Calculations

Calculations

• Forces used for the deflection

  Chooses the member forces the deflection estimate is based on.

  service force = dead case + snow case

  Truss member forces and timber checks addons/trusscraft/lib/design.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Bearing reactions

  The largest and smallest vertical reaction at each bearing and the largest horizontal reaction, over the combinations.

  Truss member forces and timber checks addons/trusscraft/lib/design.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Ceiling and floor loads of an attic truss

  The load on each bottom-chord member of an attic truss in a combination.

  w = f_D × ceiling dead × spacing + f_S × floor live × spacing (room floor only)

  Truss member forces and timber checks addons/trusscraft/lib/design.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Height of a roof face over a point

  The height of a face's plane above a plan point.

  z = start + (n·p − c) ÷ speed

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Solver tolerance

  Sets the tolerance every merge, split and overlap test in the roof solver uses.

  scale = max(1, width, depth of the outline); eps = 1e-7 × scale

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Edge lines

  The direction, inward normal and line offset of each eave edge.

  u = (b − a) ÷ |b − a|; n = (−u_y, u_x); c = n·a

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Corner velocity

  How a corner of the shrinking polygon moves per unit of height.

  n_a·v = v_a; n_b·v = v_b; determinant = n_a × n_b

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Next event height

  Finds the height at which the polygon next changes: an edge starts to move, an edge shrinks to nothing, or a reflex corner reaches another edge.

  collapse: t = T + length ÷ closing rate; split: t = T + distance ÷ approach rate

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Advance to the event

  Moves every corner to the event height and records its path as a roof line and a face boundary.

  p′ = p + v × (t_next − T)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Clean-up after an event

  Merges corners that met, removes edges folded onto each other as ridges, splits a loop a corner has cut, and closes loops with no area left.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Shared part of two folded edges

  The stretch two opposite edges on one line have in common, which becomes a ridge.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Face boundaries chained into polygons

  Joins the boundary pieces of a face into closed loops.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Collinear points removed from a face

  Drops points of a face polygon that lie on the line between their neighbors.

  removed when |u × v| ÷ max(|u|, |v|) ≤ tolerance

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Roof lines joined end to end

  Joins the pieces of one ridge, hip or valley into a single line.

  joined when ends meet within tolerance and cos θ ≥ 1 − 1e-9

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Faces kept

  Builds each face's plan polygon and drops slivers.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Polygon area

  The signed plan area of a polygon.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-skeleton.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Distance from a point to a segment

  The shortest distance from a plan point to a segment.

  t = clamp((p − a)·d ÷ |d|², 0, 1); distance = |p − a − d t|

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Eave line and edge speeds

  Moves each wall line out to the eave and sets how fast and from what height each roof edge rises.

  out = overhang − fascia thickness; speed = 1 ÷ tan(pitch); start = plate − out × tan(pitch)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Slope and pitch of each face

  The slope and the pitch in degrees stored on each roof face.

  slope = 1 ÷ speed; pitch = atan(1 ÷ speed) in degrees

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Ridge, hip or valley

  Decides what each roof line is and measures its length.

  len = √(Δx² + Δy² + Δz²)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Eave and rake edges

  Finds the face edges that lie on the eave line, tells level eaves from sloped rakes, and measures them.

  top height = face height + thickness ÷ cos(pitch)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Soffit height

  The level of the soffit under each pitched eave.

  z_eave = plate − out × tan(pitch); z = min(z_eave, z_eave + thickness ÷ cos(pitch) − fascia)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Roof area and line totals

  The roof's sloped area, its plan area, and the total length of ridges, hips, valleys, eaves and rakes.

  area = Σ |plan area of face| ÷ cos(pitch)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Outline moved out by the overhangs

  The polygon with each edge moved out by its own distance.

  corner = p₀ + u_prev × ((p₁ − p₀) × u) ÷ (u_prev × u)

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Eave line crosses itself

  Checks that the eave polygon does not cross itself and runs anticlockwise.

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Roof height over a point

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

  Roof faces, ridges and areas from an outline addons/trusscraft/lib/bim/res-roofplan.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Edges split where they cross or overlap

  Finds where two wall edges cross, touch or run along each other.

  t = (c − a) × s ÷ (r × s); u = (c − a) × r ÷ (r × s)

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Points matched on a grid

  Decides when two split points are the same point.

  key = (round(x ÷ 0.001), round(y ÷ 0.001))

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Boundary pieces

  Keeps the pieces that have a wall on one side and open space on the other.

  test points = middle ± n × min(0.5, length ÷ 4)

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Next piece at a joint

  Chooses which boundary piece a loop follows where several meet.

  a = (angle back − angle of piece), brought into (0, 2π]

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Room area and perimeter

  Tells rooms from islands and gives each room its net area and full perimeter.

  area = loop area − Σ hole areas; perimeter = loop + Σ hole perimeters

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Polygon area

  The signed area of a loop.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Polygon perimeter

  The length round a loop.

  P = Σ √(Δx² + Δy²)

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Polygon centroid

  The center of area of a loop.

  C = Σ (a + b)(a × b) ÷ (3 Σ a × b)

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Label point inside a room

  A point well inside a room for its label.

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Point inside a polygon

  Tests whether a plan point lies inside a polygon.

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Repeated and collinear points removed

  Tidies a loop before its area is taken.

  collinear when |ab × bc| ≤ 1e-7 × (|ab| |bc| + 1e-12)

  Rooms and building outline from walls addons/trusscraft/lib/bim/model-rooms.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Guard on every written measure

  Decides what is written when a value is missing or not a number.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arc angles brought into one turn

  Brings an angle into the range from 0 up to 2π before it is written.

  r = a mod 2π; r + 2π when r < 0

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arc

  Writes an arc's center, radius and two angles.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Line

  Writes a line's two end points.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Polyline vertices

  Writes the vertices of a lightweight polyline.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Vertex widths

  Writes the start and end width at a polyline vertex.

  equal widths: one value, −|width|

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Linetype pattern length

  The total length of a linetype's dash pattern.

  length = Σ |element length|

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Text direction

  The x-axis direction written for a block of text.

  x axis = (cos θ, sin θ, 0)

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Block scale

  Writes the three scale factors of a block reference in the format's compact form.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Single-line text

  Writes a text's insertion point, height, rotation, width factor and oblique angle.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Extension record values

  Writes the numbers kept in an extension record.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Block content matrix of a multileader

  The 4 × 4 matrix written for a multileader's block content when the model gives none.

  M = translate(l) · rotate_z(θ) · scale(s)

  DWG object values written and read dwg/mleader-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Line read

  Reads a line's two end points.

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit