Calculations

Calculations

• Cleaning a stored coordinate

  The rounding applied to every coordinate and angle a transform stores.

  |n − round(n)| < 10⁻⁶ → round(n); else round(n × 10⁶) ÷ 10⁶

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A member's new rotation

  The rotation that puts a member's section axis where the transform sent it.

  rotation = atan2(−want·u₀, want·v₀) × 180 ÷ π, brought into 0 to 360

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A member through the transform

  The new end points, rotation, position, holes and copes of a member.

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Mirrored angle with a top or bottom position

  Shifts a mirrored angle's line so the steel lands where the mirror image is.

  d = A·v̂·voff − v̂′·voff; start, end += d

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A footing through the transform

  The new position and rotation of a footing.

  rotate: rot + deg; mirror: 2·φ − rot; both brought into 0 to 360

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Center of a selection

  The plan middle of the selection, used as the point to rotate about.

  ((x_min + x_max) ÷ 2, (y_min + y_max) ÷ 2, z_min)

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Offset of a drag

  The offset a dragged part is moved by: onto a grid node, or in steps.

  node − held point, or round(raw ÷ step) × step

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A part's solid for drawing

  The mesh of a part: its profile extruded, with copes cut.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• Mitre ends on the mesh

  Moves the end vertices of a mesh onto the mitre's cut plane.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• The part under the pointer

  Which part a click hits and where the ray meets it.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• Tightest limit of a rule

  The minimum and maximum a rule allows when several ticked packs have it.

  min = max(minᵢ); max = min(maxᵢ)

  Regulation limits in force and how values are written addons/regs/lib/adapter.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Values written in a problem

  How a required or found value is written in a regulation problem, by unit.

  mm: round(v × 10) ÷ 10; m²: round(v × 100) ÷ 100; ratio and U: 2 decimals; R: 1 decimal; count: whole

  Regulation limits in force and how values are written addons/regs/lib/adapter.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Percentages as text

  A percentage written in the panel, in problems and on the code summary sheet.

  round(v × 10) ÷ 10, then the browser's number format with at most one decimal

  Regulation limits in force and how values are written addons/regs/lib/ui.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Values on the code summary sheet

  Required and found values on the printable code summary for a permit set.

  Regulation limits in force and how values are written addons/regs/lib/ui.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Raw double, read

  A 64-bit value read from eight bytes of the bit stream.

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Bit double, read

  A value stored as a two-bit code: a full 64-bit value, exactly 1.0 or exactly 0.0.

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Double with default, read

  A value stored as the bytes in which it differs from a default value.

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• 64-bit whole number, read

  An unsigned 64-bit whole number from two 32-bit halves.

  value = high × 2³² + low

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Bit long long, read

  A whole number of up to seven bytes, the count given by three bits.

  value = Σ byteᵢ × 256ⁱ

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Handle reference, read

  An object handle, absolute or as an offset from another handle.

  value = Σ byte × 256ᵏ; codes 6, 8, A, C: ref + 1, ref − 1, ref + value, ref − value

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

  • CadCraft
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  64-bit

• Modular char, read

  A signed whole number stored seven bits per byte.

  value = Σ (byte & 0x7F) × 2^(7i); the last byte carries 6 bits and the sign

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

  • CadCraft
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  • ModelCraft
  • TakeoffCraft
  • CivilCraft
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  64-bit

• Raw double, written

  A 64-bit value written as its eight bytes.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Bit double, written

  A value written as a two-bit code for exactly 0.0 or 1.0, or as a full 64-bit value.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Double with default, written

  A value written as a two-bit code when it equals its default, or in full.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Thickness, written

  A thickness written as one bit when it is zero, or as a bit double.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Bit long, written

  A 32-bit whole number in its short or full form.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Bit short, written

  A 16-bit whole number in its short or full form.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

  • CadCraft
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  • ModelCraft
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  • CivilCraft
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  • PartCraft
  Exact

• Bit long long, written

  A 64-bit whole number as a three-bit byte count and its bytes.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Point, written

  The three coordinates of a point as bit doubles.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Handle bytes, written

  A handle as its bytes, most significant first.

  byte = v mod 256; v = ⌊v ÷ 256⌋

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Triangulate a polygon with holes

