × 4 matrices.

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Matrix inverse

  The inverse of a general 4 × 4 matrix.

  M⁻¹ = adj(M) ÷ det(M)

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Box of placed positions

  The axis-aligned box of a mesh's corners under a matrix.

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Rigid motion test

  Checks that a matrix is a rotation and a move, with no scale or shear.

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Best rigid move between two point sets

  The rotation and move that best take one set of points onto another, and the largest leftover distance.

  R from the unit quaternion of the largest eigenvalue; t = c_B − R c_A; err = max |M pᵢ − qᵢ|

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• Largest eigenvector of a symmetric 4 × 4

  The eigenvector the rigid fit's rotation is read from.

  t = sign(θ) ÷ (|θ| + √(θ² + 1)), θ = (a_qq − a_pp) ÷ (2a_pq)

  Illustrate: vector, matrix and rigid-fit math illustrate/m4.js

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• File unit to millimeters

  The factor from a file's unit to millimeters.

  μm 0.001; mm 1; cm 10; m 1000; in 25.4; ft 304.8

  Manual: imported product meshes, copies and part volume illustrate/import.js

  • PartCraft
  Exact

• glTF accessor values

  Reads a glTF accessor's numbers, including normalized integers.

  normalized integer: max(x ÷ max, −1)

  Manual: imported product meshes, copies and part volume illustrate/import.js

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• Mesh as stored

  A part's corner positions as the manual keeps them.

  Manual: imported product meshes, copies and part volume illustrate/import.js

  • PartCraft
  32-bit in part

• Weld grid for splitting shells

  Merges corners at the same place so separate pieces of a mesh can be told apart.

  q = max(range, 1e-9) × 1e-7; key = round(x ÷ q), round(y ÷ q), round(z ÷ q)

  Manual: imported product meshes, copies and part volume illustrate/import.js

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  64-bit

• Part signature

  A short key (corner count, triangle count, area, volume) that groups parts that may be copies.

  Manual: imported product meshes, copies and part volume illustrate/import.js

  • PartCraft
  32-bit in part

• Recognizing copies of a part

  Folds parts that are rigid moves of one another into one part with several placements.

  copy when fit error ≤ 1e-5 × size and largest corner difference ≤ 4e-5 × size

  Manual: imported product meshes, copies and part volume illustrate/import.js

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• Largest corner difference after a move

  How far the moved corners of one mesh are from another's.

  Manual: imported product meshes, copies and part volume illustrate/import.js

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• Placement moved to millimeters

  A 3MF placement with its move in millimeters.

  Manual: imported product meshes, copies and part volume illustrate/import.js

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• Mesh in the manual file

  A part's mesh as written into the manual file.

  Manual: imported product meshes, copies and part volume illustrate/manual.js

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  32-bit in part

• Explode offsets

  How far each part has moved at a point in an exploded view.

  offset = Σ dir × dist × clamp(t × n − k, 0, 1) over the steps k

  Manual: imported product meshes, copies and part volume illustrate/manual.js

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• Where each part is drawn

  Each instance's matrix in a view.

  M = translation(explode offset + view move) × placement

  Manual: imported product meshes, copies and part volume illustrate/manual.js

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• Moving parts in a view

  Adds a move to parts in one view.

  Manual: imported product meshes, copies and part volume illustrate/manual.js

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• Part volume and area

  The volume and surface area of a part's mesh.

  V = |Σ a·(b × c) ÷ 6|; A = Σ |(b − a) × (c − a)| ÷ 2

  Manual: imported product meshes, copies and part volume illustrate/manual.js

  • PartCraft
  32-bit in part

• Projection onto the picture

  A model point's place in the picture and its depth.

  orthographic: u = aspect ÷ 2 + q·right ÷ 2h; perspective: u = aspect ÷ 2 + q·right ÷ (2 tan(fov ÷ 2) × depth)

  Illustrate: projection, hidden lines and vector pictures illustrate/camera.js

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  32-bit, display only

• Is a picture point hidden

  Decides whether a point of an edge is behind a triangle of another surface.

  barycentric l₁, l₂, l₃ in the picture; hidden when the triangle's depth < point depth − 10 eps

  Illustrate: projection, hidden lines and vector pictures illustrate/hlr.js

  • PartCraft
  32-bit, display only

• Feature edges

  The mesh edges drawn as lines: open edges and edges where two faces meet at more than an angle.

  drawn when open, or cos(face angle) < cos(angle)

  Illustrate: projection, hidden lines and vector pictures illustrate/edges.js

  • PartCraft
  32-bit, display only

• Numbers in the PDF

  How a coordinate is written into a PDF page.

  Illustrate: projection, hidden lines and vector pictures illustrate/pdf.js

  • PartCraft
  32-bit, display only

• Significand width of a number

  How many bits of a number this device keeps.

  bits = the first n where 1 + 2⁻ⁿ = 1

  Device number check accuracy.js Every app
  Exact

• Digits of a graphics float

  The number of significant digits stated for the graphics processor's float type.

  bits < 23: digits = max(1, ⌊(bits + 1) × log₁₀ 2⌋); bits ≥ 23: the fixed text "about 7"

  Device number check accuracy.js Every app
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• Size and position text

  A dimension, port size or port position as text in millimeters.

  text = round(x × 10⁴) ÷ 10⁴

  Library configurator sizes library-configurator.js Every app
  64-bit

• Option value used for matching

  The text an option value is compared by when the page picks the variant that matches the selected options.

  numbers: round(v × 10⁴) ÷ 10⁴ as text; other values: trimmed text

  Library configurator sizes library-configurator.js Every app
  64-bit

• Mesh buffers

  The item's box or mesh as geometry for drawing, turned from z up to y up.

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Camera position

  Where the camera sits as the view is turned and zoomed.

  position = target + dist × (sin φ sin θ, cos φ, sin φ cos θ)

  Library 3D preview library-3d.js Every app
  32-bit, display only

• Variant body buffers

  The chosen variant's box or mesh as geometry for drawing.

  Library 3D preview library-configurator.js Every app
  32-bit, display only

• Required and found values as text

  A limit or a measured value in words, such as ≤ 196.85 mm or 863.6–965.2 mm.

  text = round(x × 100) ÷ 100, then the unit

  Check report values problems.js Every app
  64-bit

• Built-in unit factors

  The factor from each built-in unit of mass, time, force, pressure, energy, power, current, voltage and volume to SI.

  lb = 0.45359237 kg; lbf = 4.4482216152605 N; psi = 6894.757293168 Pa; psf = 47.88025898 Pa

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Constants and fallback lengths

  pi, e, standard gravity g0, and the length units used when no unit table is given.

  g0 = 9.80665 m/s²; in = 0.0254 m; ft = 0.3048 m; yd = 0.9144 m

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Unit lookup

  The SI factor and dimension of a unit name.

  deg = π ÷ 180; rad = 1

  Calc sheet units, functions and driven parameters calc.js Every app
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• Dimension comparison

  Whether two values have the same dimensions, so they can be added, compared or converted.

  |aᵢ − bᵢ| < 1e-9 for each of the five exponents

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Power

  a ^ b for a value with units.

  value = aᵇ; dimensions × b

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit

• Conversion with to

  M to kN m: checks the dimension and records the unit to show the answer in.

  shown = value ÷ factor of the target unit

  Calc sheet units, functions and driven parameters calc.js Every app
  64-bit