Calculations

Calculations

• Length of a center line

  The length along a bar's center line.

  Σ straight lengths + Σ r·π ÷ 2

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Bottom mat bars

  The size, shape, count and position of the bottom bars each way.

  A = run − 2·cover; hook B = min(hook leg, room); offset_i = −width ÷ 2 + cover + d_b ÷ 2 + i·spacing

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Starter bars

  The length and position of each starter bar.

  z0 = bottom + cover + d_bX + d_bY; A = top + projection − z0; position = ((i − (n − 1) ÷ 2)·s_x, (j − (n − 1) ÷ 2)·s_y)

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Clear spacing check

  Warns when bars are closer than the minimum clear spacing.

  clear = spacing − d_b ≥ max(25.4, d_b) for ASTM bars, max(20, d_b) for BS bars

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Concrete volume

  The volume of a footing in cubic meters.

  V = L × B × H × 10⁻⁹

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• Bar marks and schedule weights

  Groups identical bars under one mark and totals their length and weight.

  total length = length × count; weight each = mass × length ÷ 1000; total weight = weight each × count

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• The schedule as a table

  The figures printed in the bending schedule and its export.

  sizes and cut length: whole mm; total length: m, 2 decimals; kg/m: 3 decimals; weights: 2 and 1 decimals

  Reinforcing bars and the bending schedule rebar.js

  • DetailCraft
  64-bit

• A dimension figure

  The number printed on a dimension line of the shop drawing.

  figure = round(value)

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Hole stations along the part

  The chain of dimensions from the start of the part through each hole to its end.

  step_i = x_i − x_{i−1}; overall = L

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Scales of the view

  The scale along the part and the scale across it.

  first n in the list with size ÷ n ≤ room; paper = X0 + x ÷ n

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Mitre cut angles

  The angle from square of each cut end, in the web's plane and across the flanges.

  angle = atan(|k|) × 180 ÷ π, 1 decimal

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Weight in the title block

  The weight of one part and of the whole quantity.

  total = weight × count

  Single-part shop drawing shop.js

  • DetailCraft
  64-bit

• Risers, run and pitch

  The number of risers, the riser height, the run and the pitch.

  n = max(2, ⌈rise ÷ max riser − 1e-9⌉); r = rise ÷ n; run = (n − 1)·going; pitch = atan2(r, going)

  Straight stair geometry stair.js

  • DetailCraft
  64-bit

• Stringer axis

  The line the stringers run on, and where it meets the lower and upper floor.

  k = r ÷ g; drop = (depth ÷ 2 − 50) ÷ cos(atan k); z(a) = k·(a + g) − drop; a0 = drop ÷ k − g, a1 = (rise + drop) ÷ k − g

  Straight stair geometry stair.js

  • DetailCraft
  64-bit

• Tread plates

  The size and position of each tread.

  depth = going + nosing; middle = (i − 1)·going − nosing + depth ÷ 2; top = i·r

  Straight stair geometry stair.js

  • DetailCraft
  64-bit

• Riser, going and comfort checks

  Warnings when the riser, the going or twice the riser plus the going is outside its range.

  102 ≤ r ≤ 178; going ≥ 279; 600 ≤ 2r + going ≤ 650

  Straight stair geometry stair.js

  • DetailCraft
  64-bit

• Rotation about a vertical line

  The matrix and offset that turn points about a point in plan.

  A = [[c, −s], [s, c]]; t = center − A·center; c = cos(deg·π ÷ 180), s = sin(deg·π ÷ 180)

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Mirror in a vertical plane

  The matrix and offset that reflect points across a line in plan.

  A = 2·d·dᵀ − I; t = p₁ − A·p₁; d = (p₂ − p₁) ÷ |p₂ − p₁|

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A point through the transform

  The new position of a point.

  p′ = A·p + t

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Cleaning a stored coordinate

  The rounding applied to every coordinate and angle a transform stores.

  |n − round(n)| < 10⁻⁶ → round(n); else round(n × 10⁶) ÷ 10⁶

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A member's new rotation

  The rotation that puts a member's section axis where the transform sent it.

  rotation = atan2(−want·u₀, want·v₀) × 180 ÷ π, brought into 0 to 360

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A member through the transform

  The new end points, rotation, position, holes and copes of a member.

