Calculations

Calculations

• Construction line direction

  The unit direction of an infinite line or ray.

  direction = (dx, dy) ÷ √(dx² + dy²)

  DXF reading: objects from the file's text dxf.js

  • CadCraft
  64-bit

• Extra sheet read back from a block

  Rebuilds a sheet and its viewports from the block an R12 file keeps them in.

  viewport center = ((x_min + x_max) ÷ 2, (y_min + y_max) ÷ 2); w = x_max − x_min; h = y_max − y_min

  DXF reading: objects from the file's text dxf.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

• Number text (R12)

  The text every real number is written as in an R12 file.

  |n| < 1e-12 → 0.0; otherwise n rounded to 15 significant digits

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Point (R12)

  Writes a 2D point as three groups.

  x → f(x); y → f(y); z → 0.0

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Arc (R12)

  An arc's center, radius and its angles in degrees.

  degrees = (a mod 2π) × 180 ÷ π

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Dimension (R12)

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

  linear: point 10 = 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); angles in degrees

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Viewport view (R12)

  A sheet viewport's twist, view height and view center.

  view height = h ÷ s

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Ellipses and splines as polylines (R12)

  Writes an ellipse or a spline as a polyline along the curve, because R12 has neither object.

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Hatches as solids or outlines (R12)

  Writes a filled triangle or quadrilateral as a SOLID and any other hatch as closed polylines of its rings.

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Text (R12)

  A text's position, height, rotation, width factor and oblique angle.

  rotation° = rot × 180 ÷ π; oblique° = obl × 180 ÷ π

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Multi-line text as single lines (R12)

  The position of each line of a multi-line text, written as separate single-line texts.

  p = T(x, y) × R(rot) × (anchor x of the text box, baseline of line k)

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Construction lines as segments (R12)

  Writes an infinite line or ray as a line across the drawing's extents.

  a = p + d × t₀; b = p + d × t₁

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Extents of what was written (R12)

  The smallest and largest x and y of the model-space objects written.

  min and max over the written points

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Linetype pattern (R12)

  A linetype's total pattern length and its dashes and gaps.

  length = Σ |elementᵢ|

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Center mark size (R12)

  The center mark size written with each dimension style.

  DIMCEN = arrow size ÷ 2 (2.5 when no arrow size is set)

  DXF writing: numbers as text dxf.js

  • CadCraft
  64-bit

• Number text (2000)

  The text every real number is written as in a DXF 2000 file.

  not finite → 0.0; |n| < 1e-12 → 0.0; otherwise n rounded to 15 significant digits

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Radians to degrees (2000)

  Converts an angle to the degrees DXF stores.

  degrees = (r × 180) ÷ π

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Point (2000)

  Writes a point as three groups.

  x → f(x); y → f(y); z → f(z); a missing coordinate → 0.0

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Arc (2000)

  An arc's center, radius and its angles in degrees.

  start° = (a₀ × 180) ÷ π; end° = (a₁ × 180) ÷ π

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Ellipse (2000)

  An ellipse's center, major axis, axis ratio and start and end parameters, with the ratio brought to 1 or less.

  ratio > 1: major′ = (−m_y × ratio, m_x × ratio); ratio′ = 1 ÷ ratio; parameters − π ÷ 2

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Hatch pattern lines (2000)

  A pattern hatch's angle, scale and each pattern line's angle, base, offset and dashes.

  angles° = (radians × 180) ÷ π

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Spline (2000)

  A spline's degree, knots, weights, control points and fit points.

  knot, control point and fit point tolerances written as 1E-10

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  64-bit

• Extended data values (2000)

  Writes the extra values attached to an object: text, reals and whole numbers.

  code 1040: f(value); code 1070: value | 0

  DXF writing: numbers as text dxf2000.js

  • CadCraft
  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

• Number text for the command line

  Writes a value taken from the pointer as text.

