Calculations

Calculations

• Line

  Writes a line's two end points.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Polyline vertices

  Writes the vertices of a lightweight polyline.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Vertex widths

  Writes the start and end width at a polyline vertex.

  equal widths: one value, −|width|

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Linetype pattern length

  The total length of a linetype's dash pattern.

  length = Σ |element length|

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Text direction

  The x-axis direction written for a block of text.

  x axis = (cos θ, sin θ, 0)

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Block scale

  Writes the three scale factors of a block reference in the format's compact form.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Single-line text

  Writes a text's insertion point, height, rotation, width factor and oblique angle.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Extension record values

  Writes the numbers kept in an extension record.

  DWG object values written and read dwg/objects-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Block content matrix of a multileader

  The 4 × 4 matrix written for a multileader's block content when the model gives none.

  M = translate(l) · rotate_z(θ) · scale(s)

  DWG object values written and read dwg/mleader-write.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Line read

  Reads a line's two end points.

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Polyline vertices read

  Reads the vertices of a lightweight polyline.

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• North direction of older geolocation data

  Turns the north angle of a version 1 geolocation object into a direction vector.

  north = (sin a, cos a)

  DWG object values written and read dwg/objects-read.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • TakeoffCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Lineweight to the file's lineweight index

  Picks the stored lineweight that is nearest to the one the layer or object has.

  index = the i with the smallest |table[i] − lineweight|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  Exact

• Ellipse with a ratio above 1

  Rewrites an ellipse whose minor axis is longer than its major axis so the file holds a ratio of 1 or less.

  major′ = (−m_y, m_x) × ratio; ratio′ = 1 ÷ ratio; start and end − π ÷ 2

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Ray and construction line direction

  Writes the direction of a ray or construction line as a unit vector.

  d′ = d ÷ |d|

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Drawing extents

  The lower left and upper right corner of model space written to the file header.

  min and max of x, y, z over the defining points

  Values changed when a DWG is written dwg/write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Default angles of a light

  The hotspot and falloff angles written for a light that has none of its own.

  hotspot = π ÷ 4; falloff = π ÷ 4 + 0.0872664626

  Values changed when a DWG is written dwg/solid-write.js

  • CadCraft
  • ModelCraft
  • CivilCraft
  • DetailCraft
  • PartCraft
  64-bit

• Arcs into chords

  Replaces each bulge arc of a path by straight chords that stay within a tolerance of the arc.

  θ = 4 atan(b); r = chord ÷ (2 sin(|θ| ÷ 2)); steps = ⌈|θ| ÷ (2 acos(1 − min(tol, r) ÷ r))⌉

  Laser job paths, fill lines and run estimate laser/laser-geom.js

  • CadCraft
  • PartCraft
  64-bit

• Signed area of a loop

  The area of a closed path, used to tell which loop is the larger when one lies in another.

  A = ½ Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)

  Laser job paths, fill lines and run estimate laser/laser-geom.js

  • CadCraft
  • PartCraft
  64-bit

• Length of a path

  The total length of a flattened path.

  L = Σ √(Δx² + Δy²)

  Laser job paths, fill lines and run estimate laser/laser-geom.js

  • CadCraft
  • PartCraft
  64-bit

• Which loop lies in which

  Counts how many other loops contain each loop, so inner shapes are cut first.

  two edge midpoints inside the other loop, and the other loop larger in area

  Laser job paths, fill lines and run estimate laser/laser-geom.js

  • CadCraft
  • PartCraft
  64-bit

• Turn into and out of the fill direction

  Rotates a point by the fill angle so the fill lines are horizontal, and back.

  x′ = x cos a − y sin a; y′ = x sin a + y cos a; a in degrees × π ÷ 180

  Laser job paths, fill lines and run estimate laser/laser-geom.js

  • CadCraft
  • PartCraft
  64-bit

• Fill lines of a closed shape

  The scan lines that fill the even–odd region of the loops, with the spans to burn on each line.

