Calculations

Calculations

• Difference between the two methods

  How far the engine's design loads are from the quick loads, per room.

  ratio = (engine − quick) ÷ quick

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Rooms the two methods disagree on

  A note for each room whose design heating differs by more than 15 %.

  note when |ratio| > 0.15

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• A parameter's value as kept

  A typed or imported value made safe for its kind.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• When two sizes are the same

  The key that tells one size of a family from another.

  key = every input value rounded to 0.001

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Parameters driven by formulas

  The value of every parameter that has a formula.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A solid's numbers

  The evaluated box, profile, depth, axis, angle, path and radius of each solid, and the check that it is not flat.

  box = (min, max) of each pair; a negative depth moves the start: at = at + depth, depth = −depth

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Copies in an array

  The solids of an array, each moved by a whole number of steps.

  copy i is moved by (dx × i, dy × i, dz × i), count = round(count expression)

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A family placed inside another

  The position and quarter-turn of a nested family.

  turns = rotation ÷ 90; accepted when round(turns × 10⁶) ÷ 10⁶ is a whole number; k = turns mod 4

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Quarter turn of a solid

  An evaluated solid turned 90° about the vertical axis.

  (x, y) → (−y, x)

  Family geometry from parameters family-model.js

  • BimCraft
  Exact

• Move a solid

  An evaluated solid moved by an offset in the family's axes.

  p → p + (dx, dy, dz), mapped to the profile plane's own axes

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Area of a profile

  The area of a profile with its arcs, used to refuse a flat outline.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ) with arcs flattened to chords

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Is the profile on one side of the axis

  Whether a revolve's profile stays on one side of its axis.

  s = ((axis direction) × (p − axis start)) ÷ |axis|; sides counted beyond ±0.01 mm

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Middle point of a profile arc

  The point halfway along an arc given by its two ends and a bulge.

  sagitta = bulge × chord ÷ 2; middle = chord middle + sagitta × (dy, −dx) ÷ chord

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Chords of a profile arc

  The points inside an arc, for outlines that cannot hold a true arc.

  θ = 4·atan(bulge); n = max(2, ⌈|θ| ÷ 15°⌉); center = circle through start, middle and end

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Profile written to the file

  A closed profile as an IFC curve: lines and true arcs in IFC4, a polyline in IFC2X3.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A solid written to the file

  One box, extrusion, revolve or swept solid as its IFC item.

  revolve axis direction = (u₁ − u₀, v₁ − v₀) ÷ L; angle = degrees × π ÷ 180 (file in radians)

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Plan outline written to the file

  The outline other programs see in plan: the family's symbol, or each solid's outline from above.

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• Plan bounds of a solid

  The smallest plan rectangle round a solid.

  revolve: R = largest distance of a profile point from the axis; bounds = axis start ± R, joined with the profile

  Family geometry from parameters family-model.js

  • BimCraft
  64-bit

• A plan symbol's numbers

  The evaluated lines, rectangles, circles, arcs, outlines and texts of a family's 2D symbol.

  Family geometry from parameters family-symbol.js

  • BimCraft
  64-bit

• Circles and arcs of a symbol

  A symbol's circle or arc as points.

  n = max(2, ⌈sweep ÷ 7.5°⌉); pᵢ = (cx + r·cos aᵢ, cy + r·sin aᵢ)

  Family geometry from parameters family-symbol.js

  • BimCraft
  64-bit

• A symbol placed in the plan

  The symbol turned by the element's rotation and moved to its place.

  (u, v) → (x + u·cos a − v·sin a, y + u·sin a + v·cos a), a = rotation × π ÷ 180

  Family geometry from parameters family-symbol.js

  • BimCraft
  64-bit

• Where a placed family stands

  A placed element's position and rotation in its level's plan.

  x = M₁₂, y = M₁₃, z = M₁₄; rotation = atan2(M₁, M₀) × 180 ÷ π

  Family geometry from parameters family-ops.js

  • BimCraft
  64-bit

• Connector written as a port

  A family's pipe or duct connector written on a placed element: its point, direction and nominal size.

  Family geometry from parameters family-ops.js

  • BimCraft
  64-bit

• Snap to a step

  A sketch coordinate moved to the nearest multiple of the grid step.

  v → round(v ÷ step) × step

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Quarter-arc bulge

  The bulge that makes a segment a quarter circle, and the cycle straight, left arc, right arc.

  bulge = tan(90° ÷ 4) = tan(π ÷ 8) = √2 − 1

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Move a sketch point

  A profile or path point moved to a new place.

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Set a segment's bulge

  Makes a profile segment straight or an arc of a given bulge.

  bulge = tan(angle ÷ 4), rounded to 12 decimals, |bulge| ≤ 10

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Bounds of a family

  The box round a family's visible solids.

