Calculations

Calculations

• Tile grid

  How many tiles across and down the pieces need.

  pw = paper w − 2·margin; ph = paper h − 2·margin − 8; step = pw − overlap, ph − overlap; cols = max(1, ⌈(W − overlap) ÷ step − 1e-9⌉)

  Printing patterns at full size addons/apparel/lib/print.js

  • CadCraft
  64-bit

• Which tiles have something on them

  Marks the tiles a point of the drawing falls on, so empty tiles are not printed.

  c from ⌈(x − pw) ÷ sx⌉ to ⌊x ÷ sx⌋; r from ⌈(−y − ph) ÷ sy⌉ to ⌊−y ÷ sy⌋

  Printing patterns at full size addons/apparel/lib/print.js

  • CadCraft
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• Placement on one tile

  Where the pieces land on the page of one tile.

  tx = c·sx; ty = −r·sy; matrix = [k, 0, 0, k, margin − tx − minX·k, (paper h − margin − 8) − ty − maxY·k]

  Printing patterns at full size addons/apparel/lib/print.js

  • CadCraft
  64-bit

• A number as file text

  The text of a coordinate, angle or text height in the DXF.

  r = round(v × 1e6) ÷ 1e6; −0 → 0

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
  64-bit

• Piece to drawing coordinates

  A point of a piece moved to where the piece lies in the drawing.

  x′ = x + cos(rot)·sx·pₓ − sin(rot)·sy·pᵧ; y′ = y + sin(rot)·sx·pₓ + cos(rot)·sy·pᵧ

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
  64-bit

• What a piece writes

  The cut line, sew line, notches, grain line and marks of one piece in one size, in drawing coordinates.

  corner on the cut line when the turn > 0.17 rad; notch angle = atan2 of the inward direction × 180 ÷ π

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Grade rule of a written point

  The move of one written point in every size, measured from the base size.

  rule = [(xₛ − x_base, yₛ − y_base) for each size s]

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Rounding and sharing rules

  Gives every rule a number; identical rules share one.

  dx, dy → round(v × 100) ÷ 100

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
  64-bit

• Rules in the RUL file

  The lines of the rule file: an x and y pair per size for every rule.

  x.toFixed(2), y.toFixed(2), four pairs to a line

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Reading a RUL file

  The sizes, sample size and rules of a rule file.

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Corners and curve points of a read outline

  Decides which points of an outline read from someone else's file are corners.

  tol = max(1e-6, 1e-7 × largest |coordinate|) + 0.02 mm (0.001 in); corner when a turn point lies within tol, or the turn > 0.35 rad

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Outline points kept from a file

  The outline of a piece read from someone else's file.

  x, y → toFixed(6)

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
  64-bit

• Seam allowance read from a file

  The allowance of each edge, from how far the file's cut line is from its sew line.

  edge width = median of the distances from the edge's sample points to the cut line → 2 decimals (mm) or 4 (in); common width = median of the edges

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
  64-bit

• Rules from a file with every size drawn

  Grade rules worked out from blocks that draw the piece in each size.

  rule = pointₛ − point_base → toFixed(4)

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Rules from a RUL file

  Grade rules of a piece from the rule numbers on its points.

  k = (25.4 or 1) ÷ (25.4 or 1); move = (ruleₛ − rule_sample) × k → toFixed(4)

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Fitting a large piece into one object

  Shrinks the data of a piece that is too large for one drawing object.

  rules → 2 decimals (mm) or 4 (in); points → 3 decimals (mm) or 5 (in); then curve points thinned at 0.02, 0.05, 0.1, 0.2, 0.3, 0.5, 1 mm

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Thinning a run of points

  Which curve points of a run must stay so the line stays within a tolerance.

  d = |(P − A) × (B − A)| ÷ |B − A|; the farthest point stays when d > tol

  DXF-AAMA and ASTM pattern files addons/apparel/lib/aama.js

  • CadCraft
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• Picked point into the piece's frame

  A point picked in the drawing as a point in the piece's own coordinates.

