Calculations

Calculations

• 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

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• 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

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• Dimension from its defining points

  Rebuilds a file's dimension as an editable dimension when its points give the measurement the file states.

  accept when |measured − file| ≤ 1e-6 × max(1, file); diameter center = (defPoint + chord point) ÷ 2

  DWG import: objects from the file's model dwg-import.js

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• Hatch boundary to polygon rings

  Turns a hatch's boundary paths (polylines with bulges, lines, arcs, ellipses, splines) into rings of points.

  arc: n = max(4, ⌈32 × sweep ÷ 2π⌉) chords; ellipse: n = max(8, ⌈48 × sweep ÷ 2π⌉); p = c + r × (cos a, sin a)

  DWG import: objects from the file's model dwg-import.js

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• Bulge arc to points

  The points along a polyline arc segment given by its two ends and its bulge.

  θ = 4 × atan(b); r = c ÷ (2 × sin(θ ÷ 2)); center = midpoint + normal × r × cos(θ ÷ 2); n = max(2, ⌈16 × |θ| ÷ π⌉)

  DWG import: objects from the file's model dwg-import.js

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• Spline edge to points

  Points along a spline edge of a hatch boundary.

  n = min(400, max(16, 8 × control points)); de Boor: d_j = (1 − a) × d_{j−1} + a × d_j, a = (u − k_i) ÷ (k_{i+p−r+1} − k_i); point = (x, y) ÷ w

  DWG import: objects from the file's model dwg-import.js

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• Picture and wipeout frame

  The corners of an image's frame or clip boundary in drawing coordinates.

  W(q) = p + (q_x + 0.5) × u + (h − 0.5 − q_y) × v

  DWG import: objects from the file's model dwg-import.js

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• Block array positions

  The insertion point of each copy of a block placed as a rows-by-columns array.

  (x, y) = insert + R(rot) × (k × column spacing, r × row spacing)

  DWG import: objects from the file's model dwg-import.js

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• Viewport scale

  The scale of a sheet viewport and the model point at its center.

  s = viewport height ÷ view height (1 when the view height is not above 0)

  DWG import: objects from the file's model dwg-import.js

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• Hatch pattern lines

  The file's own pattern lines: angle in degrees, base point, and offset along and across each line.

  angle° = angle × 180 ÷ π; dx = o_x cos a + o_y sin a; dy = −o_x sin a + o_y cos a

  DWG import: objects from the file's model dwg-import.js

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• Lineweight in millimeters

  Converts a lineweight from hundredths of a millimeter to millimeters.

  mm = v ÷ 100 for v ≥ 0; −2 and −3 kept as codes

  DWG import: objects from the file's model dwg-import.js

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• Multi-line text rotation and oblique angle

  The rotation of multi-line text from its direction vector, and its oblique angle from the text's format code.

  rot = atan2(xAxis_y, xAxis_x); oblique = degrees in the \Q code × π ÷ 180

  DWG import: objects from the file's model dwg-import.js

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• Construction line direction

  The unit direction of an infinite line or ray.

  n = √(d_x² + d_y²); direction = (d_x ÷ n, d_y ÷ n)

  DWG import: objects from the file's model dwg-import.js

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• Dimension style numbers

  Reads a dimension style's variables and brings the decimal places and flags into range.

  scale ≤ 0 → 1; dec, adec, tad, zin → clamp(round(value), 0, 8)

  DWG import: objects from the file's model dwg-import.js

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• Which viewport is the sheet

  Picks the viewport that stands for the sheet itself: at scale 1 and covering every other viewport.

  |s − 1| ≤ 1e-6; covers: |o_x − v_x| + o_w ÷ 2 ≤ v_w ÷ 2 + 1e-6 × max(1, v_w, v_h)

  DWG import: objects from the file's model dwg-import.js

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• Transparency to the file's word

  Converts a transparency percentage to the opacity byte the file stores.

  alpha = Math.round(255 × (1 − clamp(tr, 0, 90) ÷ 100)); word = 0x02000000 + alpha

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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• Opacity byte to transparency

  Converts the file's opacity byte back to a transparency percentage.

  p = Math.round((1 − alpha ÷ 255) × 100); p ≤ 0 → none; capped at 90

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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• Transparency from a file value

  Reads a transparency word or record: by block, by layer or an opacity byte.

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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• Dimension lineweight to hundredths

  Converts a dimension line or extension line weight in millimeters to the file's whole number.

  Math.round(v × 100) for v ≥ 0; −1, −2, −3 kept as codes

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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  64-bit

• Style value to a dimension variable

  Converts one dimension style setting to the value its variable holds in the file.

  real: the number (0 when not finite); int: Math.round; bool: 1 or 0; lineweight: lw100; separator: 44 or 46

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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  64-bit

• Dimension variable to a style value

  Converts one variable read from a file to the dimension style setting.

  real: parseFloat; int: Math.round(parseFloat); lineweight: x ÷ 100 for 0 ≤ x ≤ 211

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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• Tolerance mode and text gap

  Works out the tolerance mode (symmetric, deviation, limits, basic) and the text gap from the file's variables.

  symmetric when |tp − tm| < 1e-12; gap < 0 → basic and gap = −gap

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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  64-bit

• Dimension style as file variables

  Every variable of a dimension style, by name, for a DIMSTYLE record.

  basic tolerance: DIMGAP = −|gap|

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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• Hatch pattern origin as text

  Writes a hatch's pattern origin into the file as two numbers in a text field.

  text = CCHORG: followed by x, a comma and y

  Properties in DWG and DXF: transparency, lineweights, dimension variables dwg-props.js

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  64-bit

• A number from a group value

  Reads one real number from the file's text, or a default when the group is absent.

  value = parseFloat(text)

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

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• Arc angles

  An arc's center, radius and start and end angles.

  a = (degrees × π ÷ 180) mod 2π

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

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  64-bit

• Hatch boundary to polygon rings

  Turns a hatch's boundary paths (polylines with bulges, lines and arcs) into rings of points.

  arc edge: steps = max(4, ⌈32 × (a₁ − a₀) ÷ 2π⌉); p = c + r × (cos a, sin a)

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

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  64-bit

• Bulge arc to points

  The points along a bulged segment of a hatch boundary polyline.

  θ = 4 × atan(b); r = |c ÷ (2 × sin(θ ÷ 2))|; center = midpoint + normal × r × cos(θ ÷ 2); steps = max(2, ⌈16 × |θ| ÷ π⌉)

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

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  64-bit

• Hatch pattern scale, angle and lines

  A pattern hatch's scale, angle and its own pattern lines.

  pattern angle = (degrees × π ÷ 180) mod 2π; dx = o_x cos a + o_y sin a; dy = −o_x sin a + o_y cos a, a = line angle × π ÷ 180

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

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  64-bit

• Block array positions

  The insertion point of each copy of a block placed as a rows-by-columns array.

  p = T(insert) × R(rot) × (c × column spacing, r × row spacing)

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

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• Dimension defining points

  The points a dimension measures from, by dimension type.

  linear: p₁ = 13, p₂ = 14, line point = 10, angle = group 50 × π ÷ 180; diameter center = (point 15 + point 10) ÷ 2; four-point angular: vertex from the two lines

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

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• Can the dimension be measured

  Checks that a dimension's points are finite and far enough apart to measure.

  |a − b| > 1e-12

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

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  64-bit

• Viewport scale, center and twist

  A sheet viewport's scale, the model point at its center and its view twist.

  s = viewport height ÷ view height; twist = degrees × π ÷ 180 (or radians from R12 data)

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

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• Layer lineweight

  A layer's lineweight in millimeters.

  mm = n ÷ 100 for 0 ≤ n ≤ 211; otherwise default

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

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  64-bit

• Object lineweight and linetype scale

  An object's own lineweight in millimeters and its linetype scale.

  lw = n ÷ 100; linetype scale kept when |s − 1| > 1e-12

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

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• Sheet size from the plot settings

  A sheet's size in its own unit when the layout gives no limits, from the paper size in millimeters.

  size = paper mm ÷ 25.4 (inch sheets) or ÷ 1; width and height swapped when the plot rotation code is odd

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

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  64-bit

• Dimension style numbers

  Brings a dimension style's scale, unit format and decimal places into range.

  scale ≤ 0 → 1; dec, adec, tad, zin → max(0, round(value)); dec ≤ 8

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

  • CadCraft
  64-bit