Calculations

Calculations

• Block size from its label

  The width and height of a diagram block.

  w = longest line × th × 0.62 + 3 × th; h = (lines × 1.3 + 1.7) × th; diamond: w × 1.5, h × 1.6; minimum width 8 × th (diamond 10 × th)

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Symbol scale in a block

  The factor that fits a symbol drawing into a box of six text heights.

  k = 6 × th ÷ max(w, 1.4 × h)

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Symbol geometry scaled and moved

  Scales a symbol's lines, circles, arcs, polylines, hatches and text by k and moves them to the block.

  x′ = x × k + dx; y′ = y × k + dy; r′ = r × k

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Block coordinates

  The x and y of every block in a layered diagram.

  x = previous edge + w ÷ 2, gap 2.5 × th; y = Σ (layer height + 4 × th); then x → mean of neighbors' x, kept in order with the gap

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Sequence diagram positions

  The x of each lifeline and the y of each message row in a sequence diagram.

  gap ≥ 2.5 × th and ≥ (label length × th × 0.8 × 0.62 + 2 × th) ÷ lifelines crossed; row = 3.4 × th; top = box height + 2.6 × th

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Layout to drawing coordinates

  Places the laid-out diagram at a point in the drawing, turning y from downward to upward.

  X = x + px − minX; Y = y − (py − minY)

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• Arrowhead triangle

  The three corners of a connector's filled arrowhead.

  u = (to − from) ÷ |to − from|; corners: to, to − u × s ± n × 0.35 × s

  Diagram layout into drawing objects diagram.js

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

  • CadCraft
  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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

  • CadCraft
  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

  • CadCraft
  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

  • CadCraft
  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

  • CadCraft
  64-bit

• 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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

  • CadCraft
  64-bit

• 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

  • CadCraft
  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

• 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

• 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