Calculations

Calculations

• Length a bar takes

  The length of bar used by a set of pieces, with the saw kerf and the saving when mitred ends share a cut.

  used = Σ (length + kerf) − depth × min(⌊mitred ends ÷ 2⌋, mitred pieces − 1)

  Cutting profile pieces from stock bars addons/windows/lib/cutlist/bars.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Fewest bars for one stock length

  Which pieces go on which bar, and whether the count is proven to be the fewest.

  bound = ⌈Σ (length + kerf) ÷ usable − 1e-9⌉; usable = stock − trim at both ends

  Cutting profile pieces from stock bars addons/windows/lib/cutlist/bars.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Bars, cut positions, offcuts and waste

  The list of bars with each piece's start position, the offcut left on each bar and the totals.

  pos accumulates length + kerf; offcut = stock − trims − used; waste % = round((1 − piece length ÷ stock length) × 10⁴) ÷ 100

  Cutting profile pieces from stock bars addons/windows/lib/cutlist/bars.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Totals over all profiles

  The number of bars, the piece length, the stock length and the waste over every profile and color.

  waste = Σ stock length − Σ piece length

  Cutting profile pieces from stock bars addons/windows/lib/cutlist/bars.js

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

• Lineweight to stored index

  The index written for a lineweight, or the codes for by layer, by block and default.

  index of the list value with the smallest |value − lineweight|

  Lineweights in a DWG file dwg/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  Exact

• Stored index to lineweight

  The lineweight for an index read from a file.

  Lineweights in a DWG file dwg/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  Exact

• Longest clear part of a move

  The part of a straight move that stays clear of other solids.

  steps = min(160, max(4, ⌈|δ| ÷ (thin ÷ 2)⌉)); then 24 halvings between the last clear and the first blocked sample

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Thinnest dimension

  The smallest box side of the moving pieces and of everything in the way, which sets the sample spacing.

  thin = max(0.005, min over boxes of the smallest side above 1e-4)

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Edge through the inside of a face

  Whether a segment passes through a face's interior.

  sₚ = n·p − d, s_q = n·q − d; t = sₚ ÷ (sₚ − s_q)

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Point in a face

  Whether a point on a face's plane lies in one of its triangles.

  u, v from cross products ÷ |n|²; inside when u, v, 1 − u − v ≥ −1e-9

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Point inside a solid

  Whether a point lies inside the closed surface made of an object's faces.

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Ray against a triangle

  The distance along a ray to a triangle, or nothing when it misses.

  det = e₁·(d × e₂); u = (s·(d × e₂)) ÷ det; v = (d·(s × e₁)) ÷ det; t = (e₂·(s × e₁)) ÷ det

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Box of a placed component

  The bounding box in the model of a component's faces and edges, from its own coordinates and its placement matrix.

  X = (m₀x + m₄y + m₈z + m₁₂) ÷ w

  Where a moved solid stops against another m3d/collide.js

  • CadCraft
  • ModelCraft
  64-bit

• Triangles of a polygon with holes

  The triangles of a face as triples of vertex indexes.

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Orientation of three points

  Twice the signed area of a triangle, whose sign says which way three points turn.

  (q_y − p_y)(r_x − q_x) − (q_x − p_x)(r_y − q_y)

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Direction of a ring

  Whether a ring of points runs clockwise or counterclockwise.

  Σ (x_j − x_i)(y_i + y_j)

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Is a corner an ear

  Whether the triangle at a corner is convex and holds no other point of the polygon.

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Point in a triangle

  Whether a point lies in or on a triangle.

  three comparisons (c − p) × (a − p) ≥ 0, each written as product ≥ product

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Duplicate and collinear points removed

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

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Bridge from a hole to the outer ring

  The outer-ring point a hole is connected to, found by a ray to the left from the hole's leftmost point.

  x = p_x + (h_y − p_y)(n_x − p_x) ÷ (n_y − p_y); tan = |h_y − p_y| ÷ (h_x − p_x)

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Do two edges cross

  Whether two segments intersect, used to keep a diagonal from crossing the polygon.

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Is a diagonal's midpoint inside

  Whether the middle of a candidate diagonal lies inside the polygon.

  crossing count of a ray from ((a_x + b_x) ÷ 2, (a_y + b_y) ÷ 2)

  Triangulation of faces with holes m3d/earcut.js

  • CadCraft
  • ModelCraft
  • TakeoffCraft
  64-bit

• Rational tag value

  A TIFF RATIONAL (two 32-bit integers) as one number.

  value = numerator ÷ denominator

  TIFF scan resolution raster/tiff.js

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

• Resolution in dots per inch

  The horizontal and vertical resolution of a page, in dots per inch.

  dpi = resolution × 2.54 (centimeter files); dpi = resolution (inch files)

  TIFF scan resolution raster/tiff.js

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

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

• Do two segments cross

  Whether two edges intersect, including touching and collinear overlap.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Adding tile results to the picture

  The sums of red, green, blue and sample count of every pixel after a pass.

  out[pixel] += tile[pixel]

  Rendered picture: sample sums and color tables compute/cpu-render.js

  • BimCraft
  • ModelCraft
  32-bit, display only