mirror of
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728 lines
22 KiB
OpenSCAD
728 lines
22 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: math.scad
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// Math helper functions.
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// To use, add the following lines to the beginning of your file:
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// ```
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// use <BOSL2/std.scad>
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// ```
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//////////////////////////////////////////////////////////////////////
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// Section: Math Constants
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PHI = (1+sqrt(5))/2; // The golden ratio phi.
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EPSILON = 1e-9; // A really small value useful in comparing FP numbers. ie: abs(a-b)<EPSILON
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INF = 1/0; // The value `inf`, useful for comparisons.
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NAN = acos(2); // The value `nan`, useful for comparisons.
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// Section: Simple math
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// Function: sqr()
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// Usage:
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// sqr(x);
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// Description:
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// Returns the square of the given number.
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// Examples:
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// sqr(3); // Returns: 9
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// sqr(-4); // Returns: 16
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function sqr(x) = x*x;
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// Function: log2()
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// Usage:
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// foo = log2(x);
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// Description:
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// Returns the logarithm base 2 of the value given.
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// Examples:
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// log2(0.125); // Returns: -3
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// log2(16); // Returns: 4
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// log2(256); // Returns: 8
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function log2(x) = ln(x)/ln(2);
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// Function: hypot()
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// Usage:
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// l = hypot(x,y,[z]);
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// Description:
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// Calculate hypotenuse length of a 2D or 3D triangle.
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// Arguments:
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// x = Length on the X axis.
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// y = Length on the Y axis.
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// z = Length on the Z axis. Optional.
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// Example:
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// l = hypot(3,4); // Returns: 5
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// l = hypot(3,4,5); // Returns: ~7.0710678119
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function hypot(x,y,z=0) = norm([x,y,z]);
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// Function: factorial()
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// Usage:
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// x = factorial(n,[d]);
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// Description:
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// Returns the factorial of the given integer value.
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// Arguments:
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// n = The integer number to get the factorial of. (n!)
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// d = If given, the returned value will be (n! / d!)
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// Example:
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// x = factorial(4); // Returns: 24
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// y = factorial(6); // Returns: 720
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// z = factorial(9); // Returns: 362880
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function factorial(n,d=1) = product([for (i=[n:-1:d]) i]);
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// Function: lerp()
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// Usage:
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// x = lerp(a, b, u);
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// l = lerp(a, b, LIST);
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// Description:
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// Interpolate between two values or vectors.
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// If `u` is given as a number, returns the single interpolated value.
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// If `u` is 0.0, then the value of `a` is returned.
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// If `u` is 1.0, then the value of `b` is returned.
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// If `u` is a range, or list of numbers, returns a list of interpolated values.
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// It is valid to use a `u` value outside the range 0 to 1. The result will be a predicted
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// value along the slope formed by `a` and `b`, but not between those two values.
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// Arguments:
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// a = First value or vector.
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// b = Second value or vector.
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// u = The proportion from `a` to `b` to calculate. Standard range is 0.0 to 1.0, inclusive. If given as a list or range of values, returns a list of results.
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// Example:
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// x = lerp(0,20,0.3); // Returns: 6
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// x = lerp(0,20,0.8); // Returns: 16
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// x = lerp(0,20,-0.1); // Returns: -2
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// x = lerp(0,20,1.1); // Returns: 22
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// p = lerp([0,0],[20,10],0.25); // Returns [5,2.5]
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// l = lerp(0,20,[0.4,0.6]); // Returns: [8,12]
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// l = lerp(0,20,[0.25:0.25:0.75]); // Returns: [5,10,15]
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// Example(2D):
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// p1 = [-50,-20]; p2 = [50,30];
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// stroke([p1,p2]);
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// pts = lerp(p1, p2, [0:1/8:1]);
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// // Points colored in ROYGBIV order.
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// rainbow(pts) translate($item) circle(d=3,$fn=8);
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function lerp(a,b,u) =
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is_num(u)? (1-u)*a + u*b :
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[for (v = u) lerp(a,b,v)];
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// Section: Hyperbolic Trigonometry
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// Function: sinh()
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// Description: Takes a value `x`, and returns the hyperbolic sine of it.
