Calculations

Calculations

• Temperature range of the plot

  The lowest and highest temperature used for the plot scale and its tick labels.

  lo = min T, hi = max T over all vertices (all frames when transient)

  Thermal window temperature range and balance read-outs sim-thermal-ui.js

  • PartCraft
  32-bit in part

• Probed temperature and flux

  The temperature and flux text shown when a point is probed.

  Thermal window temperature range and balance read-outs sim-thermal-ui.js

  • PartCraft
  32-bit in part

• Heat balance imbalance

  The unbalanced heat in watts and as a percent of the larger of inflow and outflow.

  percent = 100 × |imbalance| ÷ max(inflow, outflow, 1e-300)

  Thermal window temperature range and balance read-outs sim-thermal-ui.js

  • PartCraft
  64-bit

• Scalar from a field

  One number per node or element from a vector or stress field.

  |u| = √(ux² + uy² + uz²); σvm as above

  Script result fields and meshes shown in the window cs-ui.js

  • PartCraft
  64-bit

• Range of the plotted values

  The lowest and highest value that set the color scale.

  hi ≤ lo → hi = lo + max(|lo|, 1) × 1e-6

  Script result fields and meshes shown in the window cs-ui.js

  • PartCraft
  64-bit

• Deformation scale

  A round scale that makes the largest displacement about 8 percent of the model size.

  raw = 0.08 × diagonal ÷ max |u|, rounded up to 1, 2, 5 or 10 × 10ᵉ

  Script result fields and meshes shown in the window cs-ui.js

  • PartCraft
  32-bit, display only

• Outer surface of a mesh

  The outer surface of a solid or surface mesh as triangles for the view.

  Script result fields and meshes shown in the window cs-ui.js

  • PartCraft
  32-bit, display only

• Mass from volume and density

  The mass of a part in grams.

  m = V × ρ ÷ 1000

  Part and assembly mass in the bill of materials, measure panel and assistant bom.js

  • PartCraft
  64-bit

• Rounding of the exported bill

  The numbers written into the bill of materials CSV.

  value = round to 3 decimals

  Part and assembly mass in the bill of materials, measure panel and assistant bom.js

  • PartCraft
  64-bit

• Mass properties reported to the assistant

  Volume, area, center, mass and inertia of the built solid.

  mass = V × ρ ÷ 1000; inertia = tensor × ρ ÷ 1000

  Part and assembly mass in the bill of materials, measure panel and assistant agents.js

  • PartCraft
  32-bit in part

• Mass properties in the measure panel

  Where the measure panel gets a body's mass properties, exact or from the mesh.

  Part and assembly mass in the bill of materials, measure panel and assistant measure-ui.js

  • PartCraft
  32-bit in part

• Number format in the measure panel

  Rounds a measure value to a number of decimals for the panel.

  toFixed(dp); |v| < 1e-12 shown as 0

  Part and assembly mass in the bill of materials, measure panel and assistant measure-ui.js

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• Default tangent modulus and its check

  Sets the slope after yield when none is given and flags one that is not below E.

  Et = E ÷ 100 when not given

  Nonlinear study fields and thermal stress history nlstudy.js

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• Contact penetration problem

  Flags a contact penetration over 1 percent of the element size, with the values it reports.

  problem when max penetration > 0.01 × h; pct = 100 × pen ÷ h

  Nonlinear study fields and thermal stress history nlstudy.js

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• Time steps solved for stress

  Chooses which time steps of the heat run get a stress solve.

  stepᵢ = round(i × steps ÷ (n − 1)), i = 0…n−1

  Nonlinear study fields and thermal stress history thermal-history.js

  • PartCraft
  Exact

• Thermal load per step

  The load vector of each stress step and the temperature range of the worst step.

  ΔT = T − Tref; f = f_mech + ft(ΔT)

  Nonlinear study fields and thermal stress history thermal-history.js

  • PartCraft
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• Solid cubes from a distance grid

  Marks each cube solid or not from its corner values.

  solid when Σ₈ corner values < 0; origin = lo × h

  Voxel grid and lattice struts field/voxels.js

  • PartCraft
  64-bit

• Lattice struts in a box

  The strut list of a lattice that fills a box.

  cells = ⌈(extent ÷ cell) − 1e-9⌉; end = corner + (i + a) × cell

  Voxel grid and lattice struts field/lattice.js

  • PartCraft
  64-bit

• Sewing tolerance from model size

  The tolerance with which patch edges are joined.

  tol = max(1e-7, 1e-7 × max |coordinate|)

  Form cage to exact solid: sewing and volume form-brep.js

  • PartCraft
  64-bit

• Sewn solid and its volume

  Sews the faces, makes a solid, and measures its volume.

