Calculations

Calculations

• Traced arc to points

  Turns an arc found on the scan into points for a line layer.

  n = max(2, ⌈|sweep| ÷ 5°⌉); point = center + r·(cos t, sin t)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Traced lines in project coordinates

  The lines and arcs traced on the scan as one line layer in project coordinates.

  each end point through the placement; kept when its length > the minimum

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit

• Point coordinates

  The x, y and z of one point record.

  x = X × scaleₓ + offsetₓ (and the same for y and z)

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Scale, offset and bounds from the header

  Reads the header's scale, offset, minimum and maximum and refuses a scale that cannot be used.

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• 64-bit counts and offsets

  Reads an unsigned 64-bit integer (LAS 1.4 point count, extended record positions and lengths).

  value = hi × 2³² + lo

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  64-bit

• Points the file really holds

  The number of whole point records between the first point and the end of the point data.

  available = ⌊(end − offset to points) ÷ record length⌋, at most the header's count

  LAS and LAZ point coordinates las.js

  • CadCraft
  • BimCraft
  • CivilCraft
  Exact

• Tightest limit of a rule

  The minimum and maximum a rule allows when several ticked packs have it.

  min = max(minᵢ); max = min(maxᵢ)

  Regulation limits in force and how values are written addons/regs/lib/adapter.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Values written in a problem

  How a required or found value is written in a regulation problem, by unit.

  mm: round(v × 10) ÷ 10; m²: round(v × 100) ÷ 100; ratio and U: 2 decimals; R: 1 decimal; count: whole

  Regulation limits in force and how values are written addons/regs/lib/adapter.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Percentages as text

  A percentage written in the panel, in problems and on the code summary sheet.

  round(v × 10) ÷ 10, then the browser's number format with at most one decimal

  Regulation limits in force and how values are written addons/regs/lib/ui.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Values on the code summary sheet

  Required and found values on the printable code summary for a permit set.

  Regulation limits in force and how values are written addons/regs/lib/ui.js

  • CadCraft
  • BimCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Raw double, read

  A 64-bit value read from eight bytes of the bit stream.

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Bit double, read

  A value stored as a two-bit code: a full 64-bit value, exactly 1.0 or exactly 0.0.

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Double with default, read

  A value stored as the bytes in which it differs from a default value.

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• 64-bit whole number, read

  An unsigned 64-bit whole number from two 32-bit halves.

  value = high × 2³² + low

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Bit long long, read

  A whole number of up to seven bytes, the count given by three bits.

  value = Σ byteᵢ × 256ⁱ

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Handle reference, read

  An object handle, absolute or as an offset from another handle.

  value = Σ byte × 256ᵏ; codes 6, 8, A, C: ref + 1, ref − 1, ref + value, ref − value

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Modular char, read

  A signed whole number stored seven bits per byte.

  value = Σ (byte & 0x7F) × 2^(7i); the last byte carries 6 bits and the sign

  Numbers in a DWG file, read and written bit for bit dwg/bits-read.js

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

• Raw double, written

  A 64-bit value written as its eight bytes.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Bit double, written

  A value written as a two-bit code for exactly 0.0 or 1.0, or as a full 64-bit value.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Double with default, written

  A value written as a two-bit code when it equals its default, or in full.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Thickness, written

  A thickness written as one bit when it is zero, or as a bit double.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Bit long, written

  A 32-bit whole number in its short or full form.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Bit short, written

  A 16-bit whole number in its short or full form.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Bit long long, written

  A 64-bit whole number as a three-bit byte count and its bytes.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Point, written

  The three coordinates of a point as bit doubles.

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

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

• Handle bytes, written

  A handle as its bytes, most significant first.

  byte = v mod 256; v = ⌊v ÷ 256⌋

  Numbers in a DWG file, read and written bit for bit dwg/bits-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Lineweight to stored index

  The index written for a lineweight, or the codes for by layer, by block and default.

  index of the list value with the smallest |value − lineweight|

  Lineweights in a DWG file dwg/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  Exact

• Stored index to lineweight

  The lineweight for an index read from a file.