  local = (insert matrix)⁻¹ · p

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
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• Piece table

  Sew and cut perimeter and area of every piece in every size, as printed and as exported to CSV.

  perimeter → toFixed(2); area ÷ k → toFixed(2), k = 100 for mm² to cm², 1 for in²

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

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• Default grain line

  The grain line a new piece gets: through its centroid, up the page.

  h = 0.3 × (maxY − minY); a = (cₓ, cᵧ − h); b = (cₓ, cᵧ + h); each → toFixed(6)

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
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• Buttonhole from two picked points

  The center, length and angle stored for a buttonhole.

  center = (q + b) ÷ 2; L = |b − q|; angle = atan2(Δy, Δx) × 180 ÷ π

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
  64-bit

• Do the notches of two seams match

  The line printed for each notch pair when two edges are walked along each other.

  match when |offset| < 0.5 × (1 mm or 0.0625 in)

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
  64-bit

• Tile overlap typed in inches

  The overlap between printed tiles, in millimeters.

  overlap = typed value × 25.4 in inch drawings

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
  Exact

• Drawing point into the marker's frame

  A drawing point as a point measured from the fabric's lower-left corner, along and across the fabric.

  x′ = cos(−rot)·(x − mₓ) − sin(−rot)·(y − mᵧ); y′ = sin(−rot)·(x − mₓ) + cos(−rot)·(y − mᵧ)

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
  64-bit

• Marker numbers after a change

  The length, used area, efficiency and piece count kept with a marker after every change to the drawing.

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
  64-bit

• Automatic nesting on a marker

  Lays the marker's pieces on the fabric and writes their new positions to the drawing.

  raster cell = width ÷ 750; time limit 3000 ms; x = mₓ + cos(rot)·pₓ − sin(rot)·pᵧ; y = mᵧ + sin(rot)·pₓ + cos(rot)·pᵧ; rotation = marker rotation + piece rotation

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
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• Marker PDF page

  The size of the marker's PDF page and the placement of the fabric on it at 1:1.

  k = 25.4 (inch) or 1; W = (x₁ − x₀)·k + 20; H = (y₁ − y₀)·k + 20 + pad; matrix = [k, 0, 0, k, 10 − x₀·k, 10 + pad − y₀·k]

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
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• A measured length as text

  The text of a seam length or walk difference on the command line.

  mm: 1 decimal, 0 below 0.05; inches: fractions to 1/16

  Apparel commands: piece table, marks and marker output addons/apparel/main.js

  • CadCraft
  64-bit

• Stock list read from a file

  A stock list with every number checked and each remnant's area, width and height worked out again from its outline.

  area = regionArea(loops); w = x₁ − x₀; h = y₁ − y₀ of the outline (arcs flattened to a sag of 0.001); outline moved so its box corner is (0, 0)

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

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  • PartCraft
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• Stock totals

  The number of available remnants and their total area per material and thickness.

  area = Σ remnant areas

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

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  • PartCraft
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• Numbers in the stock CSV

  The text of a thickness, width, height or area in the exported stock list.

  round(v × 10ᵈ) ÷ 10ᵈ; d = 3 for thickness, 2 for width and height, 1 for area

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

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  • PartCraft
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• Grid of free material

  Marks which cells of the plate are free after the parts, the spacing and narrow strips are taken out.

  cell = min(w, h) ÷ 600; sag = min(cell ÷ 8, 0.1); grow = ⌈(spacing + 2·sag) ÷ cell − 1e-9⌉ + 1 cells; strips narrower than minWidth removed by an opening of ⌊minWidth ÷ cell ÷ 2⌋ cells

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
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• Growing a region on the grid

  Marks every cell within k cells of a marked cell, along rows and then columns.

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
  Exact

• Outline of a free region

  The boundary of one connected region of free cells, as loops on grid corners.

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
  Exact

• Removing points on a straight run

  Drops grid points that lie between their neighbors on a straight line.