  y_k = (k + 0.5) × interval + offset; x = a_x + (b_x − a_x)(y − a_y) ÷ (b_y − a_y)

  Laser job paths, fill lines and run estimate laser/laser-geom.js

  • CadCraft
  • PartCraft
  64-bit

• Machine coordinates

  Moves every point so the job's lower left corner is the machine's 0, 0.

  x_machine = x − x_origin; y_machine = y − y_origin

  Laser job paths, fill lines and run estimate laser/laser-plan.js

  • CadCraft
  • PartCraft
  64-bit

• Burn length, travel and time

  The length burned, the length traveled with the laser off, and the time of the job.

  burn = Σ d × passes; time = Σ (d ÷ speed) × 60 × passes

  Laser job paths, fill lines and run estimate laser/laser-plan.js

  • CadCraft
  • PartCraft
  64-bit

• Fill lines into moves

  Turns the fill lines back to drawing coordinates and adds the overscan before and after each line.

  start = first − dir × overscan; end = last + dir × overscan

  Laser job paths, fill lines and run estimate laser/laser-plan.js

  • CadCraft
  • PartCraft
  64-bit

• Picture rows into moves

  Lays a picture's burn levels on its rectangle as rows of moves with a power for each run.

  cols = round(w ÷ interval); dx = w ÷ cols; y = y₀ + h − (r + 0.5) dy; power = min + (max − min) × level ÷ 255

  Laser job paths, fill lines and run estimate laser/laser-plan.js

  • CadCraft
  • PartCraft
  64-bit

• Gray value of each engraving cell

  The average gray of the picture's pixels under each cell of the engraving grid.

  gray = Σ w × pixel ÷ Σ w, w = overlap area of pixel and cell

  Burn levels of an engraved picture laser/laser-image.js

  • CadCraft
  • PartCraft
  32-bit in part

• Burn level of each cell

  Turns the gray values into burn levels from 0 to 255 by the chosen method.

  darkness = 1 − (gray ÷ 255)^gamma; threshold: darkness > t; gray steps: round(round(darkness × (n − 1)) ÷ (n − 1) × 255)

  Burn levels of an engraved picture laser/laser-image.js

  • CadCraft
  • PartCraft
  32-bit in part

• Arc of a glyph

  The points of the round parts of letters.

  n = max(2, ⌈|a₁ − a₀| ÷ 15⌉); p = (c_x + r_x cos a, c_y + r_y sin a)

  Text from drawings as stroked edges m3d/strokefont.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• Width of a string

  The advance of a string in drawing units, used to align and wrap text.

  width = (Σ (glyph width + 2) − 2) × h ÷ 9 × width factor

  Text from drawings as stroked edges m3d/strokefont.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• Strokes of a string

  The polylines of a string at a given height, width factor and slant.

  x = x₀ + p_x × s_x + p_y × s × tan(oblique); y = p_y × s; s = h ÷ 9

  Text from drawings as stroked edges m3d/strokefont.js

  • CadCraft
  • ModelCraft
  • PartCraft
  64-bit

• Line fit

  The best straight line through a run of center-line pixels, and how far the worst pixel lies from it.

  θ = ½ × atan2(2·Sxy, Sxx − Syy); ends = feet of the first and last points on the line through the centroid

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Circle fit

  The best circle through a run of center-line pixels, its sweep and the angles of an arc.

  Kåsa: solve the 2 × 2 system for the center about the centroid, r = √(uc² + vc² + (Suu + Svv) ÷ n); then Gauss-Newton on d − r

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Corner detection

  Where a chain of pixels turns sharply, so it can be cut there before fitting.

  turn = |atan2(r − q) − atan2(q − p)| over ± w steps; corner when turn ≥ 0.6 rad and largest nearby

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Splitting a chain into lines and arcs

  Fits a line, else an arc, else splits the chain at the point farthest from its chord, and joins neighbors that fit as one.

  distance to chord = |(P − A) × (B − A)| ÷ |B − A|

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Joining collinear lines

  Merges two lines that lie on the same straight line and nearly touch.

