Calculations

Calculations

• Hole depth

  The depth of a drilled hole, including a through hole's length past the body.

  through: depth = extent on the drilling side + 1 + 0.01 × (max − min)

  Feature tool dimensions on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Countersink cone height

  The height of a countersink from its diameter, the hole diameter and the included angle.

  h = (R − r) ÷ tan(angle × π ÷ 360)

  Feature tool dimensions on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Thread zone of a tapped hole

  The inner and outer radius of a tapped hole's thread, used when parts are checked against each other.

  r₀ = min(drill, d − 1.082532 × p) ÷ 2; r₁ = d ÷ 2

  Feature tool dimensions on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Circular pattern step

  The angle between copies of a circular pattern and the rotation applied to each copy.

  full turn: step = 360 ÷ count; otherwise step = angle ÷ (count − 1); copy i turned by step × i

  Feature tool dimensions on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Extent of the body along a normal

  How far the body reaches in front of and behind a sketch plane, for through-all cuts and through holes.

  range = min and max of (corner − o)·n over the 8 corners of the bounding box

  Feature tool dimensions on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Reference stored for a picked flat face

  Chooses the stable face reference for a picked flat triangle, or stores a fixed plane when none matches.

  match: c.n·n > 1 − 1e-6 and |(p − c.o)·c.n| < 1e-4 × max(1, |p|); else o rounded to 9 decimals, n to 12

  Feature tool dimensions on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Body mesh read back for named faces and edges

  Copies the current body's vertices and triangles so its faces and edges can be named and measured by later features.

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Fillet tangent points and arc

  Where a round of radius r touches the two faces of an edge, its center, and the points of its arc.

  s_A = ±r × (1 − n_A·n_B) ÷ (u_A·n_B); center = O + u_A × s_A ± n_A × r; angle = acos(v₀·v₁ ÷ r²)

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Chamfer distances

  The two setback distances of a chamfer, for equal, two-distance and distance-and-angle modes.

  θ = acos(u_a·u_b); angle mode: d_b = d × sin α ÷ sin(π − α − θ)

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Section and prism of a fillet or chamfer

  The cross-section that is extruded along the edge and cut from (or added to) the body.

  section pushed past both faces by 0.01 × size; prism length = edge length

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Shell by offsetting the body

  Hollows the body to a wall thickness, or thickens it outward, and opens the picked flat faces.

  inward: body − (body ⊖ ball(t)); outward: (body ⊕ ball(t)) − body

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Draft: new normal and hinge line

  The plane a drafted face turns to, and the line where the face meets the neutral plane.

  n₂ = unit(n_perp × cos a + pull × sin a); q = n × (d₁ − d₂ n·m) ÷ (1 − (n·m)²) + m × (d₂ − d₁ n·m) ÷ (1 − (n·m)²)

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  64-bit

• Draft: outline of the face

  The outline of the drafted face, extruded into the prism that is trimmed by the old and new planes.

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Thread: extent of the round face

  Where a picked cylinder face starts and ends along its axis and whether it is a shaft or a bore, which set the thread's start, length and callout.

  t₀, t₁ = min and max of (p − o)·d over the face's vertices; full length = t₁ − t₀

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Mesh body from an imported file

  Scales an imported mesh to millimeters, turns it Y up and makes it a solid body.

  (x, y, z) → (x × s, z × s, −y × s) for a Z-up file; s = unit factor

  Fillet, chamfer, draft, thread and mesh bodies on the mesh kernel kernel.js

  • PartCraft
  32-bit in part

• Matching tolerance and chord sag

  The distance within which a triangle's corners count as lying on a surface.

  sag = 1.5 × (1 − cos(π ÷ max(8, segments))); tol = 2e-6 × diagonal + 1e-7

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  64-bit

• Triangle on a surface

  Decides whether a triangle lies on a plane, cylinder, cone, sphere, torus or thread zone.

  plane: |(p − o)·n| ≤ tol; cylinder: −(tol + sag × r) ≤ ρ − r ≤ tol + 1e-6 × r

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  64-bit

• Face area and center

  The area of each named face and its area-weighted center.

  area = Σ |(b − a) × (c − a)| ÷ 2; center = Σ (triangle center × area) ÷ area

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  32-bit in part

• Edge length, ends and middle

  The length of an edge between two faces, its two ends and its middle point.

