Calculations

Calculations

• 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

• Polyline vertices read

  Reads the vertices of a lightweight polyline.

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

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

• North direction of older geolocation data

  Turns the north angle of a version 1 geolocation object into a direction vector.

  north = (sin a, cos a)

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

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

• Fit point parameters and knots

  The parameter of each fit point along the spline, and the knot vector built from them.

  u₀ = 0; uᵢ = uᵢ₋₁ + |Qᵢ − Qᵢ₋₁|; knots = [0,0,0,0, u₁ … uₙ₋₂, L,L,L,L]

  Spline through fit points dwg/spline-fit.js

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

• Cubic basis functions at a parameter

  The four B-spline basis values that weigh the control points at one fit point.

  Cox–de Boor recurrence, degree 3

  Spline through fit points dwg/spline-fit.js

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

• Start condition

  The rows that pin the first control point and set the spline's start tangent or a natural start.

  P₀ = Q₀; P₁ − P₀ = T₀ × u₄ ÷ 3 or P₀ ÷ u₄ − P₁ (1 ÷ u₄ + 1 ÷ u₅) + P₂ ÷ u₅ = 0

  Spline through fit points dwg/spline-fit.js

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

• End condition

  The rows that pin the last control point and set the spline's end tangent or a natural end.

  Pₘ₋₁ = Qₙ₋₁; Pₘ₋₁ − Pₘ₋₂ = T₁ × (L − uₘ₋₁) ÷ 3 or the zero second derivative row

  Spline through fit points dwg/spline-fit.js

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

• Solve for the control points

  Solves the banded system for the x, y and z of every control point.

  A · P = B

  Spline through fit points dwg/spline-fit.js

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

• Lineweight to the file's lineweight index

  Picks the stored lineweight that is nearest to the one the layer or object has.

  index = the i with the smallest |table[i] − lineweight|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Ellipse with a ratio above 1

  Rewrites an ellipse whose minor axis is longer than its major axis so the file holds a ratio of 1 or less.

  major′ = (−m_y, m_x) × ratio; ratio′ = 1 ÷ ratio; start and end − π ÷ 2

  Values changed when a DWG is written dwg/write.js

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

• Ray and construction line direction

  Writes the direction of a ray or construction line as a unit vector.

  d′ = d ÷ |d|

  Values changed when a DWG is written dwg/write.js

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

• Drawing extents

  The lower left and upper right corner of model space written to the file header.

  min and max of x, y, z over the defining points

  Values changed when a DWG is written dwg/write.js

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

• Default angles of a light

  The hotspot and falloff angles written for a light that has none of its own.

  hotspot = π ÷ 4; falloff = π ÷ 4 + 0.0872664626

  Values changed when a DWG is written dwg/solid-write.js

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

• Plane of a face

  The plane a face lies in, as a unit normal and a distance from the origin.

  n = Newell normal of the outer loop; d = n · p₀

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Area of a face

  The area of a face, holes taken out.

  area = |Σ (pᵢ × pᵢ₊₁)| ÷ 2 for the outer loop, minus the same for each hole

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Triangles of a face

  The triangles a face is cut into for volume, export and ray tests.

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit