Calculations

Calculations

• Sizes saved with a column

  The width, depth, angle and heights kept in the column's property set, which is what is read back.

  Columns: height and quantities model-columns.js

  • BimCraft
  64-bit

• Columns following a level

  Rebuilds columns whose height no longer matches their levels.

  rebuild when |stored − wanted| > 0.5 mm

  Columns: height and quantities model-columns.js

  • BimCraft
  64-bit

• Area of an outline

  The signed area of a polygon.

  A = ½ Σ (xᵢ yᵢ₊₁ − yᵢ xᵢ₊₁)

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Perimeter of an outline

  The total length of the outline's edges.

  P = Σ |pᵢ₊₁ − pᵢ|

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Do two edges cross

  A yes or no on whether two segments properly cross.

  cross when o(a, b, c) × o(a, b, d) < 0 and o(c, d, a) × o(c, d, b) < 0

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Is the outline usable

  Refuses an outline with fewer than 3 corners, one that crosses itself, or one with almost no area.

  refuse when |A| < 10 000 mm²

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Is a point inside the outline

  The even-odd test used to check that an opening lies in its floor.

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Saving and reading the outline

  The outline's points written as text in the file's length unit, and read back.

  text = round(x ÷ unit, 3) , round(y ÷ unit, 3)

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Perimeter, area and volume written on a floor

  The slab quantities, gross and net of the openings.

  net area = A − Σ |hole|; volume = area × thickness

  Drawn floors: outline, openings and quantities model-floors.js

  • BimCraft
  64-bit

• Flights and landings of a ramp

  Where each flight and landing starts and ends along the ramp, and at what height.

  n = max(1, ⌈rise ÷ maxRise − 1e-9⌉); flight run = rise ÷ n × slope; steep when slope < 12 − 1e-9

  Ramps: flights, landings and quantities model-ramps.js

  • BimCraft
  64-bit

• Rise of a ramp

  The height a ramp climbs: to its top level, else the rise typed.

  rise = top elevation − own elevation

  Ramps: flights, landings and quantities model-ramps.js

  • BimCraft
  64-bit

• Flight slope, length and volume

  The slope angle, sloped length and volume written on each flight.

  slope = atan(Δz ÷ len); length = √(len² + Δz²); volume written = length × width × t

  Ramps: flights, landings and quantities model-ramps.js

  • BimCraft
  64-bit

• Values saved with a ramp

  The start point, sizes, slope and the rise and run used, kept in the ramp's property set.

  required slope = atan(1 ÷ slope)

  Ramps: flights, landings and quantities model-ramps.js

  • BimCraft
  64-bit

• Ramps following a level

  Rebuilds ramps whose rise follows a level that moved.

  rebuild when |rise − rise used| > 0.5 mm

  Ramps: flights, landings and quantities model-ramps.js

  • BimCraft
  64-bit

• Grid lines by spacing

  The ends of numbered and lettered grid lines from a count, a spacing or list of spacings, an origin and an angle.

  xᵢ = xᵢ₋₁ + spacing; P = origin + R(angle) × (x, y)

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Where grid lines cross

  The crossing points of every pair of grid lines, for snapping.

  den = r × s; t = (q − p) × s ÷ den; point = p + t r

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Grid lines an elevation shows

  The lines that run within 30° of a view's direction, and where they sit across the view.

  kept when |e · d| ÷ |e| ≥ 0.866; x = a · right

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Is the grid rectangular

  A yes or no that decides the grid's type in the file.

  parallel when |d₁ × d₂| < 1e-6; square when |u · v| < 1e-6

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Grid line ends read from the file

  A grid line's two ends in building millimeters, from its polyline and the grid's placement.

  world = M × (x × unit, y × unit, 0)

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Grid lines in a story's plan

  Grid line ends moved from building coordinates into one story's plan axes.

  plan = (story world)⁻¹ × point

  Grid lines model-grids.js

  • BimCraft
  64-bit

• Link matrix through both files' map positions

  The matrix from the linked file's millimeters to the open model's, through the map grid both are placed on.

  m = S(host unit) × host map⁻¹ × S(1 ÷ host map unit) × S(link map unit) × link map × S(1 ÷ link unit)

  Placing a linked model model-links.js

  • BimCraft
  64-bit

• Link matrix from two pairs of points

  The turn and move that carry two picked points of the linked model onto two picked points of the open one.

  a = atan2(h₁ − h₀) − atan2(l₁ − l₀); t = h₀ − R(a) × l₀

  Placing a linked model model-links.js

  • BimCraft
  64-bit

• The same change in the scene

  Carries a link matrix between the file's millimeters and the viewer's scene.

