Calculations

Calculations

• Summary of the comparison

  The counts, the largest horizontal and height differences and the root mean square of the horizontal differences.

  rms = √(Σ dh² ÷ n)

  Layout point files and as-built comparison layout/layout-points.js

  • CadCraft
  • BimCraft
  64-bit

• Comparison table

  The rows of the comparison as text for the page and the CSV.

  text = v.toFixed(3)

  Layout point files and as-built comparison layout/layout-points.js

  • CadCraft
  • BimCraft
  64-bit

• Add, subtract, multiply, divide

  The four arithmetic functions on integers and reals.

  all integers: 32-bit result; any real: 64-bit result; integer ÷ integer truncates toward zero

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• FIX: a real to an integer

  Drops the fraction of a number.

  int(trunc(x))

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• Square root, exponential, logarithm and power

  SQRT, EXP, LOG and EXPT.

  Math.sqrt, Math.exp, Math.log, Math.pow

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• EQUAL with a fuzz

  Whether two numbers or lists of numbers are equal within a given amount.

  |a − b| ≤ fuzz

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• RTOS: a number as text

  Formats a length in decimal or in the drawing's other length formats.

  decimal: v.toFixed(prec); 0 when |v| < 0.5 × 10⁻ᵖʳᵉᶜ

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• ANGTOS: an angle as text

  Formats an angle in degrees, degrees-minutes-seconds, grads, radians or surveyor's bearings.

  degrees = a × 180 ÷ π; grads = a × 200 ÷ π; minutes = (deg − whole) × 60

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• ANGTOF: text to an angle

  Reads an angle written in any of the angle formats and returns radians.

  degrees × π ÷ 180; d + m ÷ 60 + s ÷ 3600; grads × π ÷ 200

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• Unit factors for CVUNIT

  The factor of each unit to its base unit: meter, radian, kilogram or square meter.

  inch 0.0254; foot 0.3048; yard 0.9144; mile 1609.344; pound 0.45359237; sq inch 0.00064516; sq foot 0.09290304; acre 4046.8564224

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• CVUNIT: convert between units

  Converts a number or a list of numbers from one unit to another of the same kind.

  result = v × from ÷ to

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• POLAR, DISTANCE and ANGLE

  A point at an angle and distance from another, the distance between two points, and the angle of the line between them.

  q = p + d (cos a, sin a); dist = √(Δx² + Δy² + Δz²); angle = atan2(Δy, Δx) into 0 to 2π

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• INTERS: where two lines meet

  The intersection of two lines or segments given by their end points.

  den = Δ₁ × Δ₂; u = ((p₃ − p₁) × Δ₂) ÷ den; q = p₁ + u Δ₁

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• ATOI and ATOF: text to a number

  Reads the leading whole number or real number of a text.

  parseInt or parseFloat of the leading number

  LISP arithmetic, conversions and geometry lisp/builtins.js

  • CadCraft
  64-bit

• A routine's number as command input

  Turns a number a routine gives to a command into the text the command reads.

  text = String(+v.toPrecision(15))

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Answers to a command's prompts

  Hands a routine's string, number, point or object to the command that is waiting for input.

  point: UCS to world, then given as a click; number: as 15-digit text

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Block-to-world matrix of a nested pick

  The transform from a block's own coordinates to the drawing for an object picked inside nested block references.

  M = M · [rotation × scale, insertion − base]; pick in block = M⁻¹ · pick

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• TRANS: between coordinate systems

  Converts a point or a direction between the world, the user coordinate system and the display.

  display: turn by the view's twist; UCS: by the active coordinate system (ucs.js)

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Current lineweight as a system variable

  The current lineweight in hundredths of a millimeter.

  CELWEIGHT = round(lineweight × 100)

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Drawing extents as system variables

  EXTMIN and EXTMAX: the box around every object.

  min and max of every object's bounds

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Date as a Julian day number

  The DATE system variable.

  Julian date = milliseconds since 1970 ÷ 86 400 000 + 2 440 587.5

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Position of a block attribute

  The world position of an attribute of a block reference, as entget reports it.

  p = insertion + R(rot) · ((d − base) × scale)

  Drawing values handed to and from LISP routines lisp/host-cad.js

  • CadCraft
  64-bit

• Angles brought into 0 to 2π

  Normalizes an arc's, text's or block reference's angle for a data list, and when a routine writes one back.

  a′ = ((a mod 2π) + 2π) mod 2π

  Drawing values handed to and from LISP routines lisp/dxflist.js

  • CadCraft
  64-bit

• Lineweight in a data list

  An object's lineweight as group 370, in hundredths of a millimeter.

  370 = round(lw × 100)

  Drawing values handed to and from LISP routines lisp/dxflist.js

  • CadCraft
  64-bit

• Lineweight from a data list

  Sets an object's lineweight in millimeters from group 370.

  lw = value ÷ 100

  Drawing values handed to and from LISP routines lisp/dxflist.js

  • CadCraft
  64-bit

• Arc from a data list

  Makes or changes an arc from its center, radius and two angles.

  center, radius as given; angles into 0 to 2π

  Drawing values handed to and from LISP routines lisp/dxflist.js

  • CadCraft
  64-bit

• Viewport scale from a data list

  Sets a layout viewport's scale from the view height a routine gives.

  scale = paper height ÷ view height

  Drawing values handed to and from LISP routines lisp/dxflist.js

  • CadCraft
  64-bit

• Linetype pattern length

  The total length of a linetype's dashes and gaps in its table record.

  length = Σ |xᵢ|

  Drawing values handed to and from LISP routines lisp/dxflist.js

  • CadCraft
  64-bit

• Length and angle of a line

  The Length, Angle and Delta properties of a line.

  length = √(Δx² + Δy²); angle = atan2(Δy, Δx) into 0 to 2π

  Drawing values handed to and from LISP routines lisp/vla-host.js

  • CadCraft
  64-bit

• Circle and arc properties

  Diameter, area and circumference of a circle; total angle, arc length and end points of an arc.

  area = π r²; circumference = 2π r; sweep = ((a₁ − a₀) mod 2π + 2π) mod 2π; arc length = r × sweep; end = c + r (cos a, sin a)

  Drawing values handed to and from LISP routines lisp/vla-host.js

  • CadCraft
  64-bit

• Ellipse radii

  The major and minor radius of an ellipse.

  major = √(m_x² + m_y²); minor = major × ratio

  Drawing values handed to and from LISP routines lisp/vla-host.js

  • CadCraft
  64-bit

• Lineweight property set by a routine

  Sets an object's lineweight in millimeters from a value in hundredths of a millimeter.

  lw = value ÷ 100

  Drawing values handed to and from LISP routines lisp/vla-host.js

  • CadCraft
  64-bit

• Plane of a face

  The plane a face lies in, as a unit normal and a distance from the origin.

  n = Newell normal of the outer loop; d = n · p₀

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Area of a face

  The area of a face, holes taken out.

  area = |Σ (pᵢ × pᵢ₊₁)| ÷ 2 for the outer loop, minus the same for each hole

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Triangles of a face

  The triangles a face is cut into for volume, export and ray tests.

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Surface area and volume of a shape

  Whether a group or component is closed, its total face area and, when closed, its volume.

  V = Σ a · (b × c) ÷ 6 over all triangles; A = Σ face areas

  Face planes, areas, triangles and solid volume m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Vertex at a point

  The vertex a drawn point becomes: an existing one, or a new one that splits the edge it lands on.

  s = (p − A) · u ÷ (u · u); on the edge when 0 < s < 1 and |A + s·u − p| ≤ EPS

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Stops along a new edge

  Where a new edge is cut by the vertices and edges it meets.

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Crossing of two edges

  The point where two edges cross inside both of them.

  n = u × w; s = ((C − A) × w) · n ÷ (n · n); t = ((C − A) × u) · n ÷ (n · n)

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Planes a new edge may close a face on

  The planes tried when a new edge might complete a face.

  n = u × (C − A), kept when |n| > 1e-9 × |u| × |C − A|

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Faces of a plane from its edges

  Which closed loops of edges on a plane are faces, which are holes, and which side each face shows.

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Loops of the planar edge graph

  The closed loops formed by the edges on a plane, and the signed area of each.

  edges round a vertex sorted by atan2(Δy, Δx); area = ½ Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Point inside a loop

  Whether a 2D point is inside a loop, used to match holes and old faces.

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Test point inside a region

  A point well inside a region, used to ask which old faces cover it.

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Welding coincident vertices

  Merges vertices at the same place and removes edges and loops that collapse.

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Removing a vertex on a straight run

  Joins two edges that continue each other in a straight line into one.

  merged when u₁ · u₂ ≤ −1 + 1e-9

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Merging coplanar faces

  Removes an edge between two faces that lie in one plane and face the same way.

  n₁ · n₂ ≥ 1 − 1e-9 and |d₁ − d₂| ≤ EPS

  Drawing an edge: welding, splitting and re-facing m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Push or pull a face

  Moves a face along its normal by a typed or dragged distance, or extrudes it into side faces.

  p′ = p + n × distance

  Push/pull, move, stretch, follow me and intersect m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Depth to the face behind

  How far a face can be pushed in before it meets the first face behind it.

  smallest ray parameter t > EPS along −n

  Push/pull, move, stretch, follow me and intersect m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit

• Moving vertices by a matrix

  The new place of each selected vertex under a move, rotate, scale or flip.

  p′ = M · p

  Push/pull, move, stretch, follow me and intersect m3d/model.js

  • CadCraft
  • ModelCraft
  64-bit