Calculations

Calculations

• 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

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• 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

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• 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

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• 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
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• 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

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  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

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• 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
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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• Clipping a polygon at a position along the wall

  Keeps the part of a polygon on one side of x = k.

  t = (k − a_x) ÷ (b_x − a_x); y = a_y + t (b_y − a_y)

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

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• Viewer coordinates to a story's plan

  The matrix from the viewer's Y-up meters to a story's plan millimeters.

  M = (story world)⁻¹ × S × C⁻¹

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

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• Pointer position to plan millimeters

  The plan point under the pointer, which the drawing tools then snap and use.

  x = (px − w ÷ 2) ÷ scale + cx; y = (h ÷ 2 − py) ÷ scale + cy

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

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  64-bit

• Cutting a story's elements

  The cut segments of every element the cut plane passes through, and the edges of what lies below or above.

  Plan view of elements drawn from their mesh model-plan.js

  • BimCraft
  32-bit, display only

• Cutting one triangle

  The segment where a triangle crosses the cut plane.

  t = (h − zᵢ) ÷ (zⱼ − zᵢ); point = pᵢ + t (pⱼ − pᵢ)

  Plan view of elements drawn from their mesh model-plan.js

  • BimCraft
  32-bit, display only

• Joining cut segments into loops

  Closed outlines from the cut segments, for the fill.

  Plan view of elements drawn from their mesh model-plan.js

  • BimCraft
  32-bit, display only

• Sheet and scale

  The paper size, the drawing's extent and the scale it prints at.

  fits when W ÷ r ≤ room width and H ÷ r ≤ room height

  Plan as a vector PDF model-pdf.js

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• Plan millimeters to the sheet

  The scale factor and offsets that place the plan on the page.

  k = 1 ÷ ratio; paper = offset + plan × k; points = paper × 72 ÷ 25.4

  Plan as a vector PDF model-pdf.js

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• Coordinate written to the PDF

  How a path coordinate in points is turned into text.

  text = Number(v.toFixed(6))

  Plan as a vector PDF model-pdf.js

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• Arcs as short lines

  Door swings and other arcs written as polylines.

  steps = max(8, ⌈|a₁ − a₀| ÷ (π ÷ 32)⌉)

  Plan as a vector PDF model-pdf.js

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• Rounding of a stored value

  Rounds a number to a given count of decimals before it is written to the file.

  round(v, d) = Math.round(v × 10ᵈ) ÷ 10ᵈ, d = 6 by default

  Numbers written into the IFC model model-write.js

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• Placement position and turn

  The origin and X direction of an element's placement from a point in millimeters and an angle in degrees.

  location = round(mm ÷ unit, 6); X direction = (round(cos θ, 12), round(sin θ, 12), 0), θ = degrees × π ÷ 180

  Numbers written into the IFC model model-write.js

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• Profile and polyline points

  A 2D point of a profile, axis or outline as it is stored.

  (round(x ÷ unit, 6), round(y ÷ unit, 6))

  Numbers written into the IFC model model-write.js

  • BimCraft
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• Extrusion base and depth

  The start height and depth of a swept solid.

  position z = round(z₀ ÷ unit, 6); depth = round(depth ÷ unit, 6)

  Numbers written into the IFC model model-write.js

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• Sloped placement frame

  A placement with its own Z and X directions, used for sloped parts.

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit

• Quantity values

  Converts a length, area or volume in millimeter units to the value stored in a quantity set.

  length = round(mm ÷ unit, 6); area = round(mm² ÷ 10⁶, 6); volume = round(mm³ ÷ 10⁹, 6)

  Numbers written into the IFC model model-write.js

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• World matrix in millimeters

  Converts a placement matrix from file units to millimeters.

  translation × unit in mm; rotation part unchanged

  Numbers written into the IFC model model-write.js

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  64-bit

• Placement relative to a parent

  Where an element sits in the axes of its level or site.

  M = P⁻¹ × C

  Numbers written into the IFC model model-write.js

  • BimCraft
  64-bit