  Form cage to exact solid: sewing and volume form-brep.js

  • PartCraft
  64-bit

• Millimeters per PDF point

  The size of one PDF point in millimeters, the base of every preset scale.

  MM_PER_PT = 25.4 ÷ 72

  Sheet scale, typed lengths and measured values units.js

  • MarkupCraft
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• Calibration from a preset scale

  Real millimeters per point for a scale chosen from the list, such as 1/4 inch = 1 foot or 1:100.

  mmPerPt = (25.4 ÷ 72) × ratio

  Sheet scale, typed lengths and measured values units.js

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• Calibration from two picked points

  Real millimeters per point from a distance picked on the sheet and the real length typed for it.

  mmPerPt = real length (mm) ÷ picked distance (pt)

  Sheet scale, typed lengths and measured values units.js

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• Fractions and mixed numbers

  Reads 1/2, 6 1/2 or 12.5 as a number.

  a/b → a ÷ b; n a/b → n + a ÷ b

  Sheet scale, typed lengths and measured values units.js

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• A typed length in millimeters

  Reads what a person types for a length (24'-0", 12' 6 1/2", 3.5 m, 900 mm, or a bare number in the chosen unit) as millimeters.

  mm = feet × 304.8 + inches × 25.4; metric: value × 1, 10 or 1000

  Sheet scale, typed lengths and measured values units.js

  • MarkupCraft
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• A typed length with arithmetic

  Reads entries such as 12'6" + 3/4" or 2*450mm as one length in millimeters.

  Sheet scale, typed lengths and measured values units.js

  • MarkupCraft
  64-bit

• Length as text

  Writes a length in millimeters in the sheet's unit: feet and inches, feet, inches, meters or millimeters.

  ft-in: round(mm ÷ 25.4 × 16) sixteenths; ft: mm ÷ 304.8; in: mm ÷ 25.4; m: mm ÷ 1000

  Sheet scale, typed lengths and measured values units.js

  • MarkupCraft
  64-bit

• Area as text

  Writes an area in square millimeters in the area unit that goes with the sheet's length unit.

  sq ft = mm² ÷ 92903.04; sq in = mm² ÷ 645.16; m² = mm² ÷ 1e6

  Sheet scale, typed lengths and measured values units.js

  • MarkupCraft
  64-bit

• Area and perimeter of an outline

  The area and the perimeter of a closed outline, in points² and points.

  area = |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| ÷ 2; perimeter = Σ hypot(Δx, Δy)

  Sheet scale, typed lengths and measured values units.js

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• Area measurement with cut-outs

  The area and perimeter text of an area markup: the outline less its cut-outs, in real units.

  area = (A_outline − Σ A_cut-out) × mmPerPt²; perimeter = (P_outline + Σ P_cut-out) × mmPerPt

  Sheet scale, typed lengths and measured values units.js

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• Length under a calibration

  A distance in points as a real length in the sheet's unit.

  length = points × mmPerPt

  Sheet scale, typed lengths and measured values units.js

  • MarkupCraft
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• Measured values of a markup

  The length, area and perimeter, count, angle or arc length listed for a markup in the Properties panel and, through valueOf, in lists, CSV and BCF.

  length = hypot(Δx, Δy) × mmPerPt; arc = r × |sweep| × mmPerPt; count = number of marks

  Sheet scale, typed lengths and measured values markupcraft.js

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  64-bit

• Pointer position on the paper

  The pointer's position on the sheet in the status line, in millimeters or inches of paper.

  mm = pt ÷ 72 × 25.4; in = pt ÷ 72

  Sheet scale, typed lengths and measured values markupcraft.js

  • MarkupCraft
  64-bit

• Scale carried to a replacement sheet

  When markups are carried to a new revision of a sheet, the old sheet's calibration is given to the new one if it has none.

  |w_old − w_new| ≤ 1 pt and |h_old − h_new| ≤ 1 pt

  Sheet scale, typed lengths and measured values markupcraft.js

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• Size of a pasted area

  The size on the sheet of a copied area pasted as a picture: the same size on paper, or the same real size when both sheets have a scale.

