Calculations

Calculations

• Arc from start, middle and end

  The signed sweep of an arc about a known center that passes from a start through a middle point to an end.

  counterclockwise when mod(a_m − a₀, 2π) < mod(a₁ − a₀, 2π); sweep = ± mod(a₁ − a₀, 2π)

  Part and stock in machine coordinates cam.js

  • PartCraft
  64-bit

• Exact outline of a flat face

  Turns a face's mesh boundary into lines and arcs whose ends are the exact edge ends.

  mesh corner within tol of an edge end → that end; mesh run within tol of an edge circle → arc on that circle

  Part and stock in machine coordinates cam.js

  • PartCraft
  64-bit

• Hole position, size and depth

  The center, radius, top and bottom of a round face along the tool axis, and whether it is a hole and goes through.

  c, r from the exact cylinder; top, bottom = mesh z range snapped to an edge end within tol

  Part and stock in machine coordinates cam.js

  • PartCraft
  64-bit

• Chaining picked edges into a loop

  Orders picked edges into one closed outline and makes each start exactly on the previous end.

  ends join when closer than tol; then next.start = previous.end

  Part and stock in machine coordinates cam.js

  • PartCraft
  64-bit

• Height grid of the part

  Samples the part's top surface on a grid for the first search of the tool-tip height.

  H[i, j] = height at cell center; cell = max(0.02, R ÷ 8)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  32-bit in part

• Tool-tip height

  The lowest height at which the tool at (x, y) touches the part without cutting into it.

  z = max(H − h(ρ)) over grid samples within R; refine at ρ* = A + r_c s ÷ √(1 + s²) uphill; then max over triangle edges by ternary search; result = max(z + leave, floor)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  32-bit in part

• Slope filter

  Whether the surface under a point is within the slope range chosen for the operation.

  s = √(g_x² + g_y²); tan(from) − 1e-9 ≤ s ≤ tan(to) + 1e-9

  3D finishing toolpaths cam-finish.js

  • PartCraft
  32-bit in part

• Finishing one straight line

  The 3D points of a straight pass over the part, dense enough to stay within the tolerance.

  split a span while |z(mid) − (z₀ + z₁) ÷ 2| > tol ÷ 2

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Thinning a pass

  Drops points that lie on a straight run between their neighbors.

  drop p when its distance to the line through the last kept point and the next point ≤ tol ÷ 10

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Parallel pass lines

  The positions of the raster lines across the part at the chosen angle.

  n = ceil((v₁ − v₀) ÷ (stepover × d) − 1e-9); line k at v₀ + (v₁ − v₀) k ÷ n

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Cusp height

  The height of the ridge left between two ball passes a given distance apart on a flat surface.

  h = R − √(R² − (s ÷ 2)²)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Pass spacing for a cusp height

  The distance between passes that leaves ridges of a given height.

  s = 2 √(2 R h − h²); s = 2 R when h ≥ R

  3D finishing toolpaths cam-finish.js

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  64-bit

• Distance over the surface

  The distance along the part's top surface from the starting cells to every other cell.

  shortest path over grid steps; step length = √((di × c)² + (dj × c)² + ΔH²)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Step directions of the distance search

  The set of grid steps the surface-distance search may take.

  all (di, dj) with |di|, |dj| ≤ 5 and no common factor

  3D finishing toolpaths cam-finish.js

  • PartCraft
  Exact

• Lines of equal surface distance

  Traces the lines at a given surface distance, which become the scallop passes.

  crossing on a cell edge at f = (level − a) ÷ (b − a)

  3D finishing toolpaths cam-finish.js

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  64-bit

• Scallop spacing and levels

  The spacing of scallop passes from the cusp height, and the surface distances they are placed at.

  R_b = ball or corner radius + leave; s = spacing(R_b, cusp); level k = (k + ½) s; grid cell = max(0.02, min(s ÷ 3, d ÷ 8))

  3D finishing toolpaths cam-finish.js

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  64-bit

• Simplifying a scallop pass

  Reduces the points of a 3D pass while staying within a quarter of the tolerance.

  keep the point farthest from the chord when its distance > tolerance ÷ 4, then repeat on both halves

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Tool grown by the stock to leave

  Models stock to leave by making the cutter larger.

  d′ = d + 2 × leave; corner radius′ = corner radius + leave (bull nose)

  3D finishing toolpaths cam-finish.js

  • PartCraft
  64-bit

• Conversion to single precision

  single(A): each value rounded to the nearest 32-bit floating-point number.

  x ← fround(x)

  CraftScript number type conversions cs-lib-core.js

  • PartCraft
  32-bit in part

• Conversion to whole-number types

  int8, int16, int32, int64 and the unsigned forms: each value rounded to a whole number.

  x ← round(x); NaN → 0

  CraftScript number type conversions cs-lib-core.js

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  64-bit

• Section of a faceted mesh

  The section view's visible lines, cut outline, extents and the cutting plane's trace.

