Calculations

Calculations

• 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
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• 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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• 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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• 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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• 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

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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

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• 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
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  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

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• 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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• 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

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• 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

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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

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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

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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

  • CadCraft
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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

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• Drawing units per job unit

  The factor that scales the cabinet job (millimeters or inches) to the drawing's unit.

  k = (25.4 or 1) ÷ mm per drawing unit

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

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• Room area in the list

  The floor area shown beside each closed polyline offered as a room.

  area = |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| ÷ 2 ÷ 1e6 m²; shown as round(area × 100) ÷ 100

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

  • CadCraft
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• Door and window openings read from blocks

  The position and width of each door or window block near the room.

  w = max(box width, box height) × f, limited to 300…3000 mm; position = insertion point × f

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

  • CadCraft
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• Where the sheets are drawn

  The point in the drawing where the shop drawing sheets start.

  intended: x = right edge of what is drawn + 0.3 × tallest sheet; y = its top edge

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

  • CadCraft
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• Cabinet solids for the 3D tab

  The faces of each cabinet as polygons in drawing units.

  point = (x ÷ f, y ÷ f, z ÷ f)

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

  • CadCraft
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• Turning a direction

  A direction turned by an angle in degrees.

  (x·cos a − y·sin a, x·sin a + y·cos a), each rounded to 6 decimals

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Turn between two walls

  The signed angle from one wall direction to the next, in degrees.

  atan2(u₀ × u₁, u₀ · u₁) × 180 ÷ π

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• End of a wall typed as length and angle

  The end point of a wall from its start, length and angle.

  (x + L·cos a, y + L·sin a), rounded to 6 decimals

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• End of an arc typed as radius and sweep

  The end point of an arc wall from its radius, sweep and the heading of its chord.

  chord = 2·R·sin(|sweep| ÷ 2); end = start + chord at the heading

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Sagitta

  How far the middle of a straight back of width w stands off a circle of radius r.

  s = r − √(r² − w² ÷ 4)

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Arc through three points

  The radius, center and signed sweep of the arc picked as start, middle and end.

  d = 2·(aₓ(bᵧ − cᵧ) + bₓ(cᵧ − aᵧ) + cₓ(aᵧ − bᵧ)); uₓ = Σ |p|²·(Δy) ÷ d; uᵧ = Σ |p|²·(Δx) ÷ d; r = |a − u|

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Arc from two ends and a sweep

  The radius, center, chord, arc length and sagitta of an arc wall.

  r = chord ÷ (2·sin(θ ÷ 2)); center = middle ± normal × r·cos(θ ÷ 2); arc length = r·θ; sagitta = r·(1 − cos(θ ÷ 2))

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Points along an arc wall

  An arc wall as n straight pieces.

  φᵢ = a₀ ± |θ|·i ÷ n; point = center + r·(cos φ, sin φ), rounded to 6 decimals

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Back line and half angle of each cabinet on an arc

  The radius of each cabinet's back line and the half angle it takes up.

  bay: H = √(R² − w² ÷ 4); bow or curved front: H = R; half angle = atan2(w ÷ 2, H), or w ÷ (2R) for a curved front; front radius = H − d

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Spacing cabinets round an arc

  The angle at which each next cabinet stands so that it just clears the one before.

  bisection on the angle step in 0…π ÷ 2, 60 halvings; clash when the footprints penetrate more than 1e-7

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Gaps and wedges between stepped cabinets

  The largest gap between each cabinet's back and the curve, and the wedge left between neighbors.

  bay gap = R − H; bow gap = √(R² + w² ÷ 4) − R; wedge back and front = distance between neighboring corners

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Length used along the arc

  How much of the arc the cabinets take, and by how much the last one passes the end.

  used = (end angle − start angle) × R; overflow = max(0, end angle − limit) × R

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Stop short of an angled corner

  How far a run of cabinets must stop before a convex corner.

  τ ≤ 90°: depth × sin τ; sharper: depth

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Void at an angled corner

  The right-triangle void left where a run stops short of an angled corner.

  leg₁ = d·sin τ; leg₂ = d·cos τ; area = leg₁·leg₂ ÷ 2

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Diagonal corner cabinet at any angle

  The outline, miter, front length and area of a diagonal-front corner cabinet at a corner of turn τ.

  ℓ = w − d·tan(τ ÷ 2); front = 2·ℓ·cos(τ ÷ 2); apex = 180° − τ; miter angle = 90° − τ ÷ 2; Q = (w − d·tan(τ ÷ 2), d)

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• Area of a footprint

  The area of a polygon.

  A = |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| ÷ 2

  Cabinets on angled and curved walls addons/cabinetcraft/lib/angled.js

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• A board along a slanted line

  The four corners of a door or plinth board that runs along a diagonal.

  n = (−Δy, Δx) ÷ L; corner = point + n × offset, rounded to 6 decimals

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Round shelf solid

  The outline of a lazy-susan shelf as drawn in 3D.

  20 points at (cx + r·cos(2πi ÷ 20), cy + r·sin(2πi ÷ 20))

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Open leg of a corner cabinet

  The basic sizes of a corner cabinet: width, depth, open leg and top height.

  a = w − d; top = kick + box height

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Lazy-susan shelf size and place

  The diameter and center of the round shelves and the pole they turn on.

  diameter = max(1, w − 2·(t + 70 mm)); clearance = back setback + back thickness + 12 mm; center = (w − r − clearance, r + clearance); pole = center ± 15

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Shelf heights

  The height of each shelf inside the cabinet.

  z = kick + t + (inside height) × (i + 1) ÷ (n + 1) − t ÷ 2

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Sizes entered in the cut list

  The length and width of each board as they go into the cut list.

  length, width → round(v × 1e6) ÷ 1e6

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Back panels

  The size of the two back panels for a grooved, between or applied back.

  grooved: height = box height − 2t + 2·groove, length + groove; between: height = box height − 2t; applied: full height and width

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Door and plinth sizes at a right-angled corner

  The door height and width and the plinth length of a corner cabinet.

  door height = box height − reveal; door width = a − reveal (L) or a·√2 − reveal (diagonal); plinth = a or a·√2

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Blank for the triangle of an angled corner

  The smallest rectangle the triangular filler of an angled corner cabinet can be cut from, and the true front length.

  axes along the triangle's first leg and across it; L = largest coordinate along, W = largest across; front = |F_B − F_A|

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Door and plinth sizes at an angled corner

  The door and plinth of a diagonal corner cabinet at a corner that is not a right angle.

  door width = front length − reveal; plinth = front length

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Mirrored corner cabinet

  The same cabinet for a corner at the start of a run.

  x → w − x, rounded to 6 decimals

  Corner cabinets: parts and solids addons/cabinetcraft/lib/corner.js

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• Rounding to 4 decimals

  Rounds a coordinate to 4 decimals.

  r4(v) = round(v × 1e4) ÷ 1e4

  Cabinet shop drawings as drawing objects addons/cabinetcraft/lib/cadents.js

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• Drawing item to drawing object

  A line, outline or text of a shop drawing as a CadCraft object.

  x, y, text height → r4; text rotation = degrees × π ÷ 180

  Cabinet shop drawings as drawing objects addons/cabinetcraft/lib/cadents.js

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