Calculations

Calculations

• Sheet points on the 2.5 mm grid

  Moves a picked point on a sheet to the nearest point of the 2.5 mm grid.

  x = round(x ÷ 2.5) × 2.5

  Schematic wires, pins and connections addons/electrical/main.js

  • CadCraft
  Exact

• A wire point landing on a pin or wire

  Moves a picked wire point onto a pin, a wire end or a wire when it is within 2 units of one.

  candidate when d² ≤ 2²; a wire's middle is ranked with d² + 0.25

  Schematic wires, pins and connections addons/electrical/main.js

  • CadCraft
  64-bit

• A wire cut under a new symbol

  Cuts a wire between two pins of a symbol placed on it.

  pin on the wire when d² < 1e-4 and 1e-6 < u < 1 − 1e-6

  Schematic wires, pins and connections addons/electrical/main.js

  • CadCraft
  64-bit

• PV one-line layout

  Positions the symbols and wires of a solar one-line diagram from the column and row of each node.

  x = x₀ + col × pitch x; y = y₀ − row × pitch y; wire bend at (sx + ex) ÷ 2

  Schematic wires, pins and connections addons/electrical/lib/pvoneline.js

  • CadCraft
  64-bit

• Transform of a schematic symbol

  The matrix that takes a symbol's pin offsets to the drawing.

  a = cos r × sx; b = sin r × sx; c = −sin r × sy; d = cos r × sy; e = x − (a bₓ + c b_y); f = y − (b bₓ + d b_y)

  Wire harness and control cabinet layout addons/harness/lib/schem.js

  • CadCraft
  64-bit

• Squared distance from a point to a wire segment

  How far a wire end or pin is from a wire segment.

  u = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); d² = |p − (a + u (b − a))|²

  Wire harness and control cabinet layout addons/harness/lib/schem.js

  • CadCraft
  64-bit

• Which wires and pins are connected

  Joins wire ends to other ends, to pins and to wires they touch, to find the nets.

  connected when distance² ≤ tol², tol = 0.05

  Wire harness and control cabinet layout addons/harness/lib/schem.js

  • CadCraft
  64-bit

• A point in a rail's frame

  The distance along a rail and off its axis of a drawing point, in millimeters.

  s = (Δx cos r + Δy sin r) ÷ k; off = (−Δx sin r + Δy cos r) ÷ k

  Wire harness and control cabinet layout addons/harness/lib/cabinet.js

  • CadCraft
  64-bit

• A rail position back in the drawing

  The drawing point at a distance along a rail.

  x = x₀ + (s cos r − off sin r) × k; y = y₀ + (s sin r + off cos r) × k

  Wire harness and control cabinet layout addons/harness/lib/cabinet.js

  • CadCraft
  64-bit

• Modules on a rail

  Which modules sit on a rail, and the stretch of rail each covers.

  s₀ = s − w ÷ 2; s₁ = s + w ÷ 2

  Wire harness and control cabinet layout addons/harness/lib/cabinet.js

  • CadCraft
  64-bit

• Modules past the end or overlapping

  Flags a module that hangs past the rail or overlaps the next one.

  past when s₀ < −0.01 or s₁ > len + 0.01; overlap when next s₀ < s₁ − 0.01

  Wire harness and control cabinet layout addons/harness/lib/cabinet.js

  • CadCraft
  64-bit

• Free length on a rail

  The rail length not taken by modules.

  free = max(0, len − Σ module widths)

  Wire harness and control cabinet layout addons/harness/lib/cabinet.js

  • CadCraft
  64-bit

• Where a new module sits

  The center of a new module on a rail: inside the rail, and flush to a neighbor when close.

  c = clamp(s, w ÷ 2, len − w ÷ 2); c = neighbor edge ± w ÷ 2 when within 3 mm

  Wire harness and control cabinet layout addons/harness/lib/cabinet.js

  • CadCraft
  64-bit

• Drawing units per millimeter

  The factor between the drawing and millimeters.

