Calculations

Calculations

• A viewport's window on the model

  The box in model space that a viewport shows, used to say when it looks at nothing.

  half width = w ÷ 2 × viewHeight ÷ h; half height = viewHeight ÷ 2; corners turned by the twist

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Picture placement

  The transform from a picture's pixels to drawing coordinates.

  world = P + u·px − v·py + v·h (pixel y runs down; P is the lower left corner)

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Lines of a paragraph of text

  Where each line of a multi-line text starts.

  pitch = h × 1.667 × line spacing; line i at insert + (top − pitch × i) along the up direction

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Text position, height and angle

  One line of text carried through the entity's transform.

  H = h × |second column of M|; angle = atan2(m₁, m₀) ± rotation (− when M mirrors)

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Paper unit of a sheet

  Whether a sheet is in inches or millimeters.

  unit = mm when the sheet is wider than 100 units, else inches

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Line weight in millimeters

  A stored line weight, in hundredths of a millimeter, as millimeters.

  mm = v ÷ 100 for 0 ≤ v ≤ 211, else 0.25

  DWG and DXF drawings compiled for the plan view dwg-compile.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Pointer position in drawing coordinates

  The drawing coordinates under the pointer, for the coordinate readout.

  x = cx + (px − W ÷ 2) ÷ zoom; y = cy − (py − H ÷ 2) ÷ zoom

  DWG and DXF drawings compiled for the plan view dwg-view.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Model to sheet through a viewport

  The transform that carries a model point onto the sheet through one viewport.

  k = h ÷ viewHeight; paper = center + k · R(twist) · (model − view point)

  DWG and DXF drawings compiled for the plan view dwg-view.js

  • BimCraft
  • TakeoffCraft
  64-bit

• Millimeters per paper unit

  The size of one paper unit of a sheet in millimeters, for line weights.

  1 for millimeters, 25.4 for inches

  DWG and DXF drawings compiled for the plan view dwg-view.js

  • BimCraft
  • TakeoffCraft
  Exact

• Combine two 3D transforms

  The product of two 3 × 4 transforms.

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Transform a point

  A point carried through a 3 × 4 transform.

  x′ = m₀·x + m₁·y + m₂·z + m₃ (and the same for y′, z′)

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Extrusion direction

  The unit extrusion direction of an entity, or straight up when it has none.

  N = (x, y, z) ÷ √(x² + y² + z²)

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Object coordinate system

  The transform from an entity's own plane to world coordinates.

  Ax = unit(Wz × N) (or Wy × N when |Nx| and |Ny| < 1/64); Ay = unit(N × Ax); columns Ax, Ay, N

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Thickness vector

  The offset between the bottom and top of an entity that has thickness.

  up = M · (N × thickness), without the translation

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Block insert transform in 3D

  Where the content of a block lands in 3D, with rows and columns.

  M = OCS · T(insert) · Rz(rotation) · T(col × colSpacing, row × rowSpacing, 0) · S(sx, sy, sz) · T(−base)

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Ellipse in 3D

  An ellipse or elliptical arc as 3D points.

  minor = (N × major) × ratio; p(t) = c + cos t · major + sin t · minor

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Half width of a wide polyline

  The offset to each side of a polyline that has a start and end width.

  w(k) = (sw + (ew − sw) × length so far ÷ segment length) ÷ 2, along the normal of the path at k

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Spline in 3D

  A spline as 3D points: its fit points, or samples of the B-spline from its control points.

  de Boor on (w·x, w·y, w·z, w); point = (Σ w·P) ÷ Σ w

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Extents of the drawing

  The smallest box round everything drawn, in drawing units.

  DWG and DXF drawings in 3D dwg-compile3d.js

  • BimCraft
  64-bit

• Section plane offset

  Where a section plane cuts the drawing, from a typed offset in drawing units.

  at = lo + clamp(offset × s, 0, hi − lo); offset shown = (at − lo) ÷ s, s = 100 ÷ largest extent

  DWG and DXF drawings in 3D dwg-view3d.js

  • BimCraft
  64-bit

• Section range

  The largest offset a section plane can take along an axis, in drawing units.

  size = (max − min) ÷ s

  DWG and DXF drawings in 3D dwg-view3d.js

  • BimCraft
  64-bit

• Drawing coordinates to scene coordinates

  The positions sent to the GPU: centered on the drawing and scaled to about 100 units across.

  scene = (p − center) × 100 ÷ largest extent

  DWG and DXF views on screen dwg-view3d.js

  • BimCraft
  32-bit, display only

• Nearest line to the pointer

  The distance in pixels from the pointer to a line, for picking.