  k = mmPerPx ÷ mmPerPt (both scaled), else ptPerPx; w = px_w × k; h = px_h × k

  Sheet scale, typed lengths and measured values markupcraft.js

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• Arc through three points

  The center, radius, start angle and signed sweep of the arc from the first point through the second to the third.

  d = 2·(aₓ(m_y − b_y) + mₓ(b_y − a_y) + bₓ(a_y − m_y)); cₓ = Σ (x² + y²)·Δy ÷ d; r = hypot(a − c)

  Arc through three points and angle measurement arcs.js

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  64-bit

• Arc as Bézier pieces

  The arc as cubic Bézier segments of at most 90° each, for drawing and for the saved appearance.

  n = ⌈|sweep| ÷ (π ÷ 2) − 1e-9⌉; k = (4 ÷ 3)·tan(step ÷ 4)

  Arc through three points and angle measurement arcs.js

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  64-bit

• Arc length

  The length of an arc markup in points.

  length = r × |sweep|

  Arc through three points and angle measurement arcs.js

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  64-bit

• Angle between two legs

  The angle at a vertex between the directions to two other points, from 0° to 180°.

  θ = acos((u·w) ÷ (|u|·|w|)) × 180 ÷ π

  Arc through three points and angle measurement arcs.js

  • MarkupCraft
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• Angle as text

  Writes the angle with a degree sign.

  round(deg × 10ᵖ) ÷ 10ᵖ, p = 1 by default

  Arc through three points and angle measurement arcs.js

  • MarkupCraft
  64-bit

• Snap to 45°

  Moves a point onto the nearest 45° direction from the point before it, keeping its distance.

  a = round(atan2(dy, dx) ÷ (π ÷ 4)) × (π ÷ 4); p = from + (cos a, sin a) × hypot(dx, dy)

  Markup geometry while drawing and editing geom.js

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• Square from a corner

  Makes the box from a fixed corner to the pointer square.

  s = max(|dx|, |dy|); p = a + (sign dx, sign dy) × s

  Markup geometry while drawing and editing geom.js

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• Resize by a grip

  The new box or points when a grip of a markup is dragged.

  box: dragged edges = pointer; stroke: x′ = x₀ + (x − box x₀) ÷ box width × new width

  Markup geometry while drawing and editing geom.js

  • MarkupCraft
  64-bit

• Move a markup

  Shifts a markup's points, box and cut-outs by a distance.

  x′ = x + dx; y′ = y + dy

  Markup geometry while drawing and editing geom.js

  • MarkupCraft
  64-bit

• Simplify a freehand stroke

  Drops the points of a pen or highlighter stroke that lie within a tolerance of the line through their neighbors.

  d = |dy·pₓ − dx·p_y + bₓ·a_y − b_y·aₓ| ÷ L

  Markup geometry while drawing and editing geom.js

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  64-bit

• Inverse of a transform

  The inverse of a 2-D affine transform.

  det = a·d − b·c; inverse = adjugate ÷ det

  Markup geometry while drawing and editing geom.js

  • MarkupCraft
  64-bit

• Line-up through two pairs of points

  The move, turn and uniform scale that carries two picked points on one sheet onto two picked points on another.

  s = |b| ÷ |a|; θ = atan2(b) − atan2(a); M = [s·cos θ, s·sin θ, −s·sin θ, s·cos θ, e, f]

  Markup geometry while drawing and editing geom.js

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• Next point from a typed length and angle

  Places the next point of a line or outline at a typed real length, along a typed angle or toward the pointer.

  len = mm ÷ mmPerPt; a = (deg + page turn) × π ÷ 180; p = from + (cos a, sin a) × len

  Markup geometry while drawing and editing sketch.js

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  64-bit

• Cleaned pen stroke to a markup

  Turns what the stroke cleaner recognized (line, circle, arc, outline) into the points or box of a line, ellipse, arc, rectangle, polyline or polygon markup.

  circle → box (c − r, c + r); arc → points at a₀, a₀ + sweep ÷ 2, a₁ on the circle

  Markup geometry while drawing and editing pen-clean.js

  • MarkupCraft
  64-bit

• Finished freehand stroke

  What is stored when a pen or highlighter stroke is finished.

  tolerance = 0.6 ÷ zoom (points)

  Markup geometry while drawing and editing markupcraft.js

  • MarkupCraft
  64-bit