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Height range of a solid

  The lowest and highest point of one solid.

  sweep: path z ± radius; revolve on the floor plane: at ± largest |profile point|

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Which parameter moves which face

  Finds, for each input length, the face of the family it pushes out.

  nudge the parameter by 10 mm; the face that moves most, and by more than 0.5 mm, is its handle

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Solve for a parameter

  The parameter value that puts a face or a hotspot at the dragged position.

  secant: c = b − f(b)·(b − a) ÷ (f(b) − f(a)); then bisection on a bracket; stop at |f| < 10⁻⁷

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Drag a hotspot

  The size values after a hotspot is dragged along its axis.

  x = solve(position(x) = dragged position); kept value = round(x × 1000) ÷ 1000

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Drag a size or solid handle

  The recipe or the size values after a handle is dragged to a position.

  literal field: value = round(position × 1000) ÷ 1000; bound field: the input parameter solved, then rounded to 0.001

  Family editor: sketch points, handles and solved sizes family-edit.js

  • BimCraft
  64-bit

• Position of a 3D grip along its axis

  How far along a hotspot's axis the pointer's ray comes closest, when a grip is dragged in the 3D view.

  t = (b·e − c·d) ÷ (c − b²), b = axis · ray, c = ray · ray, d = axis · w, e = ray · w

  Family editor: sketch points, handles and solved sizes family-ui.js

  • BimCraft
  64-bit

• Pointer in the family's own axes

  The plan pointer position turned into the axes of a placed family, for dragging a hotspot in the plan.

  (dx, dy) = p − element position; local = (dx·cos a − dy·sin a, dx·sin a + dy·cos a), a = −rotation × π ÷ 180

  Family editor: sketch points, handles and solved sizes family-ui.js

  • BimCraft
  64-bit

• Rotation shown in Properties

  A placed family's rotation in the Properties panel, and the value taken when it is changed.

  shown = round(rotation × 100) ÷ 100

  Family editor: sketch points, handles and solved sizes family-ui.js

  • BimCraft
  64-bit

• A piece as stored

  One stud, plate, header, joist or rafter with its length and its place in the panel.

  stored value = round(v × 10) ÷ 10

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Stud length of a wall

  The length of a full-height stud: the wall height less the plates.

  stud length = H − (top plates + 1) × plate thickness

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Studs on the spacing grid

  Where the regular studs stand, left out where an opening is.

  center c = spacing, 2 × spacing, …; stud from c − face ÷ 2 to c + face ÷ 2

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Framing round an opening

  The jack studs, header, cripples and sill of one opening.

  jack = sill + opening height − bottom plate; header = opening width + 2 × stud face; cripple above = H − top plates − header top

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Floor panel

  The joists, rim joists and blocking of a floor panel.

  joist length = span − 2 × rim thickness; blocking = clear gap between neighboring joists

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Roof panel

  The rafters and ridge board of a gable roof panel, and its pitch.

  slope = √(run² + rise²); rafter = slope + overhang × slope ÷ run; pitch = atan2(rise, run) × 180 ÷ π

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Piece count and total length

  How many pieces a panel has and their total length in meters.

  meters = Σ piece lengths ÷ 1000, rounded to 0.01

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Cut list

  One row per mark: size, length, count and total length.

  total (m) = round(length × count) ÷ 1000

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Panel placed in the model

  A point of the panel turned by the panel's angle and moved to its place in the model.

  P = O + u·(cos a, sin a) + n·(−sin a, cos a) + (0, 0, z), each coordinate rounded to 0.1 mm

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Timber profile and weight

  The profile a placed timber piece gets: its dressed size and a density for its weight.

  b × t = dressed size, rounded to 0.1 mm; density = 500 kg/m³

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Scale of the shop sheet

  The scale the panel is drawn at on its sheet, and the scale printed in the title block.

  k = min(drawing width ÷ panel width, drawing height ÷ panel height); printed scale = 1 : round(1 ÷ k)

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Scale text in the title block

  The line of the title block that states the scale and the piece count.

  text = "1:" + max(1, round(1 ÷ k))

  Framing panels and cut lists framing.js

  • BimCraft
  • DetailCraft
  64-bit

• Corners of a piece

  The four plan corners of a piece, or of the zone kept clear round it.

  corner = (x + u·cos r − v·sin r, y + u·sin r + v·cos r), u ∈ ±(w ÷ 2 + side), v ∈ [−front, d]

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Do two pieces overlap

  Whether two rectangles overlap by more than a hair.

  separate when, on any edge normal of either, a_max ≤ b_min + 1 mm or b_max ≤ a_min + 1 mm

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit