Calculations

Calculations

• Machining time

  The time a program takes: cutting moves at their feed, rapid moves at the machine's rapid rate, plus tool changes.

  seconds = 60 × (Σ L ÷ feed + Σ L ÷ rapid) + changes × change time

  Stock simulation and machining time cam-sim.js

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• Arc center words I and J

  The arc center written relative to the arc's start point.

  I = round₃(c_x − round₃(start_x)); J = round₃(c_y − round₃(start_y))

  G-code and toolpath exports cam-post.js

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  64-bit

• Axis words

  Writes X, Y and Z only when they change at the output resolution.

  write an axis when round₃(new) ≠ round₃(last written)

  G-code and toolpath exports cam-post.js

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• Toolpath as CSV

  Writes every segment's start, end, arc center, sweep and feed as text.

  value = toFixed(6); sweep in degrees = sweep × 180 ÷ π

  G-code and toolpath exports cam-post.js

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• Toolpath as JSON

  Writes the setup, tools and every operation's moves.

  JSON.stringify of the moves

  G-code and toolpath exports cam-post.js

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• Spindle speed and feeds

  The spindle speed, cutting feed, plunge feed and ramp feed for a tool.

  rpm = round(1000 vc ÷ (π d)), limited to the machine's range; feed = rpm × flutes × f_z; plunge = feed ÷ 3; ramp = feed ÷ 2

  Cutting speeds, feeds and tool profiles cam-tools.js

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• Rounding feeds to one decimal

  Rounds a feed rate to tenths.

  round1(v) = round(v × 10) ÷ 10

  Cutting speeds, feeds and tool profiles cam-tools.js

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• Tool tip profile

  The height of the cutting surface above the tool's tip at a given distance from its axis.

  ball: R − √(R² − ρ²); bull: r_c − √(r_c² − (ρ − a)²) beyond a = R − r_c; drill and chamfer: (ρ − r_t) ÷ tan(angle ÷ 2); flat: 0

  Cutting speeds, feeds and tool profiles cam-tools.js

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• Unit factors

  The factor from the file's units to millimeters.

  mm 1; cm 10; m 1000; in 25.4

  Nested sheets from DXF to toolpaths cam-sheets.js

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  Exact

• Bulged segments to arcs

  Turns a polyline with bulges into lines and true arcs.

  r = (d ÷ 2)(1 + b²) ÷ (2|b|); offset = (d ÷ 2)(1 − b²) ÷ (2b); sweep = 4 atan(b)

  Nested sheets from DXF to toolpaths cam-sheets.js

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• Extent of an outline

  The box round a sheet or a part outline, used for sheet size and for placing parts on sheets.

  min and max over points sampled along each piece at 0.05 chord tolerance

  Nested sheets from DXF to toolpaths cam-sheets.js

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• Part coordinates on its sheet

  Moves a part's points so its sheet's lower left corner is the origin, in millimeters.

  x′ = (x − sheet x₀) × k; y′ = (y − sheet y₀) × k

  Nested sheets from DXF to toolpaths cam-sheets.js

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• Elementary functions

  The one-argument math functions a script can call: roots, exponentials, logarithms, trigonometry, hyperbolic functions, rounding and angle conversion.

  log1p(x) = x − x² ÷ 2 + x³ ÷ 3 for |x| < 1e-4, else log(1 + x); asinh(x) = sign × log(|x| + √(x² + 1)); atanh(x) = ½ log((1 + x) ÷ (1 − x)); sind(x) = sin(x × π ÷ 180)

  CraftScript core math functions cs-lib-core.js

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• Rounding to a number of decimals

  round(x, d): rounds to d decimal places.

  round(x × 10^d) ÷ 10^d

  CraftScript core math functions cs-lib-core.js

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• Gamma function and factorial

  Γ(x), and factorial(n) = Γ(n + 1).

  whole x < 171: (x − 1)! by product; x < 0.5: π ÷ (sin(πx) Γ(1 − x)); else √(2π) t^(x − ½) e^(−t) Σ c_i ÷ (x − 1 + i), t = x + 6.5

  CraftScript core math functions cs-lib-core.js

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• Binomial coefficient

  nchoosek(n, k): the number of ways to choose k of n.

  r ← r × (n − m + i) ÷ i for i = 1 … m, m = min(k, n − k); result = round(r)

  CraftScript core math functions cs-lib-core.js

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• Spacing of numbers

  eps(x): the gap between x and the next larger 64-bit number.

  2^(floor(log₂|x|) − 52); eps(0) = 5e-324

  CraftScript core math functions cs-lib-core.js

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• Evenly spaced values

  linspace(a, b, n): n values from a to b.

  value i = a + (b − a) × i ÷ (n − 1)

  CraftScript core math functions cs-lib-core.js

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• Logarithmically spaced values

  logspace(a, b, n): n values from 10^a to 10^b.

  value i = 10 ^ (a + (b − a) × i ÷ (n − 1))

  CraftScript core math functions cs-lib-core.js

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• Running sum and product

  cumsum and cumprod along a dimension.

  acc ← acc + x_k (or acc × x_k), stored at each step

  CraftScript core math functions cs-lib-core.js

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• Variance and standard deviation

  var and std of a set of values.

  m = Σx ÷ n; var = Σ(x − m)² ÷ (n − 1), or ÷ n with weight 1; std = √var

  CraftScript core math functions cs-lib-core.js

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• Median

  The middle value of a set, or the mean of the two middle values.

  sorted s; n odd: s[(n − 1) ÷ 2]; n even: (s[n ÷ 2 − 1] + s[n ÷ 2]) ÷ 2

  CraftScript core math functions cs-lib-core.js

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  64-bit

• Dot product

  dot(a, b): the sum of products of two vectors.

  Σ a_i b_i

  CraftScript core math functions cs-lib-core.js

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  64-bit

• Trapezoid integration

  trapz(y) or trapz(x, y): the area under sampled data.

  Σ (x_i − x_{i−1}) (y_i + y_{i−1}) ÷ 2

  CraftScript core math functions cs-lib-core.js

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• One-dimensional interpolation

  interp1(x, y, xi): linear, nearest or previous-value interpolation in a table.

  y = y_lo + (y_hi − y_lo)(q − x_lo) ÷ (x_hi − x_lo)

  CraftScript core math functions cs-lib-core.js

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• Polynomial evaluation

  polyval(p, x): the value of a polynomial.

  s ← s × x + c for each coefficient (Horner)

  CraftScript core math functions cs-lib-core.js

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• Polynomial fit

  polyfit(x, y, n): the least-squares polynomial of degree n through data.

  V_ij = x_i^(n − j); solve V p ≈ y

  CraftScript core math functions cs-lib-core.js

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• Matrix to text

  mat2str(A): text that can be typed back in to recreate a matrix.

  each value written with toPrecision(15) by default

  CraftScript core math functions cs-lib-core.js

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• Number to text

  num2str(x): a short text form of a number.

  whole numbers in full; otherwise max(ceil(log₁₀|x|), 1) + 4 significant digits

  CraftScript core math functions cs-lib-core.js

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• Text to number

  str2double(s): reads a number from text.

  Number(text) for text matching a decimal pattern, else NaN

  CraftScript core math functions cs-lib-core.js

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• Conversion to single precision

  single(A): each value rounded to the nearest 32-bit floating-point number.

  x ← fround(x)

  CraftScript number type conversions cs-lib-core.js

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  32-bit in part

• Conversion to whole-number types

  int8, int16, int32, int64 and the unsigned forms: each value rounded to a whole number.

  x ← round(x); NaN → 0

  CraftScript number type conversions cs-lib-core.js

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• Read an STL file

  Reads the triangles of a binary or text STL file into a model's node coordinates.

  CraftScript file readers and writers cs-lib-io.js

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• Weld STL vertices

  Merges the repeated corners of an STL triangle list into shared nodes.

  CraftScript file readers and writers cs-lib-io.js

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  Exact

• Write a binary STL file

  Writes a triangle surface with a unit normal per triangle.

  n = (b − a) × (c − a) ÷ |(b − a) × (c − a)|

  CraftScript file readers and writers cs-lib-io.js

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• Write an OBJ file

  Writes node coordinates and triangle corner numbers as text.

  CraftScript file readers and writers cs-lib-io.js

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• Read an OBJ file

  Reads vertex lines and face lines into node coordinates and triangles.

  CraftScript file readers and writers cs-lib-io.js

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• Read a CSV file

  Reads a table of numbers into a matrix.

  CraftScript file readers and writers cs-lib-io.js

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• Write a CSV file

  Writes a matrix as rows of text.

  CraftScript file readers and writers cs-lib-io.js

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• Values to JSON

  Prepares a script value for a JSON file.

  CraftScript file readers and writers cs-lib-io.js

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• Read an NPY file

  Reads a NumPy array file into a tensor.

  CraftScript file readers and writers cs-lib-io.js

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• Write an NPY file

  Writes a tensor as a NumPy array file.

  CraftScript file readers and writers cs-lib-io.js

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• Write a tensor to HDF5

  Writes a tensor as an HDF5 dataset in row-major order.

  CraftScript file readers and writers cs-lib-io.js

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• Read an HDF5 dataset

  Reads a dataset into a number, a logical value or a tensor.

  CraftScript file readers and writers cs-lib-io.js

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• Plot data as CSV

  Writes the x and y values of a script plot as a CSV file.

  CraftScript file readers and writers cs-plot-export.js

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• One CSV cell

  Turns one value into the text of a CSV cell.

  CraftScript file readers and writers cs-plot-export.js

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• Matrix product

  The product of two dense matrices.

  C_ij = Σ_p A_ip × B_pj

  CraftScript dense linear algebra cs-lib-linalg.js

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  64-bit

• LU factorization

  Factors a square matrix with row exchanges.

  P A = L U

  CraftScript dense linear algebra cs-lib-linalg.js

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• Solve with an LU factorization

  Forward and back substitution for one or more right-hand sides.

  CraftScript dense linear algebra cs-lib-linalg.js

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• Cholesky factorization

  Factors a symmetric positive definite matrix as RᵀR.

  R_jj = √(A_jj − Σ_k R_kj²)

  CraftScript dense linear algebra cs-lib-linalg.js

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  64-bit