Calculations

Calculations

• 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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• Arc walls as chords

  Writes each arc wall out as short chords so the room can be tested as a polygon.

  step = 2 × acos(max(0, 1 − 0.5 ÷ r)); n = ⌈|sweep| ÷ step⌉, between 4 and 400

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

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• Free outline with slanted and arc walls

  Checks an outline of any angle with arc edges and returns its corners, arcs and overall width and depth.

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

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• Wall frames, lengths and corner turns

  For each wall: its length, direction, the frame cabinets are placed in, its angle and the turn at each corner.

  chord = √(Δx² + Δy²); u = Δ ÷ chord; n = (−u_y, uₓ); angle = atan2(u_y, uₓ) × 180 ÷ π

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

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• Point inside the room

  Tests whether a point is inside the outline; the boundary counts as inside.

  on edge when |cross| < 1e-4 × max(1, edge length); else even-odd count of edges crossed by a ray

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

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• Cabinet footprint inside the room

  Decides whether a polygon lies inside the room.

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

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• Distance from a point to a wall segment

  The shortest distance from a point to a segment.

  t = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); d = |p − (a + t (b − a))|

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

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• Clearance from a footprint to the nearest wall

  The smallest distance between a footprint and any wall, 0 when they touch or cross.

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

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• Door and window positions along a wall

  Clamps each opening's width, offset, height and sill to its wall and the room height.

  inch default = mm default × (1 ÷ 25.4); at ≤ chord − w

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

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• Floor strip in front of an opening

  The four corners of the strip of floor in front of a door or window, in room coordinates.

  P(s, o) = origin + u × s + n × o

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

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• Typed corner coordinates

  Reads x,y pairs typed by a person.

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

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• Outline from edge lengths and turns

  Corners of a right-angled outline from the length of each edge and a left or right turn at each corner.

  pᵢ₊₁ = pᵢ + dir × lengthᵢ; dir turns by ±90°

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

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• Outline from typed walls

  Corners and arcs of an outline from typed wall lengths, directions and arc radii.

  next = p + len × (cos θ, sin θ); arc chord = 2 r sin(|sweep| ÷ 2)

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

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• Room outline from a host model, cleaned

  Drops repeated and in-line points from a room outline given by the host app and makes it counter-clockwise.

  drop b when |ab| < 1 or |(b − a) × (c − b)| < 1e-3 × max(1, |ab| × |bc|)

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

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• Host room moved to (0, 0) and rounded

  Shifts the host's outline so its lower-left corner is the origin and converts it to the job unit.

  mm job: round(v × 10) ÷ 10; inch job: round(v ÷ 25.4 × 16) ÷ 16

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

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