  Drawing section view of a faceted part drawing.js

  • PartCraft
  32-bit in part

• Minimum safety factor

  The yield stress divided by the largest nodal von Mises stress.

  safety = S_y ÷ σ_max

  Voxel stress analysis: 32-bit steps in loads and results fea.js

  • PartCraft
  32-bit in part

• Values on the plot mesh

  Stress, displacement size and displacement vector at each vertex of the plot mesh, read by the hover probe and the legend.

  Voxel stress analysis: 32-bit steps in loads and results fea.js

  • PartCraft
  32-bit in part

• Force and pressure on faces

  Shares a force or a pressure over the nodes of the picked faces.

  node force = magnitude × weightᵢ ÷ Σ weight × direction; pressure magnitude = p × area

  Voxel stress analysis: 32-bit steps in loads and results fea.js

  • PartCraft
  32-bit in part

• The mesh handed to the flow solver

  Builds the job for a flow study from the part and the study's settings.

  Flow study: 32-bit steps in the mesh and the result fields flow-study.js

  • PartCraft
  32-bit in part

• Cell fields, maximum speed and pressure range

  Velocity and pressure of every cell in physical units, and the largest speed and lowest and highest pressure the results state.

  v = u × c_u; p = p_ref + (ρ − 1) ÷ 3 × c_p; v_max = max |v|

  Flow study: 32-bit steps in the mesh and the result fields flow-worker.js

  • PartCraft
  32-bit in part

• Pressure on the part's surface

  The static pressure at each vertex of the plot mesh, sampled a little way into the fluid.

  p = Σ (wᵢ + 1e-6) pᵢ ÷ Σ (wᵢ + 1e-6) over the fluid cells around the sample point

  Flow study: 32-bit steps in the mesh and the result fields flow-worker.js

  • PartCraft
  32-bit in part

• Result probe

  Shows the speed, velocity and pressure of the cell under the pointer, or the surface pressure.

  speed = √(v_x² + v_y² + v_z²)

  Flow study: 32-bit steps in the mesh and the result fields flow-ui.js

  • PartCraft
  32-bit in part

• Lattice Mach number warning

  The fastest cell's speed as a share of the lattice speed of sound.

  Ma = v_max × dt ÷ dx × √3

  Flow study: 32-bit steps in the mesh and the result fields flow-ui.js

  • PartCraft
  32-bit in part

• Model constants

  The constants of the turbulence model.

  c_w1 = c_b1 ÷ κ² + (1 + c_b2) ÷ σ

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Spalding's law of the wall

  y⁺ as a function of u⁺.

  y⁺ = u⁺ + e^(−κB) (e^(κu⁺) − 1 − κu⁺ − (κu⁺)² ÷ 2 − (κu⁺)³ ÷ 6)

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Friction velocity

  Solves the wall law for the friction velocity from the speed at a distance from the wall.

  find u_τ with spalding(U ÷ u_τ) = y u_τ ÷ ν

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Inverse wall law

  u⁺ as a function of y⁺.

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Wall cells: normal and wall distance

  Each wall cell's wall normal and its true distance to the wall, and the model's starting fields.

  n = Σ wᵢ nᵢ ÷ |Σ wᵢ nᵢ|; y = Σ wᵢ c_n (q c_n) ÷ Σ wᵢ c_n over links with c_n > 0.3, y ≥ 0.05

  Flow study: turbulence model and wall functions flow-turb.js

  • PartCraft
  32-bit in part

• Wall distance of every cell

  The distance from each fluid cell to the nearest wall point.

  d(m) = |v(n) − c| carried from a settled neighbor n along the link c

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Model update in a cell

  The wall function in wall cells and one pseudo-time step of the model equation elsewhere.

  ν̃_new = (ν̃ + Δt × rhs) ÷ (1 + Δt c_w1 f_w ν̃ ÷ d²); wall cell: ν̃ = κ u_τ y

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Pseudo-time step

  The model's time step from the advection and diffusion limits.

  Δt = max(0.05, min(every, 0.5 ÷ u_max, 0.8 σ ÷ (6 (ν + ν̃_max))))

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• First-cell y⁺ statistics

  The minimum, maximum, mean and percentiles of y⁺ over the wall cells.

  percentile p = sorted[⌊p × n⌋]

  Flow study: turbulence model and wall functions flow-turb.js

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  64-bit

• Wall force correction for slip

  The term added to the momentum-exchange force on walls that carry a slip velocity.

  F += Σ u_w (f_in − f_out)

  Flow study: turbulence model and wall functions flow-turb.js

  • PartCraft
  64-bit

• Hull mesh taken from the built part

  Copies the part's triangle mesh for the hull calculation.

  Hull hydrostatics and righting arms hydrostatics.js

  • PartCraft
  32-bit in part

• Volume, moments and waterplane under a waterline

  Clips the mesh at the waterline and sums the wet volume, its first moments, the wetted area and the waterplane's boundary integrals.

  V = Σ a·(b × c) ÷ 6; ∫x dV = ½ ∮ x² nₓ dS; A = ½ Σ (pₓ q_z − qₓ p_z); ∫z² dA = Σ (p_z² + p_z q_z + q_z²)(pₓ q_z − qₓ p_z) ÷ 12

  Hull hydrostatics and righting arms hydrostatics.js

  • PartCraft
  32-bit in part

• Hydrostatic properties at a draft

  Volume, displacement, KB, LCB, waterplane area and centroid, BM, KM, block and waterplane coefficients, and mass per unit immersion.

  V = V_skin + h × A ÷ 3; I_T = ∫z² dA − A × c_z²; BM = I ÷ V; KM = KB + BM; Δ = V × 1e-9 × ρ

  Hull hydrostatics and righting arms hydrostatics.js

  • PartCraft
  32-bit in part

• Righting arms at fixed displacement

  The righting arm GZ at each heel angle, the metacentric height GM, the largest GZ and the angle where stability vanishes.

  GZ = z(B) − (keel + KG) × sin θ; GM = KM_T − KG; vanishing angle by linear interpolation between samples

  Hull hydrostatics and righting arms hydrostatics.js

  • PartCraft
  32-bit in part

• Units and rounding of the answer

  Converts the hull results to meters, square meters, cubic meters and tonnes for the tool's answer.

  value_m = round(value_mm ÷ 1000 × 10⁴) ÷ 10⁴; volume_m³ = round(V ÷ 1e9 × 10⁴) ÷ 10⁴

  Hull hydrostatics and righting arms hydrostatics.js

  • PartCraft
  32-bit in part

• Coordinate and direction text

  Formats a coordinate or a direction component as a STEP real.

  text = v.toFixed(digits), trailing zeros removed; digits = 6 for points, 12 for directions

  IFC export of parts, assemblies and library items ifc-export.js

  • PartCraft
  64-bit

• Quantity and property value text

  Formats a volume, area, mass, length or parameter value as a STEP real.

  text = Number(v.toPrecision(12))

  IFC export of parts, assemblies and library items ifc-export.js

  • PartCraft
  64-bit

• Triangulated body

  Writes the vertices and triangles of the built mesh as an IfcTriangulatedFaceSet.

  (x, y, z) → (x, −z, y), each written with 6 decimals

  IFC export of parts, assemblies and library items ifc-export.js

  • PartCraft
  32-bit in part

• Volume, area, weight and overall size

  The quantity sets of an element: net volume in m³, net surface area in m², net weight in kg and the box dimensions in mm.

  V_m³ = V_mm³ × 1e-9; A_m² = A_mm² × 1e-6; weight_kg = V_mm³ × density_g/cm³ × 1e-6; size = |max − min|

  IFC export of parts, assemblies and library items ifc-export.js

  • PartCraft
  64-bit

• Volume and area of a library item's body

  Volume, surface area and bounding box of a library item's mesh for its quantities.

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

  IFC export of parts, assemblies and library items ifc-export.js

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  64-bit

• Placement of an assembly instance

  Turns an instance's 4 × 4 matrix into an IFC axis placement: location, local z axis and local x axis.

  location = C(column 3); Axis = C(column 1); RefDirection = C(column 0); C(x, y, z) = (x, −z, y)

  IFC export of parts, assemblies and library items ifc-export.js

  • PartCraft
  64-bit