  text = value rounded to 10 decimals, trailing zeros dropped

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

  • CadCraft
  64-bit

• Point in absolute coordinates

  One scan point, from Cartesian or spherical fields, moved by the scan's pose.

  spherical: x = r cos e cos a, y = r cos e sin a, z = r sin e; then p′ = R × p + T

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Rotation matrix from the pose quaternion

  The 3 × 3 rotation of a scan from its quaternion (w, x, y, z).

  q ÷ |q|; R = [1 − 2(y² + z²), 2(xy − zw), 2(xz + yw); 2(xy + zw), 1 − 2(x² + z²), 2(yz − xw); 2(xz − yw), 2(yz + xw), 1 − 2(x² + y²)]

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Field values of a packet

  Decodes one field of a data packet into numbers: 64-bit floats, 32-bit floats or scaled integers.

  float: as stored; integer: (raw + minimum) × scale + offset

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Bit-packed integer

  Reads an unsigned integer of up to 64 bits from a bit position in a packet.

  value = Σ chunkᵢ × 2^(32 i), chunks of up to 32 bits

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Bits from the stream

  Extracts up to 32 bits starting at any bit of a byte buffer, least significant bit first.

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Field description from the XML

  How many bits an integer field uses, and its minimum, scale and offset.

  bits = smallest b with 2ᵇ > maximum − minimum (at most 64)

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Thinning to the point budget

  How many points are kept and at what rate when a file has more points than the budget.

  cap = max(1, min(listed, ⌊budget⌋)); rate = min(1, cap ÷ listed); keep a point each time the running sum of rate reaches 1

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Points from the library's text

  Parses the x y z lines the web-e57 library returns and keeps the bounds and the thinned points.

  x, y, z = Number of each field of a line

  E57 point cloud reading e57.js

  • CadCraft
  • BimCraft
  64-bit

• Unit factors

  What a number with a unit is multiplied by to give millimeters or degrees.

  mm 1; cm 10; m 1000; in 25.4; ft 304.8; deg 1; rad 180 ÷ π

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• A number with a unit

  Reads a number and converts it by the unit written right after it.

  v = Number(text) × factor

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Sine, cosine and tangent in degrees

  sin, cos and tan of an angle given in degrees.

  sin(x) = clean(Math.sin(x × π ÷ 180)); tan refused when |cos| < 1e-12

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Trig result rounded to 15 digits

  Rounds a sine, cosine or tangent to 15 significant digits and turns a value below 1e-15 into 0.

  |x| < 1e-15 → 0; otherwise Number(x.toPrecision(15))

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Inverse trigonometry and square root

  asin, acos, atan, atan2 in degrees, and sqrt.

  asin(x) = Math.asin(clamp(x, −1, 1)) ÷ (π ÷ 180); sqrt(x) = √max(0, x)

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Power, exponential and logarithms

  pow, exp, ln and log.

  pow(a, b) = aᵇ; ln and log need x > 0

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• ceil, floor and int

  Rounds up, down or toward zero to a whole number.

  ceil(x) = ⌈x − ε⌉; floor(x) = ⌊x + ε⌋; int(x) = trunc(x + sign(x) × ε); ε = 1e-9 × max(1, |x|)

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• round(x, digits)

  Rounds to a number of decimal places from 0 to 10, halves away from zero.

  y = |x| × 10ᵈ; r = ⌊y + 0.5 + 1e-9 × max(1, y)⌋; result = ± r ÷ 10ᵈ

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Comparisons

  The six comparison operators, giving 1 or 0.

  tol = 1e-9 × max(1, |a|, |b|); a == b when |a − b| ≤ tol; a < b when a < b − tol

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Arithmetic operators

  Addition, subtraction, multiplication, division, remainder and power.

  a % b = a − b × ⌊a ÷ b⌋; division and remainder refuse b = 0

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit

• Number as text

  The text a number is written as when it is put back into an expression or a message.

  Number(v.toPrecision(12)) as text

  Parameter expressions expr.js

  • CadCraft
  • BimCraft
  • PartCraft
  64-bit