  k = (1 ÷ per) × (1 ÷ 25.4 for inch rules)

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• A harness moved, turned or scaled

  Applies a move, rotation or scale to a harness: its nodes and its scale.

  k′ = k × √(m₀² + m₁²); node′ = M · node

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• Module positions in millimeters

  Each placed module's position for routing wires to it.

  x mm = x ÷ k; y mm = y ÷ k

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• Total length of a harness

  The summed length of a harness's segments for the bill of materials.

  mm = Σ segment length

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• Wire count and bundle diameter per segment

  The number of wires in each harness segment and the diameter of their bundle, kept on the harness.

  od = round(bundleDiameter × 10) ÷ 10

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• Rail length and angle from two points

  The length in millimeters and the angle of a rail drawn between two points.

  len = √(Δx² + Δy²) ÷ k; rot = atan2(Δy, Δx)

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• Modules placed in a row

  Places every remaining module along a rail, one after the other.

  center = s + w ÷ 2; s ← s + w; stop when s + w > len + 1e-9

  Wire harness and control cabinet layout addons/harness/main.js

  • CadCraft
  64-bit

• Segment length and bundle labels

  The length written beside each harness segment, and its wire count and diameter.

  mm = typed length, or √(Δx² + Δy²) ÷ k; label = round(mm)

  Wire harness and control cabinet layout addons/harness/lib/draw.js

  • CadCraft
  64-bit

• Length of a position

  The length of a pipe, truss or floor line along its points.

  L = Σ √(Δx² + Δy²)

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

  • CadCraft
  64-bit

• Where a point is on a position

  The distance along a position to the point nearest a fixture, and the fixture's distance from the line.

  u = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); s = length before + u × |b − a|; off = |p − q|

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

  • CadCraft
  64-bit

• Position a fixture belongs to

  The nearest named position within reach of a point.

  nearest with off ≤ tol

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

  • CadCraft
  64-bit

• Fixture data checked

  Checks a fixture's stored data: scale, wattage, DMX footprint and aim angle.

  aim = ((aim mod 360) + 360) mod 360

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

  • CadCraft
  64-bit

• Wattage of a fixture

  The watts of a fixture: its own value, or its type's typical value.

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

  • CadCraft
  64-bit

• Point at a distance along a position

  The drawing point a given distance along a position's line.

  u = clamp((s − run) ÷ l, 0, 1); p = a + (b − a) × u

  Stage lighting plot: positions, fixtures and loads addons/lighting/main.js

  • CadCraft
  64-bit

• Fixtures spread along a position

  Places n fixtures evenly along a position.

  sᵢ = L × (i + 0.5) ÷ n

  Stage lighting plot: positions, fixtures and loads addons/lighting/main.js

  • CadCraft
  64-bit

• A position moved, turned or scaled

  Applies a move, rotation or scale to a position's points and its scale.

  k′ = k × √(m₀² + m₁²); p′ = M · p

  Stage lighting plot: positions, fixtures and loads addons/lighting/main.js

  • CadCraft
  64-bit

• Fixture symbol turned to its aim

  Rotates a fixture's symbol by its aim angle.

  x′ = x cos a − y sin a; y′ = x sin a + y cos a

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/draw.js

  • CadCraft
  64-bit

• Position length in millimeters

  The length of a position for the schedule and the capacity warning.

  mm = length in drawing units ÷ k

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/draw.js

  • CadCraft
  64-bit

• Legend totals

  The total number of fixtures and total watts at the foot of the legend.

  total = Σ count; total watts = Σ watts

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/draw.js

  • CadCraft
  64-bit

• A drawing object as a nest loop

  Turns a circle or closed polyline into a loop of points with bulges.

  circle = (cx + r, cy) and (cx − r, cy), each with bulge 1

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

  • CadCraft
  64-bit

• Outline as chords for containment

  Points along an outline, with each arc as 8 chords, used to test which outline contains which.

