Calculations

Calculations

• Continued and baseline dimensions

  The origins and line position of each dimension added by DIMCONTINUE or DIMBASELINE.

  baseline: loc = previous loc + dli × scale × side × (−sin rot, cos rot), dli defaults to 3.75

  Where dimensions are attached commands.js

  • CadCraft
  64-bit

• Origin and X axis from two points

  The coordinate system with its origin at a picked point and its X axis toward a second point.

  origin = o; angle = atan2(pₓ − o) (ucs.js threePoint)

  User coordinate system set by command commands.js

  • CadCraft
  64-bit

• Rotation about Z

  The coordinate system turned by a typed angle about its own origin.

  angle = current angle + a (a defaults to π ÷ 2)

  User coordinate system set by command commands.js

  • CadCraft
  64-bit

• Quarter turn

  The coordinate system turned a quarter left or right, or set back to the world.

  angle = current angle ± π ÷ 2

  User coordinate system set by command commands.js

  • CadCraft
  64-bit

• What UCS prints

  The origin and angle of the coordinate system as printed in the command history.

  angle shown = (angle mod 2π) × 180 ÷ π, at most 4 decimals

  User coordinate system set by command commands.js

  • CadCraft
  64-bit

• Viewport from two corners

  The size and center of a new viewport, and what it shows.

  w = |Δx|; h = |Δy|; center = (a + b) ÷ 2

  Viewports on a sheet commands.js

  • CadCraft
  64-bit

• Scale that fits a named view

  The viewport scale at which a saved view of the model fills the viewport.

  s = min(viewport w ÷ view w, viewport h ÷ view h)

  Viewports on a sheet commands.js

  • CadCraft
  64-bit

• Measured value

  The length, radius, diameter or angle a dimension reports.

  linear = |(p₂ − p₁) · (cos r, sin r)|; aligned = |p₂ − p₁|; radius = |p₁ − c|; diameter = 2 × |p₁ − c|; angular = sweep

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Sector of an angular dimension

  The start angle, end angle and counterclockwise sweep an angular dimension measures.

  a₁ = atan2(p₁ − c); a₂ = atan2(p₂ − c); sweep = (end − start) mod 2π

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Ends of the dimension line

  Where the two extension lines meet the dimension line, square or at an obliquing angle.

  square: q = loc + u × ((p − loc) · u); oblique: q = p + d × ((loc − p) · n) ÷ (d · n)

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Angular dimension between two lines

  The vertex where two lines cross and a point on each leg bounding the sector that holds the text point.

  den = d₁ × d₂; t = ((l₂ − l₁) × d₂) ÷ den; c = l₁ + d₁ × t

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Linear and aligned dimension parts

  The extension lines, dimension line, arrowheads and text point of a linear or aligned dimension.

  extension line: from p + exo to q + exe; arrows inside when length ≥ 2 × asz; text at the middle, offset by gap

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Angular dimension parts

  The arc, extension lines, arrowheads and text point of an angular dimension.

  R = |loc − c|; arc from a₀ to a₁ at R; arrows outside when R × sweep < 2 × asz; text at c + (R + gap) at a₀ + sweep ÷ 2

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Radius and diameter dimension parts

  The center mark, leader or dimension line, arrowheads and text point of a radius or diameter dimension.

  r = |p₁ − c|; P = c + r × (cos u, sin u); Q = c − r × (cos u, sin u); center mark half-length = asz ÷ 2

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Closed arrowhead

  The three corners of the default filled arrowhead.

  base = tip − asz along the arrow; corners = base ± asz ÷ 6 across

  Dimension measurement and geometry dims.js

  • CadCraft
  64-bit

• Text for a measurement

  The main text, alternate-unit text and tolerance text a dimension style writes for a measured value.

  m = round(v × |lfac|, rnd); alternate = round(m × altf, altrnd); limits: upper = base + tp, lower = base − tm

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Decimal number text

  Writes a value with a fixed number of decimal places and the style's zero suppression.

  d = clamp(round(dec), 0, 8); |v| < 0.5 × 10⁻ᵈ → 0; text = v to d places

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Round-off to a multiple

  Rounds a value to the nearest multiple of the style's round-off.

  r > 0: Math.round(v ÷ r) × r; else v

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Length text

  Writes a length as a decimal number or, for other unit formats, through the shared length formatter.

  Dimension text: units, rounding and tolerances dimstyle.js

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  64-bit

• Angle text

  Writes an angle in decimal degrees, degrees-minutes-seconds, grads or radians.

  degrees = radians ÷ (π ÷ 180); minutes = (degrees − ⌊degrees⌋) × 60; seconds = (minutes − ⌊minutes⌋) × 60; grads = degrees ÷ 0.9

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Millimeters in each text unit

  The size of the units a dimension can write its value in.

  mm = 1; cm = 10; m = 1000; km = 1 000 000

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  Exact

• Measurement scale for a text unit

  Sets the scale that makes a dimension write its value in mm, cm, m or km.

  lfac = mmPerUnit ÷ mm in the unit

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Which text unit a style writes

  Recognizes a style's scale and suffix as mm, cm, m or km, as drawn, or custom.

  |lfac − mmPerUnit ÷ unit| ≤ 1e-9 × max(1, lfac); as drawn: |lfac − 1| < 1e-12

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Millimeters in one drawing unit

  The size of a drawing unit, or of a sheet's paper unit, in millimeters.

  paper in inches: 25.4; paper in mm: 1; model: mmPerDrawingUnit; unitless: 1 (assumed)

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Refit after the drawing units change

  Gives dimensions that write in mm to km a new scale when the drawing's unit changes.

  lfac′ = new mm per unit ÷ mm in the unit

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Arrowhead shapes

  The lines, circle or filled outline of each arrowhead style at a tip, direction and size.

  half-width = size ÷ 6; open 30°: tan(15°) × size; dot radius = size ÷ 4 (small: size ÷ 8), drawn with 16 sides; tick at 45°, half-length size ÷ 2

  Dimension text: units, rounding and tolerances dimstyle.js

  • CadCraft
  64-bit

• Number rounded for comparison

  The text a number is compared by: its value on a grid of 0.0001.

  Math.round(v ÷ 0.0001) × 0.0001, written with at most 4 decimals

  Drawing compare drawing-compare.js

  • CadCraft
  64-bit

• Center and size of an object

  The middle of an object's bounding box and the length of its diagonal, used to pair objects.

  cx = (minX + maxX) ÷ 2; cy = (minY + maxY) ÷ 2; d = √((maxX − minX)² + (maxY − minY)²)

  Drawing compare drawing-compare.js

  • CadCraft
  64-bit

• Pairing by distance

  Pairs each leftover object with the nearest object of the other version that is close enough.

  d = |center_a − center_b|; candidate when d ≤ max(size_a, size_b) + 1e-9; nearest first

  Drawing compare drawing-compare.js

  • CadCraft
  64-bit

• Moved or reshaped

  Says whether a changed object only moved: every x shifted by one amount and every y by another.

  |Δxᵢ − Δx₀| ≤ 1e-3 and |Δyᵢ − Δy₀| ≤ 1e-3 for every coordinate; other numbers equal on the 0.0001 grid

  Drawing compare drawing-compare.js

  • CadCraft
  64-bit

• Lineweight in hundredths of a millimeter

  Converts a lineweight in millimeters to the whole number the file stores.

  Math.round(w × 100) for w ≥ 0; negative codes kept

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Spline: fit points or control points

  Decides whether a spline's fit points are written with it, by checking that they still give its control points.

  every |recomputed − stored| ≤ 1e-7 × max(1, max(|x| + |y|))

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Multi-line text anchor and oblique angle

  Moves baseline-anchored text to a top anchor one text height up, and writes the oblique angle as a format code.

  anchor = (x, y) + R(rot) × (0, h); code = \Q followed by degrees to 6 decimals

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Hatch boundary rings

  Writes a hatch's rings as closed polylines, or a 3 or 4 cornered solid fill as a SOLID.

