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

• 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

• Is a point in the room

  Whether a point lies inside the room's outline.

  even-odd count of edges crossed by a ray toward +x

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Does a piece fit in the room

  Whether a rectangle lies inside the room and outside its holes.

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Which way the outline runs

  The signed area of the room's outline, used to turn it counter-clockwise.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Zone kept clear at a door

  The rectangle round a door where nothing is placed.

  width = door width + 300 mm; depth = one door width on each side of the wall

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• A piece against a wall

  The first free place for a piece along a wall, with its back on the wall.

  t = w ÷ 2 + side, then every 100 mm; (x, y) = wall start + direction × t + inward normal × depth; kept: round(x), round(y), rotation to 0.001°

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• A piece in the middle of the room

  The first free place for a free-standing piece, starting at the middle of the room.

  middle of the outline's box, then offsets of k × 150 mm (k = 1…20) along ±x and ±y, at the longest wall's angle and at 90° to it

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Footprint of a placed piece

  The four plan corners of a piece from its stored position.

  Furniture layout of a room furnish.js

  • BimCraft
  • ModelCraft
  64-bit

• Room depth at each time sample

  The water depth in every room at each time step, from the outside level and the openings the water has passed.

  level(t) = linear between hydrograph points; depth = max(0, level − floor) for a room the water reaches

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Maximum depth, first wet time and wet duration

  For each room: the deepest water, the first sample time it was wet and how long it stayed wet.

  maxDepth = round(max × 1000) ÷ 1000; wetFor = (number of wet samples) × dt

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Hydrostatic push on a wall

  The force of standing water on one meter of wall, from the depth.

  F = ½ × ρ × g × d² (ρ = 1000 kg/m³, g = 9.80665 m/s²)

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Wind force, shear and moment by story

  The wind force on each story and the shear and overturning moment summed from the top story down.

  V = V10 × (max(z, 5) ÷ 10)^α; q = ½ ρ V²; force = q × G × (Cp,w + Cp,l) × width × h; shear = Σ force above; moment = Σ force × z

  Flood depth and wind load playback hazard.js

  • BimCraft
  64-bit

• Eigenvalues of a symmetric matrix

  The eigenvalues and eigenvectors behind the building's periods and mode shapes.

  t = sign(θ) ÷ (|θ| + √(θ² + 1)), θ = (a_qq − a_pp) ÷ (2 a_pq); c = 1 ÷ √(t² + 1); s = t × c

  Earthquake time-history of a building hazard.js

  • BimCraft
  64-bit