Calculations

Calculations

• Faces and their areas

  Every closed region the boundary pieces make, with the signed area used to choose among them.

  area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Hatch boundaries and pattern lines hatch.js

  • CadCraft
  64-bit

• Point inside a face

  Whether the picked point, or an island, lies inside a face.

  Hatch boundaries and pattern lines hatch.js

  • CadCraft
  64-bit

• Pattern scale and angle

  The pattern's line families at the hatch's scale, angle and origin.

  k = scale ÷ (1 metric, 25.4 inch); origin = R(angle)·(x, y)·k; spacing and dashes × k

  Hatch boundaries and pattern lines hatch.js

  • CadCraft
  64-bit

• Pattern lines clipped to the boundary

  The dashes of every pattern line that fall inside the hatch.

  line k origin = O + k·(dx·u + dy·n); crossing: t = d₁ ÷ (d₁ − d₂) along an edge

  Hatch boundaries and pattern lines hatch.js

  • CadCraft
  64-bit

• Chaining pieces into paths

  Joins line and arc pieces that follow one another into open or closed paths.

  arc → bulge = tan((a1 − a0) ÷ 4); full circle → two half arcs with bulge 1

  Drawing to laser paths laser-cad.js

  • CadCraft
  64-bit

• A path through a block transform

  A path placed by its block reference, keeping arcs where the transform allows.

  Drawing to laser paths laser-cad.js

  • CadCraft
  64-bit

• Drawing units to millimeters

  The one scale factor that puts the drawing into millimeters.

  k = millimeters per drawing unit, or 1 when the drawing has no units

  Drawing to laser paths laser-cad.js

  • CadCraft
  64-bit

• Picture placement

  Where a picture lies on the laser bed and how large it is.

  w = u_x × picture width; h = v_y × picture height, u and v the picture's axes through the transform

  Drawing to laser paths laser-cad.js

  • CadCraft
  64-bit

• Landing and text start

  Where the landing ends and where the text starts.

  end = last + dir·(landing length, 0); text = end + dir·(gap, 0)

  Multileader geometry leader.js

  • CadCraft
  64-bit

• Leader line, arrowhead and text

  The polyline, the solid arrowhead and the text a multileader is drawn and exploded as.

  u = (tip − next) ÷ |tip − next|; base = tip − u·a; corners = base ± (−u_y, u_x)·a ÷ 6; text top = landing y + h ÷ 2

  Multileader geometry leader.js

  • CadCraft
  64-bit

• abs, round, ceil and floor

  The four functions an expression may call.

  round(x) = floor(x + 0.5) for x ≥ 0, −floor(−x + 0.5) for x < 0; ceil(x) = ⌈x − 1e-9·max(1, |x|)⌉; floor(x) = ⌊x + 1e-9·max(1, |x|)⌋

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Adding and subtracting

  Sums and differences of lengths, left to right.

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• Multiplying and dividing

  Products and quotients of a length and plain numbers, left to right.

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• The answer

  The final value and whether it is a length or a plain number.

  Arithmetic on typed lengths lencalc.js

  • CadCraft
  • ModelCraft
  • MarkupCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  64-bit

• 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