Calculations

Calculations

• Rounding of stored values

  The two rounding helpers every stored number of an item goes through.

  r4(v) = round(v × 10000) ÷ 10000; r2(v) = round(v × 100) ÷ 100

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Block to millimeters

  The transform from a block's own coordinates and units to the item's millimeters.

  M = [mm, 0, 0, mm, −base.x·mm, −base.y·mm]; scale of a transform = √|det|; angle = r4(atan2(y, x) in degrees)

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Lines, circles and arcs of a block

  A block's lines, circles and arcs as plan entities in millimeters.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Nested block references

  The transform of a block reference inside the block, with its rows and columns.

  local = T(insert) · R(rotation) · S(sx, sy) · T(−base + column·spacing ÷ sx, row·spacing ÷ sy)

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Mesh body from a block's 3D faces

  The item's 3D body and height when the block holds 3D faces.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Arcs as points, 5° steps

  The points that replace a circle or arc that cannot stay an arc.

  n = max(8, ⌈sweep ÷ 5°⌉); point = c + r·(cos a, sin a)

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Splines as points

  The points that replace a block's spline in the item's plan.

  de Boor recurrence at u = lo + (hi − lo)·s ÷ n, n = max(16, 8 × control points)

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Arc points for bounds

  The points of an arc used to find a plan's bounds.

  n = max(4, ⌈sweep ÷ 10°⌉); point = c + r·(cos a, sin a)

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Bounds of a plan

  The box round an item's plan, from which its width and depth are taken.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Box body on a plan

  A box body standing on the plan's bounds with a given height.

  w = max x − min x; d = max y − min y; each of x, y, z, w, d, h rounded to 4 decimals

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Item from a mesh file

  A mesh file's triangles as an item body in millimeters, with its footprint and sizes.

  p = file point × unit in mm; Y-up: (x, y, z) → (x, −z, y); stored = r4(p − (center x, max y, min z))

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• STL corners

  The corner points of an STL file's triangles.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• glTF accessor values

  The numbers of a glTF position or index accessor.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• glTF node transforms

  The matrix that places each glTF node's mesh.

  M = T · R(q) · S, R from the quaternion (qx, qy, qz, qw)

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Convex hull footprint

  The outline round a mesh item's points, used as its plan.

  monotone chain; turn = (a − o) × (b − o), popped when ≤ 0

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Box of a body

  The box a body fills: a box body itself, or the extent of a mesh body.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Box item from width, depth and height

  The rectangle plan and box body of an item given only by its sizes.

  x from −w ÷ 2 to +w ÷ 2; y from −d to 0; label height = min(0.18 d, 150), reduced to fit 90% of w

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Sizes from attributes

  Width, depth and height read from a block's attributes.

  Library item geometry from blocks, meshes and tables libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Millimeters per unit

  The table of unit factors.

  in 25.4; ft 304.8; yd 914.4; mi 1 609 344; mil 0.0254; µm 0.001

  Lengths and units for Library items libitem.js

  • CadCraft
  • BimCraft
  Exact

• Length from text

  A typed or stored length in millimeters.

  with a unit: n × factor; feet and inches: (feet × 12 + inches + a ÷ b) × 25.4; bare number: n × mm per unit

  Lengths and units for Library items libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Drawing units

  The millimeters per drawing unit of a DWG or DXF file.

  Lengths and units for Library items libitem.js

  • CadCraft
  • BimCraft
  Exact

• Pipe size in eighths of an inch

  A decimal inch size written as a fraction, such as 1 1/2".

  eighths = round((n − ⌊n⌋) × 8)

  Lengths and units for Library items libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Size label on the preview

  The overall width and depth printed on an item's preview picture.

  millimeters: round(mm); inches: round(mm ÷ 25.4 × 8) eighths

  Lengths and units for Library items libitem.js

  • CadCraft
  • BimCraft
  64-bit

• Millimeters to drawing units

  The factor that puts an item's millimeters into the drawing's units.

  k = 1 ÷ (mm per drawing unit), or 1 when the drawing has no units

  Library item placed as a block libplace.js

  • CadCraft
  64-bit

• Plan entities in drawing units

  Each line, circle, arc, polyline, ellipse, text, point and hatch of the item as a drawing object.

  length × k; angle in degrees × π ÷ 180, reduced to [0, 2π)

  Library item placed as a block libplace.js

  • CadCraft
  64-bit

• Size attributes

  The width, depth, height and weight written as attributes on the block.

  Library item placed as a block libplace.js

  • CadCraft
  64-bit

• Count and quantity of each item

  How many times each Library item is placed and the total of their quantities, for the credits and schedule.

  placed = number of references; quantity = Σ parseFloat(quantity attribute), 1 when not above 0

  Library item placed as a block libplace.js

  • CadCraft
  64-bit

• Pattern in drawing units

  The dash and gap lengths of a linetype for this drawing.

  metric drawing: inch pattern × 25.4

  Linetype dashes linetypes.js

  • CadCraft
  64-bit

• Dashes along lines and arcs

  The pieces of each line or arc that are drawn.

  piece from fraction s ÷ length to (s + step) ÷ length; arc length = r × sweep

  Linetype dashes linetypes.js

  • CadCraft
  64-bit

• Warp plan for a picture or tile

  How finely a map image is cut into patches so that it lands in the right place on screen.

  tolerance = 0.25 ÷ zoom project units, rounded to a half power of 2

  Map layers under the drawing maplayers.js

  • CadCraft
  • BimCraft
  32-bit, display only

• Drawing the patches

  Each patch of a map image drawn on the canvas.