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Mirrored angle with a top or bottom position

  Shifts a mirrored angle's line so the steel lands where the mirror image is.

  d = A·v̂·voff − v̂′·voff; start, end += d

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A footing through the transform

  The new position and rotation of a footing.

  rotate: rot + deg; mirror: 2·φ − rot; both brought into 0 to 360

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Center of a selection

  The plan middle of the selection, used as the point to rotate about.

  ((x_min + x_max) ÷ 2, (y_min + y_max) ÷ 2, z_min)

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• Offset of a drag

  The offset a dragged part is moved by: onto a grid node, or in steps.

  node − held point, or round(raw ÷ step) × step

  Move, rotate and mirror transform.js

  • DetailCraft
  64-bit

• A part's solid for drawing

  The mesh of a part: its profile extruded, with copes cut.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• Mitre ends on the mesh

  Moves the end vertices of a mesh onto the mitre's cut plane.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• The part under the pointer

  Which part a click hits and where the ray meets it.

  3D view view3d.js

  • DetailCraft
  32-bit, display only

• Viewport scale from 1:n

  Paper units per model unit for a drawing scale 1:n.

  s = mm per model unit ÷ mm per paper unit ÷ n

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Scale 1:n from a viewport scale

  The n of 1:n that a viewport's stored scale stands for.

  n = mm per model unit ÷ mm per paper unit ÷ s

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• List of standard and custom scales

  The scales offered for a drawing: the standard ones and the drawing's own that the standard list lacks.

  custom n = drawing ÷ paper; kept when |n − listed n| ≥ 1e-6 × n for every listed scale

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Name of a viewport scale

  The text a viewport scale reads as: a standard name when it is one, else 1:n.

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Ratio text for a scale that is not listed

  Writes 1:n or n:1 for a scale with no standard name.

  n ≥ 1: "1:n"; n < 1: "(1 ÷ n):1"

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Largest standard scale that fits

  Picks the largest listed scale at which the window still fits the viewport.

  largest s with s ≤ sFit × (1 + 1e-9)

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Viewport center and scale for a model window

  The model point a viewport looks at and the scale at which a model window fits it.

  sFit = min(w ÷ Δx, h ÷ Δy); center = ((minX + maxX) ÷ 2, (minY + maxY) ÷ 2)

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Standard paper for a sheet size

  Finds the standard paper a sheet of w × h is, either way round.

  |standard side − side| ≤ 0.005 × side, both sides in mm

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Space for viewports on a sheet

  The rectangle inside the border and above the title block, in paper units.

  x0 = sheet x0 + 15 mm × k; y0 = sheet y0 + 47 mm × k; x1 = sheet x0 + (W − 15 mm) × k; y1 = sheet y0 + (H − 15 mm) × k; k = 1 ÷ mm per paper unit

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Viewport of a new sheet

  The size, paper position, model center and scale of the viewport a new sheet starts with.

  Paper sizes, drawing scales and viewport aim sheets.js

  • CadCraft
  64-bit

• Clusters of the model

  Groups the model's visible objects whose bounding boxes are within a gap of each other, and returns each group's box.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Gap that separates parts

  The distance below which two objects count as one part.

  gap = max(Δx, Δy, 1e-9) × 0.04

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Size of a part's viewport at a scale

  The paper width and height a part needs at a scale 1:n, with padding and a caption band.

  w = Δx × s + 2 × 4 mm × k; h = Δy × s + 2 × 4 mm × k + 7 mm × k; k = 1 ÷ mm per paper unit

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Shelf packing

  Places boxes in rows inside the free zone and returns each box's lower-left corner, or nothing when they do not fit.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Scale and place for every part on one paper

  Chooses the scale or scales and the position of each viewport on a given paper.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Scale on automatic paper

  With no scale given and automatic paper, the scale the largest part gets on the default paper.

  Automatic sheet layout autosheet.js

  • CadCraft
  64-bit

• Viewport placed for a part

  The viewport stored for each part: paper size and center, model center and scale.

  h = packed h − 7 mm × k; paper center = (x + w ÷ 2, y + 7 mm × k + h ÷ 2); model center = midpoint of the window

  Automatic sheet layout autosheet.js

  • CadCraft
  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