  θ = 4 atan(b); r = c ÷ (2 sin(θ ÷ 2)); center = chord middle + normal × r cos(θ ÷ 2)

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

  • CadCraft
  64-bit

• Parts and their holes

  Groups outlines into parts with holes and moves each part to its own corner.

  parent = smallest larger outline containing the first point; shifted point = p − (x₀, y₀)

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

  • CadCraft
  64-bit

• A part's object placed on the sheet

  Moves and turns one object of a part to where the engine placed it.

  q = at + (x, y) + R(rot) · (p − origin)

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

  • CadCraft
  64-bit

• Sheet rectangles and labels

  A rectangle for each sheet, side by side, and the part names over the copies.

  xₖ₊₁ = xₖ + w + gap, gap = max(20, 0.1 × h) by default; label at the mean of the outline's points

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

  • CadCraft
  64-bit

• Size units per drawing unit

  How many inches or millimeters one drawing unit is, from the drawing's unit setting.

  factor = (meters per drawing unit) ÷ 0.0254 or ÷ 0.001

  P&ID line geometry and connections addons/pid/lib/core.js

  • CadCraft
  64-bit

• Length of a line

  The length of a P&ID line along its corner points.

  length = Σ √(Δxᵢ² + Δyᵢ²)

  P&ID line geometry and connections addons/pid/lib/core.js

  • CadCraft
  64-bit

• Nearest point on a line

  The point of a line closest to a given point, its distance, and how far along the line it lies.

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

  P&ID line geometry and connections addons/pid/lib/core.js

  • CadCraft
  64-bit

• Label position on the longest segment

  The middle and direction of a line's longest segment, where its line number is written.

  mid = (a + b) ÷ 2; angle = atan2(Δy, Δx)

  P&ID line geometry and connections addons/pid/lib/core.js

  • CadCraft
  64-bit

• Numbers in CSV exports

  How a number cell is written when a P&ID list is exported as CSV.

  P&ID line geometry and connections addons/pid/lib/core.js

  • CadCraft
  64-bit

• Cleaning a line's points

  Checks a line's data and removes repeated corner points before it is stored.

  P&ID line geometry and connections addons/pid/lib/lines.js

  • CadCraft
  64-bit

• Line ends and their directions

  The two end points of a line and the direction in which the line leaves each.

  a = atan2(end − neighbor)

  P&ID line geometry and connections addons/pid/lib/lines.js

  • CadCraft
  64-bit

• Move, rotate, scale or mirror a line

  The line's points, symbol size and text height after a transform.

  x′ = m₀x + m₂y + m₄; y′ = m₁x + m₃y + m₅; s = √|m₀m₃ − m₁m₂|

  P&ID line geometry and connections addons/pid/lib/lines.js

  • CadCraft
  64-bit

• Symbol connection points in the drawing

  Turns a point of a symbol's own frame into drawing coordinates using the symbol's position, rotation and scale.

  x′ = x₀ + (x·sx)·cos θ − (y·sy)·sin θ; y′ = y₀ + (x·sx)·sin θ + (y·sy)·cos θ

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Connection tolerance

  How close a line end must be to a connection point, a line end or a line for the two to count as joined.

  tol = 0.04 × max(size a, size b, 1e-6); joined when √(Δx² + Δy²) ≤ tol

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Candidate search grid

  Limits which symbol connections and lines are tested against each line end.

  cell = max(tol of the largest size, 1e-9); index = floor(v ÷ cell)

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Line end on the body of another line

  Decides whether a line end lands on another line between its ends, which makes it a branch.

  u = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); hit when |p − (a + u (b − a))| ≤ tol

  P&ID line geometry and connections addons/pid/lib/model.js

  • CadCraft
  64-bit

• Connection points of a symbol

  Where lines attach to a placed symbol, in the symbol's own frame.

  x = x_unit × l; y = y_unit × l

  P&ID line geometry and connections addons/pid/lib/symbols.js

  • CadCraft
  64-bit