  Map layers under the drawing maplayers.js

  • CadCraft
  • BimCraft
  32-bit, display only

• Local placement record

  The scale, rotation and point pair that tie drawing coordinates to grid coordinates.

  scale = m per drawing unit ÷ m per grid unit; from = (x, y); to = (e, n)

  Drawing placed on a map grid maplayers.js

  • CadCraft
  • BimCraft
  64-bit

• Meters per drawing unit

  The table that converts drawing units to the 3D model's meters.

  inch 0.0254; foot 0.3048; yard 0.9144; mile 1609.344; no unit 0.001

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  Exact

• Outline of a closed 2D object

  The ring of points a solid is extruded from, and its area.

  circle: 48 points at radius r; arc: steps of at most 7.5°; area = ½ |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• Extruded solid

  A solid made by pushing a ring up or down by a height.

  local ring = ring − (min x, min y); placed at (min x, min y, z₀)

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• Cylinder

  A cylinder from a center, radius and height.

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• Volume of each solid

  The volume listed for every closed solid.

  volume = |V of the definition| × |det of the placement's 3 × 3 part|

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• Changing the drawing's units

  Scales the 3D model so it stays the same size on the drawing when the units change.

  ratio = m per new unit ÷ m per old unit; every vertex and placement offset × ratio

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• 3D faces written to a file

  The model's faces as 3D faces in drawing units for DWG and DXF.

  file point = placed vertex in meters ÷ k, k = meters per drawing unit

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• 3D faces inside blocks

  Places the 3D faces a block holds once for every reference of that block.

  (x′, y′) = M·(x, y); z′ = z

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• 3D faces read from a file

  A file's loose 3D faces brought into the model in meters.

  corner in meters = file corner × k

  3D solids, faces and units in a drawing model3d.js

  • CadCraft
  64-bit

• Axes of an object's own coordinate system

  The X, Y and Z axes of the plane an object was drawn on, from its extrusion direction.

  Z = N ÷ |N|; X = (Wy × Z or Wz × Z) ÷ length; Y = Z × X

  Objects on a tilted or flipped plane mapped to the plan ocs.js

  • CadCraft
  64-bit

• Is the plane the drawing's own

  Whether an extrusion direction is straight up, so that nothing needs mapping.

  Objects on a tilted or flipped plane mapped to the plan ocs.js

  • CadCraft
  64-bit

• Plane to plan matrix

  The transform from an object's own (x, y) at its elevation to the plan.

  M = [X.x, X.y, Y.x, Y.y, Z.x·elevation, Z.y·elevation]

  Objects on a tilted or flipped plane mapped to the plan ocs.js

  • CadCraft
  64-bit

• Mapped circle, arc or ellipse

  The circle, arc or ellipse that has exactly the points of the original after the map.

  t* = ½·atan2(2 u·v, |u|² − |v|²); U = u·cos t* + v·sin t*; V = −u·sin t* + v·cos t*; a = |U|, b = |V|

  Objects on a tilted or flipped plane mapped to the plan ocs.js

  • CadCraft
  64-bit

• Polyline arcs as points

  A polyline's arc segments as points, for a map that does not keep shapes.

  k = max(4, ⌈64 × |sweep| ÷ 2π⌉); point = c + r·(cos a, sin a)

  Objects on a tilted or flipped plane mapped to the plan ocs.js

  • CadCraft
  64-bit

• Mapping each kind of object

  A drawing object in its own coordinate system put through the plane's matrix.

  text: rotation = atan2(M·d); height × |M·d × M·up| ÷ |M·d|; block: scales and rotation read from the mapped axes

  Objects on a tilted or flipped plane mapped to the plan ocs.js

  • CadCraft
  64-bit

• Automatic constraints

  Which ends are joined and which lines are made horizontal or vertical.

  coincident when |a − b| ≤ distance; horizontal when |sin α| ≤ sin(tolerance); vertical when |cos α| ≤ sin(tolerance)

  Automatic constraints and dimension conversion pcommands.js

  • CadCraft
  64-bit

• Dimension to constraint

  The constraint a plain dimension stands for, when its points sit on constrainable geometry.

  tol = 1e-7 × max(1, largest |x| or |y|)

  Automatic constraints and dimension conversion pcommands.js

  • CadCraft
  64-bit

• Underlay shapes and text

  The underlay's paths as plotted segments and fills, and its text.

  B(t) = (1 − t)³·P₀ + 3(1 − t)²t·P₁ + 3(1 − t)t²·P₂ + t³·P₃, t = s ÷ 8; line width = max(0.05, w × √|det|); text height = h × √|det| ÷ FONT_EM

  PDF underlay in a plot pdf-emit.js

  • CadCraft
  64-bit