  (b − a) × (c − b) ≠ 0 → keep

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
  Exact

• Simplifying an outline

  Removes outline points within half a cell of the simplified line.

  d = |(r − p) × (q − p)| ÷ |q − p|; kept when d > tol

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

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  • PartCraft
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• Remnant outline, size and area

  Each leftover region as an outline with holes, its area and its bounding size.

  point = grid corner × cell, clamped to the plate; simplified by cell ÷ 2; area = regionArea(outline and holes); kept when area ≥ minArea (2 percent of the plate by default)

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
  64-bit

• Does a remnant match the job

  Whether a remnant has the job's material and thickness.

  |thickness − wanted| < 1e-6

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
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• Job efficiency

  The share of the material used by the parts over all remnants and plates of a job.

  efficiency = Σ part areas ÷ Σ (remnant area or w × h of each plate)

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

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• Adding a job's remnants to the stock

  Marks the remnants a job used and adds the ones it leaves, numbered.

  stored outline = outline − (x₀, y₀); w, h and area as found by leftovers

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
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• Exact re-check of remnants against parts

  Confirms on the polygons that no remnant touches a placed part and that the spacing is kept.

  distance between every pair of edges; overlap when ≤ 1e-6 or one contains the other's first point; too close when < spacing − 1e-6

  Offcut stock after nesting addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
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• Label position and text height

  The point where a remnant's number is written and the height of that text.

  d = chamfer distance in cells (steps 1 and 1.4142); x = (i + 0.5) × cell; y = (j + 0.5) × cell; h = max(cell, min(0.6 × d × cell, height ÷ 4))

  Where a remnant's number is written addons/apparel/lib/nest/nest-stock.js

  • CadCraft
  • PartCraft
  32-bit in part

• Rule units per drawing unit

  The factor between the drawing's unit and the cabinet rules' unit, and its reciprocal.

  per = meters per drawing unit ÷ (0.0254 or 0.001); k = 1 ÷ per

  Cabinets along a wall line addons/cabinet/main.js

  • CadCraft
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• Placing a cabinet on the run

  The insertion point and rotation of a new cabinet, and where the next one starts.

  w = typed × per; x = runₓ + cos(ang)·pos·k; y = runᵧ + sin(ang)·pos·k; next pos = pos + w

  Cabinets along a wall line addons/cabinet/main.js

  • CadCraft
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• Cabinets of a front view

  Which cabinets stand on a wall line and how far along it, for the front view.

  on the run when |sin(rot − ang)| ≤ 1e-6, cos(rot − ang) ≥ 0 and |offset| ≤ 0.5 × depth × k; x = s ÷ k − smallest x, rounded to 6 decimals

  Cabinets along a wall line addons/cabinet/main.js

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• Area as text

  The area of a material group on the command line.

  in² ÷ 144 = ft²; mm² ÷ 1e6 = m²; 3 decimals

  Cabinets along a wall line addons/cabinet/main.js

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• Edge banding length as text

  The length of edge banding on the command line.

  in ÷ 12 = ft; mm ÷ 1000 = m; 3 decimals

  Cabinets along a wall line addons/cabinet/main.js

  • CadCraft
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• Sheet use in percent

  The share of each material's sheets covered by parts, as printed after nesting.

  percent = round(efficiency × 100)

  Cabinets along a wall line addons/cabinet/main.js

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• Millimeters in one drawing unit

  The factor from the drawing's unit to millimeters.

  mm per unit = meters per unit ÷ 0.001; inch 0.0254, foot 0.3048, yard 0.9144, cm 0.01, m 1

  CabinetCraft in a drawing: units, room outline and solids addons/cabinetcraft/host.js

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• Room outline from a polyline

  The corners of a closed polyline in millimeters, with arcs turned into chords.

  sweep = 4·atan(bulge); steps = max(1, ⌈|sweep| ÷ 15°⌉); r = chord ÷ (2·sin(|sweep| ÷ 2)); point = (c + r·(cos, sin)) × f

  CabinetCraft in a drawing: units, room outline and solids addons/cabinetcraft/host.js

  • CadCraft
  64-bit