Calculations

Calculations

• 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

  • CadCraft
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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
  64-bit

• 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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• Dimensions

  The linear dimensions of a shop drawing as dimension objects.

  p₁, p₂ → r4; line position = p + offset → r4; dimension scale = max(0.01, text height ÷ 2.5) → r4

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

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• Scaling to the drawing's unit

  Every coordinate, text height and dimension scale multiplied by the drawing units per job unit.

  v → r4(v × k)

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

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• Scaling all sheets

  All blocks and sheets scaled to the drawing's unit.

  k = 1 → unchanged; else every block and sheet through scaleEnts, sheet w and h × k

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

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• Moving a sheet into place

  The objects of a sheet moved by an offset.

  x → r4(x + dx); y → r4(y + dy)

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

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• Triangles of a panel outline

  Cuts a panel's outline into triangles for drawing.

  ear when (b − a) × (c − a) > 1e-9 and no other point is inside the triangle

  Cabinets as 3D viewport bodies addons/cabinetcraft/lib/bodies3d.js

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• Room coordinates to viewport coordinates

  A point of the room in the viewport's axes and millimeters.

  k = 25.4 (inch job) or 1; (x, y, z) → (x·k, z·k, −y·k)

  Cabinets as 3D viewport bodies addons/cabinetcraft/lib/bodies3d.js

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• Board corners in the blank's own frame

  Turns a board's corners from the cabinet frame into the frame of its blank, and takes the blank's length and width.

  x′ = (p − o)·uₓ; y′ = (p − o)·u_y; L = max x′; W = max y′

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• Arm boards and triangle of a corner cabinet

  The outlines of the bottom and top boards for each corner form, from the cabinet's width, depth and panel thickness.

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• Joint lines two boards share

  Finds where an edge of one board lies along an edge of another, and the length of the overlap.

  offset = (q − p₀) × u; s = (q − p₀)·u; overlap = [max(0, min s), min(L, max s)]

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• System hole grid along a side

  The positions of the system holes along a side panel.

  x = sysStart, sysStart + pitch, … while x ≤ len − sysStart

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• Hinge plate holes

  Places the two plate holes of each hinge on the system grid of the side panel.

  center = reveal ÷ 2 + hinge spot; first hole = grid hole nearest (center − pitch ÷ 2); second = first + pitch

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• Fixing holes along a joint

  Places the dowel or cam holes on the edge two boards share, in each board's own frame.

  P = p + (q − p) ÷ len × u, u = sysStart and len − sysStart, or len ÷ 2

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• Edge holes kept on the blank

  Moves an edge hole back onto the blank when the cut part is a little smaller than the drawn board.

  x = min(max(x, 0), part length); y = min(max(y, 0), part width)

  Corner cabinet drilling positions addons/cabinetcraft/lib/cornerdrill.js

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• Corners of a rectangle, L or U room

  The corner list of a room from its width, depth and notch.

  U notch start a = (W − notch w) ÷ 2

  Room outline, walls and openings addons/cabinetcraft/lib/room.js

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• Right-angled outline made safe

  Checks a typed outline with right angles, drops repeated and collinear corners, makes it counter-clockwise and moves it to (0, 0).

  2A = Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ); reject when |2A| < 1

  Room outline, walls and openings addons/cabinetcraft/lib/room.js

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• Do two edges cross

  Decides whether two outline edges properly cross.

  o(p, q, r) = (q − p) × (r − p); cross when the signs differ on both segments

  Room outline, walls and openings addons/cabinetcraft/lib/room.js

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