Calculations

Calculations

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  64-bit

• 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

  • BimCraft
  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

• Where two face lines meet

  The point where two lines, each given by a point and a direction, cross.

  s = ((p₂ − p₁) × d₂) ÷ (d₁ × d₂); point = p₁ + s·d₁

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Nodes and tees

  Groups wall ends that meet and finds ends that land on another wall's side.

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Corner points at a node

  The mitre or corner point between each pair of neighboring walls at a node.

  c = left face of A ∩ right face of B; kept when |c − node| ≤ 4 × max(h_A, h_B) + tol

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Faces of curved walls

  Where a straight face meets a circular face, or two circular faces meet, nearest a given point.

  line and circle: t = −b ± √(b² − c); two circles: x = (d² + r₁² − r₂²) ÷ 2d, y = √(r₁² − x²)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Curved wall outline

  The outline of a curved wall with each arc edge kept as a bulge.

  bulge = tan(sweep ÷ 4)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Removing repeated and collinear points

  Drops outline points that repeat or lie on a straight run.

  collinear when |ab × bc| ≤ 1e-6 × (|ab|·|bc| + 1e-12) and ab·bc ≥ 0

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Signed outline area

  The signed area of an outline, used for the footprint and to check its direction.

  A = ½ Σ (xᵢ·yᵢ₊₁ − yᵢ·xᵢ₊₁)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Outline validity test

  Decides whether an outline is anticlockwise and does not cross itself.

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Location line offset

  How far a wall's location line is from its center line for each justification.

  face: ± t ÷ 2; core: ± (t ÷ 2 − layer thickness up to the core face or core middle)

  Wall joins and plan outlines model-walls.js

  • BimCraft
  64-bit

• Layers of a wall type at another thickness

  The layer thicknesses of a starter wall type made thicker or thinner.

  thickest layer = wanted thickness − Σ other layers

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Type key for a thickness

  Names the wall type that has a given total thickness.

  key = base@(Math.round(mm × 10) ÷ 10)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Total thickness of a type

  The sum of a wall type's layer thicknesses.

  t = Σ layer thickness

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Wall ends from the stored placement

  The start point, end point, length and thickness of a wall as read back from the file.

  a = (M₁₂, M₁₃); b = a + (M₀, M₁) ÷ |(M₀, M₁)| × chord; chord = chordFor(Length, Bulge)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Wall height

  A wall's height from the level its top follows, or its own fixed height.

  h = (top elevation + top offset) − (base elevation + base offset)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Walls cut by another level's plan

  Finds walls of other levels that pass through a level's plan cut height.

  base + 1 < level elevation + cut < top − 1 (mm)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• New wall: angle and stored sizes

  The placement angle and the Length, Thickness, Height and offsets stored for a new wall.

  angle = atan2(b_y − a_y, b_x − a_x) × 180 ÷ π; Length = arc length (chord when straight)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Moved wall: placement and length

  Rewrites a wall's start point, angle and Length after its ends move.

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Whether a wall's shape is out of date

  Compares the stored outline, depth and axis length with the ones just computed.

  |stored − computed| < 0.001 mm for depth, length and every outline point

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Outline in the wall's own axes

  Turns the plan outline into coordinates along and across the wall.

  x′ = (x − a_x)·cos θ + (y − a_y)·sin θ; y′ = −(x − a_x)·sin θ + (y − a_y)·cos θ

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Stored shape read back

  The outline, extrusion depth and axis length a wall's shape holds now.

  arc axis length = R × |Δangle|

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Wall quantities

  Footprint area, side areas and volumes of a wall, with its openings taken off the net values.

  footprint = |shoelace(outline)|; gross side = length × height; net side = max(0, gross side − Σ w·h); gross volume = footprint × height; net volume = max(0, gross volume − Σ w·h·t)

  Wall dimensions, heights and quantities model-walls.js

  • BimCraft
  64-bit

• Outline area

  The signed area of the site outline.

  A = ½ Σ (xᵢ·yᵢ₊₁ − yᵢ·xᵢ₊₁)

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Site area and perimeter

  The GrossArea and GrossPerimeter stored for the site.

  A = |shoelace|; P = Σ √(Δx² + Δy²)

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Outline saved as text

  The site outline written to the CadCraft_Site Points property.

  x,y;x,y;… each rounded to 3 decimals of the file unit

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Building position and angle on the site

  Where the building sits on the site and how far it is turned.

  M = site⁻¹ × building; at = (M₁₂, M₁₃); angle = atan2(M₁, M₀) × 180 ÷ π

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Plan points to site axes

  Moves points drawn on a level's plan into the site's own axes.

  p′ = site⁻¹ × level × p

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Building placed on the site

  Writes the building's new position and turn relative to the site.

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Levels at given elevations

  Adds levels at heights above the building's base.

  z = base + e; height = next e − e, at least 1000 mm

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Height split into equal levels

  Divides a building height into a number of equal levels.

  h = T ÷ n; zᵢ = base + i × h

  Site outline, building placement and levels model-site.js

  • BimCraft
  64-bit

• Footprint of a site-study mass

  The outline of a mass in world millimeters, read from its extruded profile.

  p = world matrix × (profile point × unit)

  Site outline, building placement and levels model-site-mass.js

  • BimCraft
  64-bit

• A point inside the footprint

  Finds a point inside a possibly concave outline, used as the seed for the floor.

  x = aₓ + (y − a_y) ÷ (b_y − a_y) × (bₓ − aₓ); seed = middle of the widest span

  Site outline, building placement and levels model-site-mass.js

  • BimCraft
  64-bit

• Walls round the footprint

  Makes a wall along every edge of the mass footprint on each of its levels.

  Site outline, building placement and levels model-site-mass.js

  • BimCraft
  64-bit