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

  DWG and DXF views on screen dwg-view3d.js

  • BimCraft
  32-bit, display only

• Zoom to the drawing

  The zoom and center that show the whole drawing or sheet.

  zoom = min(W ÷ w, H ÷ h) × 0.92; center = middle of the bounds

  DWG and DXF views on screen dwg-view.js

  • BimCraft
  32-bit, display only

• Viewport windows on the model

  For each sheet viewport, the half width and half height of the model area it shows.

  k = h ÷ viewHeight; half width = w ÷ 2 ÷ k; half height = h ÷ 2 ÷ k

  Equipment list from drawing tags dwg-equipment.js

  • BimCraft
  64-bit

• Sheets that show a point

  Which sheets show a given model point.

  u = dx·cos − dy·sin, v = dx·sin + dy·cos; inside when |u| ≤ half width and |v| ≤ half height

  Equipment list from drawing tags dwg-equipment.js

  • BimCraft
  64-bit

• Quantity of a row

  The scheduled quantity of an item tagged in several places.

  qty = Σ tag quantities

  Equipment list from drawing tags dwg-equipment.js

  • BimCraft
  64-bit

• Heat capacity of air per volume

  The energy to warm one cubic meter of air by one kelvin, in watt-hours.

  ρ·c = 1.2 kg/m³ × 1005 J/kgK ÷ 3600 = 0.335 Wh/m³K

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Does a ray reach a box

  Whether a ray passes through an element's bounding box within its reach.

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Where a ray crosses triangles

  Every distance along a ray at which it crosses a triangle of an element.

  det = e₁ · (d × e₂); u = (t · (d × e₂)) ÷ det; v = (d · (t × e₁)) ÷ det; distance = (e₂ · (t × e₁)) ÷ det

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Is a point inside a room

  Whether a point lies inside the closed shell of a space.

  inside when a slanted ray crosses the shell an odd number of times

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Room volume

  The volume enclosed by a room's triangles.

  V = |Σ a · (b × c)| ÷ 6 over the triangles

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Sample pieces of a room's surface

  Cuts each triangle of the room's shell into small pieces and starts one ray from each.

  k = ⌈longest edge ÷ 0.25 m⌉; k² pieces of area (triangle area ÷ k²); start = piece center + 1e-4 m × normal

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• What lies beyond a bounding element

  Whether a piece of the room's surface faces another room, the ground or the outside.

  probe = start + normal × (farthest crossing + 0.25 m)

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Window and door areas

  Sets each window's and door's area to its own width times height and takes the difference from its wall.

  A = OverallWidth × OverallHeight (in m); wall area = wall area − (A − sampled area)

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• U-value from material layers

  The U-value of an element from the thickness and conductivity of its layers.

  U = 1 ÷ (Rsi + Σ dᵢ ÷ λᵢ + Rse); Rsi, Rse = 0.13, 0.04 sideways; 0.10, 0.04 upward; 0.17, 0.04 downward

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Heating load, annual energy and cooling peak

  Each room's design heat loss, its degree-day year and its cooling peak.

  H_vent = 0.335 × n × V; heat = H_out·ΔT + H_ground·ΔT_g + H_vent·ΔT; annual kWh = (H_out + H_vent + H_ground × ΔT_g ÷ ΔT) × DD × 24 ÷ 1000

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• Degree-days from a CSV file

  The sum of the degree-day column of a CSV file, for a year.

  total = Σ of the last numeric cell of each row

  Heating and cooling loads per room energy-bim.js

  • BimCraft
  64-bit

• A number in the file

  A value written into the input file as text.

  text = round(x × 10ᵈ) ÷ 10ᵈ, d = 4 unless stated

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Triangles grouped into planes

  The triangles of a room's shell sorted into the flat faces they belong to.

  key = (round(1000·n), round(1000·d)), n = unit normal, d = n · A

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Outline of a face

  One polygon from the triangles of a flat face.

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Which way a polygon faces

  The normal of a polygon, used to order its corners counter-clockwise seen from outside.

  n = Σ ((yᵢ − yⱼ)(zᵢ + zⱼ), (zᵢ − zⱼ)(xᵢ + xⱼ), (xᵢ − xⱼ)(yᵢ + yⱼ))

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Construction by U-value

  The thermal resistance written for a wall, roof or floor that has no layer build-up.

  R = max(0.001, 1 ÷ U − Rs), Rs = 0.17 wall, 0.14 roof, 0.21 floor

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Mean U-value of a room's walls, roof and floor

  The area-weighted U-value of each kind of surface in a room.

  U = Σ (Aᵢ × Uᵢ) ÷ Σ Aᵢ

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Boundary of a surface

  Whether a surface of a room faces another room, the ground or the outside, and its corners as written.

  probe = mean of the corners + 0.6 m × outward normal

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Window rectangle on its wall

  The four corners of a window as written on the wall it faces.

  k = √(area ÷ (span × height)); half width = span × k ÷ 2; half height = height × k ÷ 2; corners projected onto the wall plane

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Glazing written for every window

  The one window construction every window in the file uses.

  U = 1.4 W/m²K, solar heat gain 0.6, visible transmittance 0.7

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Site and time zone

  The latitude, longitude and time zone written to the file.

  time zone = round(longitude ÷ 15)

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Design loads read back

  Each zone's design heating and cooling load in watts, from the engine's sizing report.

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit

• Yearly energy per zone

  Each zone's yearly heating and cooling energy in kilowatt-hours.

  kWh = J ÷ 3.6 × 10⁶

  Energy model input file (IDF) and its results energy-ep.js

  • BimCraft
  64-bit