  len = Σ |pᵢ − pᵢ₋₁|; middle = the point at len ÷ 2 along the polyline

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  32-bit in part

• Straight edge or circle

  Classifies an edge as a line, a circle or a curve and gives a circle its center, axis and radius.

  line: every point within 10 × tol of the chord; circle: every point at one radius and one height about a round face's axis

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  32-bit in part

• Circle edge points put on the circle

  Moves a circular edge's ends and middle exactly onto its circle.

  p′ = c + r × w ÷ |w|, w = (p − c) − n × ((p − c)·n); closed circle: middle = 2c − a

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  32-bit in part

• Surfaces of pattern and mirror copies

  Moves a tool's named planes, axes and centers with the matrix of a pattern or mirror copy.

  point′ = M × point; direction′ = unit(linear part of M × direction)

  Named faces and edges from the body mesh meshfaces.js

  • PartCraft
  64-bit

• Circle of an edge

  Center, radius and axis of a circular edge from its two ends and its middle point.

  c = A + ((n × ab) |ac|² + (ac × n) |ab|²) ÷ (2 |n|²), n = ab × ac; full circle: c = (a + middle) ÷ 2, r = |a − middle| ÷ 2

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Area of a picked group of facets

  The area and normal of a picked face when no face table is available.

  area = Σ |(b − a) × (c − a)| ÷ 2; plane if |Σ cross| > 0.999 × 2 × area

  Measuring and mass properties in 3D measure.js

  • PartCraft
  32-bit in part

• Closest point on a triangle

  The point of a facet nearest to a given point, for the fallback distance.

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Closest points of two segments

  The nearest pair of points on two mesh edges, for the fallback distance.

  s = (b·f − c·e) ÷ (a·e − b²), t = (b·s + f) ÷ e, clamped to 0…1

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Minimum distance over the facets

  The smallest distance between two picked entities when the exact kernel's distance is not available.

  min over point–point, point–triangle, point–segment and segment–segment pairs

  Measuring and mass properties in 3D measure.js

  • PartCraft
  32-bit in part

• Distance, angle and gaps between two picks

  Point-to-point distance, the angle between planes, lines or axes, the gap between parallel planes and the distance between centers or parallel axes.

  angle = acos(clamp(d₁·d₂)) in degrees; plane gap = |(o₂ − o₁)·n|; axis gap = |w − d (w·d)|

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Volume, center of mass and inertia from the mesh

  Mass properties of a closed triangle mesh at density 1.

  V = Σ a·(b × c) ÷ 6; ∫xxᵀ dV = Σ V_t ÷ 20 × (Σ pᵢpᵢᵀ + (Σpᵢ)(Σpᵢ)ᵀ); about the center: C − V g gᵀ

  Measuring and mass properties in 3D measure.js

  • PartCraft
  32-bit in part

• Mass properties of a placed part

  Mass in grams and the inertia tensor in world axes for one placed part.

  I_world = (density ÷ 1000) × R I Rᵀ; center_world = M × center

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Mass properties of several parts together

  Total mass, combined center of mass and inertia tensor of an assembly.

  center = Σ mᵢ cᵢ ÷ Σ mᵢ; I = Σ (Iᵢ + mᵢ (|dᵢ|² E − dᵢ dᵢᵀ)), dᵢ = cᵢ − center

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Principal moments and axes

  The eigenvalues and eigenvectors of the inertia tensor.

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

  Measuring and mass properties in 3D measure.js

  • PartCraft
  64-bit

• Exact minimum distance

  The minimum distance between two picked faces, edges, points or bodies and the two closest points.

  Measuring and mass properties in 3D measure-brep.js

  • PartCraft
  64-bit

• Exact volume, area, center and inertia

  Mass properties of the part's exact body at density 1.