  The triangles of a polygon, as indexes into its point list.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Winding of a ring

  Whether a ring runs clockwise or counterclockwise.

  sum = Σ (xⱼ − xᵢ) × (yᵢ + yⱼ)

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Orientation of three points

  On which side of the line through two points a third point lies.

  area = (q.y − p.y) × (r.x − q.x) − (q.x − p.x) × (r.y − q.y)

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Removing duplicate and collinear points

  Drops points that repeat their neighbor or lie on the line between their neighbors.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Ear test

  Whether a corner can be cut off as a triangle: it is convex and no other point of the ring lies inside it.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Point in triangle

  Whether a point lies inside or on a triangle.

  three cross products of (corner − point) pairs, each ≥ 0

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Bridge from a hole to the outer ring

  The point of the outer ring a hole is connected to.

  x = p.x + (h.y − p.y) × (p′.x − p.x) ÷ (p′.y − p.y); tan = |h.y − p.y| ÷ (h.x − p.x)

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
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  • ModelCraft
  • TakeoffCraft
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  64-bit

• Do two segments cross

  Whether two edges intersect, including touching and collinear overlap.

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
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  • ModelCraft
  • TakeoffCraft
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  64-bit

• Is the middle of a diagonal inside the polygon

  Whether a diagonal between two corners runs through the inside of the polygon.

  midpoint = ((a.x + b.x) ÷ 2, (a.y + b.y) ÷ 2); even-odd count of edges crossed by a ray

  Polygon triangulation (ear clipping) usd/earcut.js

  • CadCraft
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  64-bit

• Material a set of cuts needs

  The bar length a group of cuts takes, with trim and saw kerf.

  need = trim + Σ lengths + kerf × cuts

  Cut-list nesting of bars nest.js

  • BimCraft
  • DetailCraft
  64-bit

• Nesting pieces on stock bars

  Which pieces are cut from which bar, each bar's drop, and the bought, used and waste totals.

  length = round(length × 10) ÷ 10; fits if need ≤ stock + kerf; drop = stock − trim − used − kerf × cuts; waste = 1 − used ÷ bought

  Cut-list nesting of bars nest.js

  • BimCraft
  • DetailCraft
  64-bit

• Cut list tables

  The summary per profile and the list of bars as printed.

  m = mm ÷ 1000, 2 decimals; waste % = waste × 100, 1 decimal

  Cut-list nesting of bars nest.js

  • BimCraft
  • DetailCraft
  64-bit

• Mesh handed to the solid kernel

  Welds the mesh's corners and passes it to manifold-3d.

  weld grid = 10⁻⁶ × max(Δx, Δy, Δz); positions → Float32Array

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
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  32-bit in part

• Boolean of two solids

  The difference, union or intersection of two element meshes.

  c = center of a's box; R = (a − c) OP (b − c); result = R + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Element minus all its openings

  Subtracts every opening from an element, one after another.

  A₀ = base − c; Aᵢ = Aᵢ₋₁ − (cutterᵢ − c); result = Aₙ + c

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part

• Face planes of a convex cutter

  Finds the outward planes of a cutter and decides whether it is convex.

  n = (b − a) × (c − a) ÷ |…|; d = n · a; convex when n · p − d ≤ 10 ε for every corner p

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Polygon split by a plane

  Cuts a convex polygon into the part in front of a plane and the part behind it.

  t = dₐ ÷ (dₐ − d_b); x = a + (b − a) t

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Mesh clipped by a plane

  Keeps the part of a mesh on one side of a plane and closes the cut.

  dᵢ = (pᵢ − p) · n; ε = 10⁻⁹ × (d_max − d_min); cut point = a + (b − a) dₐ ÷ (dₐ − d_b)

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
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  64-bit

• Cap of a cut

  Joins the cut segments into loops, sorts outer loops from holes and fills them.

  key = round(x ÷ tol), round(y ÷ tol), round(z ÷ tol); area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)|

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Half-space cut

  Removes the part of an element behind a plane, optionally only inside a polygon boundary.

  L = 4 × max(1, box diagonal) + |P₀ − box min|; prism height = 2 L

  IFC openings, clippings and half-space cuts ifc/geo-bool.js

  • BimCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  32-bit in part