  Lineweights in a DWG file dwg/model.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  Exact

• Rational tag value

  A TIFF RATIONAL (two 32-bit integers) as one number.

  value = numerator ÷ denominator

  TIFF scan resolution raster/tiff.js

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

• Resolution in dots per inch

  The horizontal and vertical resolution of a page, in dots per inch.

  dpi = resolution × 2.54 (centimeter files); dpi = resolution (inch files)

  TIFF scan resolution raster/tiff.js

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

• Triangulate a polygon with holes

  The triangles of a polygon, as indexes into its point list.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Winding of a ring

  Whether a ring runs clockwise or counterclockwise.

  sum = Σ (xⱼ − xᵢ) × (yᵢ + yⱼ)

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Orientation of three points

  On which side of the line through two points a third point lies.

  area = (q.y − p.y) × (r.x − q.x) − (q.x − p.x) × (r.y − q.y)

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Removing duplicate and collinear points

  Drops points that repeat their neighbor or lie on the line between their neighbors.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Ear test

  Whether a corner can be cut off as a triangle: it is convex and no other point of the ring lies inside it.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Point in triangle

  Whether a point lies inside or on a triangle.

  three cross products of (corner − point) pairs, each ≥ 0

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Bridge from a hole to the outer ring

  The point of the outer ring a hole is connected to.

  x = p.x + (h.y − p.y) × (p′.x − p.x) ÷ (p′.y − p.y); tan = |h.y − p.y| ÷ (h.x − p.x)

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Do two segments cross

  Whether two edges intersect, including touching and collinear overlap.

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Is the middle of a diagonal inside the polygon

  Whether a diagonal between two corners runs through the inside of the polygon.

  midpoint = ((a.x + b.x) ÷ 2, (a.y + b.y) ÷ 2); even-odd count of edges crossed by a ray

  Polygon triangulation (ear clipping) usd/earcut.js

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

• Is a ray to the sun blocked

  Whether the line from a point toward the sun meets a triangle of the model.

  det = e₁ · (d × e₂); u = (t · (d × e₂)) ÷ det; v = (d · (t × e₁)) ÷ det; hit if 0 ≤ u, 0 ≤ v, u + v ≤ 1 and distance > tMin

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Sample points on the modules

  The points on each module from which rays are cast.

  p = bilinear blend of the four corners at ((a + ½) ÷ k, (b + ½) ÷ k) + normal × lift

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Shade fraction by month and hour

  The share of the sample points in shadow at each of 12 × 24 sun positions.

  frac = shaded points ÷ points

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Beam light lost to shadows

  The share of the direct sunlight the array loses to shading, over the year or chosen months.

  loss = Σ beam × frac ÷ Σ beam

  Solar array shading pv-shade.js

  • BimCraft
  • CivilCraft
  64-bit

• Module voltage at a temperature

  The open-circuit voltage of a module at a cell temperature.

  V(T) = V × (1 + β × (T − 25))

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• Longest and shortest string

  The most and the fewest modules a string may have.

  nMax = min(⌊V_limit ÷ (Voc,cold × f) + 1e-9⌋, ⌊MPPT max ÷ Vmp,cold + 1e-9⌋); nMin = ⌈MPPT min ÷ Vmp,hot − 1e-9⌉

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• String length and number of strings

  The string length inside the window that leaves the fewest modules over.

  count = ⌊modules ÷ n⌋; left = modules − count × n

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  Exact

• String voltage checks

  The string's cold and hot voltages against the inverter's and the system's limits.

  V_string = round(n × round(V_module, 2 decimals), 2 decimals)

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• Strings per inverter input

  How many strings one input can carry by its current limits, and how many inputs are needed.

  per input = min(⌊I_dc max ÷ Imp + 1e-9⌋, ⌊I_sc max ÷ Isc + 1e-9⌋); inputs needed = ⌈count ÷ per input⌉

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• DC to AC ratio

  The array's peak power against the inverter's AC rating.

  kWp = n × count × Wp ÷ 1000; DC ÷ AC = kWp ÷ (P_ac × inverters)

  Solar string sizing pv-string.js

  • BimCraft
  • CivilCraft
  64-bit

• Cell temperature

  The temperature of the cells from the air temperature and the light on the module.

  T_cell = T_amb + (NOCT − 20) ÷ 800 × G

  Solar yield estimate pv-yield.js

  • BimCraft
  • CivilCraft
  64-bit