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Hatch pattern lines for the file

  The pattern's line families in drawing units: angle in radians, base point and offset in world axes.

  k = scale ÷ (1 metric, 25.4 otherwise); base = R(turn) × (x, y) × k + origin; offset = (dx cos a − dy sin a, dx sin a + dy cos a)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Dimension points and measurement

  The defining points, text point and measurement written for a dimension.

  measurement = dimMeasure; linear: defPoint = end of the dimension line on the second extension line; radial: near = c + r × (cos a, sin a), far = c − r × (cos a, sin a)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Viewport view height

  The model height a sheet viewport shows, and its view center.

  view height = h ÷ s (s taken as 1 when not above 0)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Sheet paper size and limits

  The paper size in millimeters, the sheet's limits and the sheet viewport's center.

  paper mm = w × 25.4 (inch sheets) or w; limits = (x₀, y₀) to (x₀ + w, y₀ + h); center = (x₀ + w ÷ 2, y₀ + h ÷ 2)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Drawing extents

  The smallest and largest x and y of everything in model space, written to the file's header.

  min and max over the bounds of every object

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Closing point of a ring

  Drops a ring's last point when it repeats the first.

  |first − last| < 1e-12

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Construction line direction

  The unit direction written for an infinite line or ray.

  direction = (dx, dy) ÷ √(dx² + dy²)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• User coordinate system axes

  The origin and the x and y axis vectors of a user coordinate system.

  x axis = (cos θ, sin θ); y axis = (−sin θ, cos θ)

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• Linetype pattern length

  The total length of one repeat of a linetype's dashes and gaps.

  length = Σ |elementᵢ|

  DWG save: objects to the file's model dwg-save.js

  • CadCraft
  64-bit

• A group value by its code

  Turns one group's text into a real number, a whole number, a true or false, or text.

  codes 10–59, 110–149, 210–239, 460–469, 1010–1059: parseFloat; 60–99, 160–179, 270–289, 370–389, 400–409, 420–429, 440–459, 1060–1071: parseInt

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Arc angles

  An arc's start and end angles in radians.

  angle = degrees × (π ÷ 180)

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Multi-line text direction

  The direction vector of multi-line text, from the file's vector or from its rotation angle.

  x axis = group 11 when present; otherwise (cos(a), sin(a)), a = degrees × (π ÷ 180)

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Hatch arc and ellipse edges

  The center, radius or axes, and start and end angles of the curved edges of a hatch boundary.

  angle = degrees × (π ÷ 180); missing end angle = 360 degrees

  DXF reading into the shared drawing model dxf-model.js

  • CadCraft
  • BimCraft
  • TakeoffCraft
  • CivilCraft
  64-bit

• Pointer with the locked fields applied

  The point shown and used while fields are locked: a typed distance or angle from the base point, or a typed X or Y.

  polar: p = base + d × (cos a, sin a), a = typed degrees × π ÷ 180 or atan2 of the pointer; xy: (typed X or pointer x, typed Y or pointer y)

  Dynamic input: points from typed distance, angle, X and Y dynin.js

  • CadCraft
  64-bit

• Field values while the pointer moves

  The distance and angle from the base point, or X and Y, that the fields show.

  d = √(Δx² + Δy²); a = atan2(Δy, Δx) × 180 ÷ π, brought into 0 to 360

  Dynamic input: points from typed distance, angle, X and Y dynin.js

  • CadCraft
  64-bit

• Text sent on Enter

  The coordinate text the command line receives: a relative distance and angle, or an absolute X and Y.

  @d<a from the last point; otherwise #x,y with x = base_x + d × cos a, y = base_y + d × sin a

  Dynamic input: points from typed distance, angle, X and Y dynin.js

  • CadCraft
  64-bit