  A = F × m × F⁻¹; m = F⁻¹ × A × F

  Placing a linked model model-links.js

  • BimCraft
  64-bit

• Saving the link matrix

  The matrix written into the model as text.

  entry = round(v × 10⁹) ÷ 10⁹

  Placing a linked model model-links.js

  • BimCraft
  64-bit

• Boxes of the things that move

  The plan box of each wall, drawn floor, column and placed item.

  wall corners = end ± n × t ÷ 2

  Move, align and distribute model-modify.js

  • BimCraft
  64-bit

• Align

  The move that brings each element's chosen side or middle to a common line.

  move = target − own; middle = (min + max) ÷ 2

  Move, align and distribute model-modify.js

  • BimCraft
  64-bit

• Distribute

  The moves that space elements evenly between the first and the last.

  gap = (span − Σ sizes) ÷ (n − 1)

  Move, align and distribute model-modify.js

  • BimCraft
  64-bit

• Where placed items stand

  The position and rotation of each placed library item in its story's plan.

  rot = atan2(M[1], M[0]) × 180 ÷ π

  Move, align and distribute model-move.js

  • BimCraft
  64-bit

• Moving and turning placed items

  The new position and rotation of an item moved by an amount or turned, on its own or about a shared point.

  p′ = c + R(Δ) × (p − c); rot = ((rot mod 360) + 540) mod 360 − 180

  Move, align and distribute model-move.js

  • BimCraft
  64-bit

• Rejoining wall corners after a type change

  The new corner point of two walls that met end to end, after their center lines moved.

  s = ((B.a − A.a) × v) ÷ (u × v); p = A.a + s u

  Move, align and distribute model-ops.js

  • BimCraft
  64-bit

• Doors and windows when a wall end slides

  How far a wall's start moved along its own line, so that what it hosts keeps its place.

  shift = (B.a − A.a) · u_A; new offset = offset − shift

  Move, align and distribute model-ops.js

  • BimCraft
  64-bit

• Fitting an opening in a wall

  The offset along the wall at which an opening of a given width fits.

  offset = max(gap, min(len − width − gap, offset))

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Sill of a door

  Whether a door stands on its wall's own level or on an upper level the wall passes.

  kept when |level elevation − base elevation − sill| ≤ 1 mm

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Offset, size and sill read back

  Where an existing door or window sits and how big it is, from the file.

  sill = M[14] + base offset; width = stored × unit

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Default offset and height check

  Where a new opening goes when no offset is given, and the check that it is not taller than the wall.

  offset = (len − W) ÷ 2; refused when sill + height > wall height + 1

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• The box that cuts the wall

  The body of the opening that is subtracted from the wall.

  box: x from 0 to width, y from −t ÷ 2 − 10 to t ÷ 2 + 10, z from 0 to height

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Width, height and area written

  The quantities and sizes written on a door or window.

  area = width × height

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Shift of a wall's start along its line

  How far a wall's start moved along the wall, so hosted openings can keep their place in the world.

  shift = (a′ − a) · u

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Door body

  The boxes a starter door is built from: frame, leaves, glass.

  frame = min(1.5 in, W ÷ 6)

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Window body

  The boxes a starter window is built from: frame, rails, stiles, glass and an optional well.

  frame = min(2 in, W ÷ 6, H ÷ 6)

  Doors and windows in walls model-openings.js

  • BimCraft
  64-bit

• Slope and outline kind

  Turns the pitch into a slope and chooses the method for the outline.

  s = tan(pitch)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Faces of a roof over a convex outline

  Each pitched edge's face, the eave, the ridges and the area.

  keep p where (nᵢ − nⱼ) · p ≤ nᵢ · aᵢ − nⱼ · aⱼ; area = plan area × √(1 + s²)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Clipping a polygon by a half-plane

  Keeps the part of a convex polygon on one side of a line.

  t = f_a ÷ (f_a − f_b); point = a + t (b − a)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Where two offset edges meet

  The corner of the eave where two neighboring edges, pushed out by the overhang, cross.

  t = ((p₂ − p₁) × d₂) ÷ (d₁ × d₂)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Roof over an outline with square corners

  A hip roof for every largest rectangle that fits in the outline with its overhang.

  m = min(w, h) ÷ 2; ridge from (x₀ + m, c_y) to (x₁ − m, c_y)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Height of the roof over a point

  The roof's underside height above the top of the walls at a plan point.

  z = z₀ + s × (distance inside the face's eave edge)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Is the outline convex

  Chooses between the two roof methods.

  convex when every corner turns the same way

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Plan area of a polygon

  The shoelace area used for the eave and the faces.

  A = ½ Σ (xᵢ yᵢ₊₁ − yᵢ xᵢ₊₁)

  Roof planes over an outline model-roof.js

  • BimCraft
  64-bit

• Dimension chain of a wall

  The overall length of a wall along one face and the chain of lengths between its ends and its openings.

  overall = e₁ − e₀; piece = sᵢ₊₁ − sᵢ with s rounded to 0.01 mm

  Plan view: picked points, wall outlines and dimensions model-plan.js

  • BimCraft
  64-bit

• Wall outline with openings taken out

  The pieces of a wall's plan outline left between the openings the cut plane passes through.

  Plan view: picked points, wall outlines and dimensions model-plan.js

  • BimCraft
  64-bit