  I_xy = I((x + y) ÷ √2) − (I_xx + I_yy) ÷ 2, and the same for yz and xz

  Measuring and mass properties in 3D measure-brep.js

  • PartCraft
  64-bit

• Curved edges of an assembly drawing view

  Turns each visible or hidden curve of a hidden-line view into the line segments the drawing keeps.

  n = clamp(⌈span ÷ size × 160⌉, 8, 240) equal parameter steps

  Measuring and mass properties in 3D measure-brep.js

  • PartCraft
  64-bit

• Sketch plane from a picked flat face

  The plane reference stored when a sketch is put on a picked flat face that has no stable name.

  o = each coordinate rounded to 9 decimals; n = each component rounded to 12 decimals

  Values stored from picks in the workspace partcraft.js

  • PartCraft
  64-bit

• Mate plane from a picked face of an instance

  The plane stored in an assembly mate when a flat face of a placed part is picked.

  o rounded to 9 decimals, n to 12 decimals, when the face has no stable name

  Values stored from picks in the workspace partcraft.js

  • PartCraft
  64-bit

• Anchor point on a drawing view

  The point in a view's own coordinates where a note, dimension or detail view is attached.

  u = u₀ + (x − x_view) ÷ scale, snapped to the nearest drawn line within 2.5 ÷ scale, then rounded to 4 decimals

  Values stored from picks in the workspace partcraft.js

  • PartCraft
  64-bit

• Default section plane offset

  The offset of a new section view's cutting plane: the middle of the part's bounding box along the view direction.

  offset = dir · (min + max) ÷ 2, rounded to 4 decimals

  Values stored from picks in the workspace partcraft.js

  • PartCraft
  64-bit

• Arc through three points

  Center, radius, start angle and signed sweep of an outline arc given by its start, middle and end.

  c_x = (|a|²(m_y − b_y) + |m|²(b_y − a_y) + |b|²(a_y − m_y)) ÷ d, d = 2 (a_x(m_y − b_y) + m_x(b_y − a_y) + b_x(a_y − m_y))

  Circuit board outline, holes and part boxes kicad.js

  • PartCraft
  64-bit

• Arc as straight segments

  The points that replace an arc or circle of the board outline.

  steps = max(2, ⌈|sweep| ÷ 7.5°⌉); pₖ = c + r (cos aₖ, sin aₖ), aₖ = a₀ + sweep × k ÷ steps

  Circuit board outline, holes and part boxes kicad.js

  • PartCraft
  64-bit

• Joining outline pieces into loops

  Chains lines and arcs of the edge layer into closed outlines.

  Circuit board outline, holes and part boxes kicad.js

  • PartCraft
  64-bit

• Footprint point on the board

  Moves a point of a footprint (a pad, a corner of its box) to board coordinates.

  x = at_x + l_x cos a − l_y sin a; y = −at_y + l_x sin a + l_y cos a; l_y = −p_y, a = rotation × π ÷ 180

  Circuit board outline, holes and part boxes kicad.js

  • PartCraft
  64-bit

• Board thickness parameter

  The part parameter that drives the board's extrusion depth.

  board_t = thickness rounded to 4 decimals

  Circuit board outline, holes and part boxes kicad.js

  • PartCraft
  64-bit

• Binary STL coordinates

  Reads the corner coordinates of each triangle from a binary STL file.

  Mesh import, repair and storage meshimport.js

  • PartCraft
  64-bit

• 3MF vertex placement

  Applies the unit of each model file and the chain of build and component transforms to every vertex.

  p′ = [x s, y s, z s, 1] × M (row vectors, 4 × 3); s = unit of the part file ÷ unit of the root file

  Mesh import, repair and storage meshimport.js

  • PartCraft
  64-bit

• Welding coincident points

  Merges points that lie within a tolerance of each other and maps every index to the point that is kept.

  merge when (Δx² + Δy² + Δz²) ≤ tol²; the earliest point is kept

  Mesh import, repair and storage meshimport.js

  • PartCraft
  64-bit

• Repair tolerances from the mesh size

  Sets the weld distance, the gap-closing distance and the smallest triangle area kept, then welds and cleans.

  exact = 1e-7 × size; gap = 1e-3 × size; area limit = 1e-14 × size²; size = bounding-box diagonal

  Mesh import, repair and storage meshimport.js

  • PartCraft
  64-bit

• Closing small gaps

  Merges boundary points that lie within the gap distance of another boundary point.

  Mesh import, repair and storage meshimport.js

  • PartCraft
  64-bit

• Outward orientation by signed volume

  Turns each closed shell so that it encloses positive volume.

  6 V = Σ (a − o)·((b − o) × (c − o)), o = the shell's first point

  Mesh import, repair and storage meshimport.js

  • PartCraft
  64-bit