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Squaring level and plumb lines

  Makes nearly horizontal and vertical lines exactly so, and gives lines of one wall the same coordinate.

  y = (y₁ + y₂) ÷ 2; shared coordinate = Σ(coordinate × length) ÷ Σ length

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Closing corners

  Moves a line end to the point where its line meets a nearby line.

  s = ((B₁ − E) × v) ÷ (u × v); new end = E + s·u

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Lines and arcs in image coordinates

  The traced lines and arcs with the window offset added and the arc end points worked out.

  start = (cx + r·cos a₀, cy + r·sin a₀); end = (cx + r·cos a₁, cy + r·sin a₁)

  Tracing a scan into lines and arcs raster/trace.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Crossing of two traced lines

  The point where two traced line segments cross.

  d = (a₂ − a₁) × (b₂ − b₁); t = ((b₁ − a₁) × (b₂ − b₁)) ÷ d; point = a₁ + t·(a₂ − a₁)

  Tracing a scan into lines and arcs raster/snap.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Snap points of a trace

  The ends, middles, arc centers, corners and crossings offered for snapping.

  middle = (p₁ + p₂) ÷ 2; arc middle at angle (a₀ + a₁) ÷ 2; corner = mean of the ends within 3 px

  Tracing a scan into lines and arcs raster/snap.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Black-and-white level (Otsu)

  The grey level that best separates ink from paper for the whole sheet.

  maximize w_B × w_F × (m_B − m_F)² over the 256 levels

  Scan clean-up and JPEG decoding raster/image.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Local threshold (Sauvola)

  Decides ink or paper for each pixel from the mean and spread of the pixels around it.

  ink when v ≤ mean × (1 + k × (sd ÷ 128 − 1)); sd = √(Σv² ÷ n − mean²)

  Scan clean-up and JPEG decoding raster/image.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Sheet skew angle

  The angle by which the long lines of a scanned sheet are rotated.

  score(angle) = Σ rows² + Σ columns² of the ink projected at that angle; best angle on a 0.25° then 0.02° grid

  Scan clean-up and JPEG decoding raster/image.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Rotating the image

  Turns a grey image by an angle about its middle.

  source = c + R(angle) × (pixel − c); value = bilinear mix of the 4 nearest source pixels

  Scan clean-up and JPEG decoding raster/image.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• JPEG inverse cosine transform

  Turns the stored frequency coefficients of an 8 × 8 block back into pixel values.

  pixel = round(Σ_u Σ_v C(x,u)·C(y,v)·coef(u,v) + 128), clamped to 0–255

  Scan clean-up and JPEG decoding raster/jpeg.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• JPEG color conversion

  Converts the decoded luminance and color-difference values to red, green and blue.

  R = Y + 1.402·Cr; G = Y − 0.344136·Cb − 0.714136·Cr; B = Y + 1.772·Cb

  Scan clean-up and JPEG decoding raster/jpeg.js

  • CadCraft
  • BimCraft
  • ModelCraft
  • CivilCraft
  • PartCraft
  64-bit

• Table values in millimeters

  Converts each published row to millimeters, mm² and kg/m.

  mm = in × 25.4; mm² = in² × 25.4 × 25.4; kg/m = lb/ft × 1.48816394; r = (k_des − t_f) × 25.4

  Steel section dimensions, areas and outlines shapes/sections.js

  • CadCraft
  • BimCraft
  • DetailCraft
  • PartCraft
  64-bit

• Exact section area

  The cross-section area worked out from the dimensions, with fillets and rounded corners included.

  I: 2·b_f·t_f + (d − 2t_f)·t_w + (4 − π)·r²; RHS: 2t(h + b − 2t) − (4 − π)(r_o² − r_i²); CHS: π(D − t)·t

  Steel section dimensions, areas and outlines shapes/sections.js

  • CadCraft
  • BimCraft
  • DetailCraft
  • PartCraft
  64-bit