Calculations

Calculations

• Dimension labels on the elevation picture

  The span, overhang, pitch, rise and heel written on the truss elevation.

  Truss geometry, cut list and shop outputs addons/trusscraft/lib/drawing.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Outline area

  The signed area of the roof outline.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Truss layout over a roof addons/trusscraft/lib/layout.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Where a truss line crosses the outline

  The points where a station line enters and leaves the roof outline.

  v = a_v + (u − a_u) ÷ (b_u − a_u) × (b_v − a_v)

  Truss layout over a roof addons/trusscraft/lib/layout.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Trusses along an outline

  The station, end points and span of each truss over a plain outline, and the actual spacing.

  bays = ceil(length ÷ spacing); step = length ÷ bays; span = v₁ − v₀

  Truss layout over a roof addons/trusscraft/lib/layout.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Ridge direction

  The direction the ridge runs, which the trusses span across.

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Valley pairs of a roof plan

  Finds pairs of valley lines that meet at a wing's ridge, with the wing's axis and reach.

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Valley truss set

  The span, rise, base height and position of each valley truss of a wing roof over a main roof.

  ridge height = (W ÷ 2) tan(wing pitch); rise = d × tan(main pitch); span = 2 d tan(main pitch) ÷ tan(wing pitch)

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Stations along the ridge

  The truss stations of a roof and the stretches of each station that lie inside the outline.

  bays = ceil(length ÷ spacing); u = u₀ + inset + i × step

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• A truss from a roof section

  Decides the form of the truss at a station, its design key, and the values stored for it.

  common truss pitch = atan(2 × apex ÷ span)

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Jack trusses in a hip end

  The jack and corner trusses between the end wall and a girder truss, and where each bears on the girder.

  count = ceil((width − 2 × inset) ÷ spacing); v = v₀ + inset + k × step

  Truss layout over a roof addons/trusscraft/lib/roofset.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  64-bit

• Member lines for the picture

  The 3D end points of every member, for drawing.

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• View projection

  Turns 3D points into picture coordinates for a view direction.

  x′ = x cos A − y sin A; y′ = −(z cos E + (x sin A + y cos A) sin E)

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• Picture output

  Scales the projected lines to the picture size and writes them as SVG.

  Truss layout 3D picture addons/trusscraft/lib/view3d.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • PartCraft
  32-bit, display only

• 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