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function sinh(x) =
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(exp(x)-exp(-x))/2;
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// Function: cosh()
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// Description: Takes a value `x`, and returns the hyperbolic cosine of it.
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function cosh(x) =
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(exp(x)+exp(-x))/2;
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// Function: tanh()
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// Description: Takes a value `x`, and returns the hyperbolic tangent of it.
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function tanh(x) =
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sinh(x)/cosh(x);
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// Function: asinh()
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// Description: Takes a value `x`, and returns the inverse hyperbolic sine of it.
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function asinh(x) =
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ln(x+sqrt(x*x+1));
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// Function: acosh()
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// Description: Takes a value `x`, and returns the inverse hyperbolic cosine of it.
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function acosh(x) =
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ln(x+sqrt(x*x-1));
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// Function: atanh()
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// Description: Takes a value `x`, and returns the inverse hyperbolic tangent of it.
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function atanh(x) =
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ln((1+x)/(1-x))/2;
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// Section: Quantization
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// Function: quant()
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// Description:
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// Quantize a value `x` to an integer multiple of `y`, rounding to the nearest multiple.
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// If `x` is a list, then every item in that list will be recursively quantized.
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// Arguments:
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// x = The value to quantize.
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// y = The multiple to quantize to.
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// Example:
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// quant(12,4); // Returns: 12
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// quant(13,4); // Returns: 12
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// quant(13.1,4); // Returns: 12
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// quant(14,4); // Returns: 16
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// quant(14.1,4); // Returns: 16
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// quant(15,4); // Returns: 16
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// quant(16,4); // Returns: 16
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// quant(9,3); // Returns: 9
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// quant(10,3); // Returns: 9
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// quant(10.4,3); // Returns: 9
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// quant(10.5,3); // Returns: 12
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// quant(11,3); // Returns: 12
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// quant(12,3); // Returns: 12
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// quant([12,13,13.1,14,14.1,15,16],4); // Returns: [12,12,12,16,16,16,16]
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// quant([9,10,10.4,10.5,11,12],3); // Returns: [9,9,9,12,12,12]
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// quant([[9,10,10.4],[10.5,11,12]],3); // Returns: [[9,9,9],[12,12,12]]
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function quant(x,y) =
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is_list(x)? [for (v=x) quant(v,y)] :
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floor(x/y+0.5)*y;
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// Function: quantdn()
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// Description:
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// Quantize a value `x` to an integer multiple of `y`, rounding down to the previous multiple.
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// If `x` is a list, then every item in that list will be recursively quantized down.
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// Arguments:
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// x = The value to quantize.
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// y = The multiple to quantize to.
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// Examples:
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// quantdn(12,4); // Returns: 12
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// quantdn(13,4); // Returns: 12
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// quantdn(13.1,4); // Returns: 12
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// quantdn(14,4); // Returns: 12
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// quantdn(14.1,4); // Returns: 12
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// quantdn(15,4); // Returns: 12
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// quantdn(16,4); // Returns: 16
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// quantdn(9,3); // Returns: 9
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// quantdn(10,3); // Returns: 9
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// quantdn(10.4,3); // Returns: 9
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// quantdn(10.5,3); // Returns: 9
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// quantdn(11,3); // Returns: 9
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// quantdn(12,3); // Returns: 12
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// quantdn([12,13,13.1,14,14.1,15,16],4); // Returns: [12,12,12,12,12,12,16]
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// quantdn([9,10,10.4,10.5,11,12],3); // Returns: [9,9,9,9,9,12]
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// quantdn([[9,10,10.4],[10.5,11,12]],3); // Returns: [[9,9,9],[9,9,12]]
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function quantdn(x,y) =
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is_list(x)? [for (v=x) quantdn(v,y)] :
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floor(x/y)*y;
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// Function: quantup()
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// Description:
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// Quantize a value `x` to an integer multiple of `y`, rounding up to the next multiple.
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// If `x` is a list, then every item in that list will be recursively quantized up.
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// Arguments:
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// x = The value to quantize.
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// y = The multiple to quantize to.
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// Examples:
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// quantup(12,4); // Returns: 12
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// quantup(13,4); // Returns: 16
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// quantup(13.1,4); // Returns: 16
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// quantup(14,4); // Returns: 16
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// quantup(14.1,4); // Returns: 16
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// quantup(15,4); // Returns: 16
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// quantup(16,4); // Returns: 16
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// quantup(9,3); // Returns: 9
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// quantup(10,3); // Returns: 12
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// quantup(10.4,3); // Returns: 12
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// quantup(10.5,3); // Returns: 12
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// quantup(11,3); // Returns: 12
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// quantup(12,3); // Returns: 12
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// quantup([12,13,13.1,14,14.1,15,16],4); // Returns: [12,16,16,16,16,16,16]
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// quantup([9,10,10.4,10.5,11,12],3); // Returns: [9,12,12,12,12,12]
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// quantup([[9,10,10.4],[10.5,11,12]],3); // Returns: [[9,12,12],[12,12,12]]
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function quantup(x,y) =
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is_list(x)? [for (v=x) quantup(v,y)] :
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ceil(x/y)*y;
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// Section: Constraints and Modulos
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// Function: constrain()
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// Usage:
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// constrain(v, minval, maxval);
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// Description:
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// Constrains value to a range of values between minval and maxval, inclusive.
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// Arguments:
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// v = value to constrain.
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// minval = minimum value to return, if out of range.
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// maxval = maximum value to return, if out of range.
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// Example:
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// constrain(-5, -1, 1); // Returns: -1
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// constrain(5, -1, 1); // Returns: 1
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// constrain(0.3, -1, 1); // Returns: 0.3
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// constrain(9.1, 0, 9); // Returns: 9
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// constrain(-0.1, 0, 9); // Returns: 0
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function constrain(v, minval, maxval) = min(maxval, max(minval, v));
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// Function: posmod()
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// Usage:
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// posmod(x,m)
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// Description:
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// Returns the positive modulo `m` of `x`. Value returned will be in the range 0 ... `m`-1.
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// Arguments:
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// x = The value to constrain.
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// m = Modulo value.
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// Example:
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// posmod(-700,360); // Returns: 340
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// posmod(-270,360); // Returns: 90
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// posmod(-120,360); // Returns: 240
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// posmod(120,360); // Returns: 120
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// posmod(270,360); // Returns: 270
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// posmod(700,360); // Returns: 340
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// posmod(3,2.5); // Returns: 0.5
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function posmod(x,m) = (x%m+m)%m;
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// Function: modang(x)
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// Usage:
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// ang = modang(x)
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// Description:
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// Takes an angle in degrees and normalizes it to an equivalent angle value between -180 and 180.
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// Example:
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// modang(-700,360); // Returns: 20
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// modang(-270,360); // Returns: 90
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// modang(-120,360); // Returns: -120
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// modang(120,360); // Returns: 120
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// modang(270,360); // Returns: -90
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// modang(700,360); // Returns: -20
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function modang(x) =
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let(xx = posmod(x,360)) xx<180? xx : xx-360;
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// Function: modrange()
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// Usage:
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// modrange(x, y, m, [step])
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// Description:
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// Returns a normalized list of values from `x` to `y`, by `step`, modulo `m`. Wraps if `x` > `y`.
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// Arguments:
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// x = The start value to constrain.
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// y = The end value to constrain.
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// m = Modulo value.
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// step = Step by this amount.
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// Examples:
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// modrange(90,270,360, step=45); // Returns: [90,135,180,225,270]
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// modrange(270,90,360, step=45); // Returns: [270,315,0,45,90]
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// modrange(90,270,360, step=-45); // Returns: [90,45,0,315,270]
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// modrange(270,90,360, step=-45); // Returns: [270,225,180,135,90]
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function modrange(x, y, m, step=1) =
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let(
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a = posmod(x, m),
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b = posmod(y, m),
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c = step>0? (a>b? b+m : b) : (a<b? b-m : b)
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) [for (i=[a:step:c]) (i%m+m)%m];
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// Section: Random Number Generation
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// Function: rand_int()
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// Usage:
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// rand_int(min,max,N,[seed]);
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// Description:
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// Return a list of random integers in the range of min to max, inclusive.
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// Arguments:
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// min = Minimum integer value to return.
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// max = Maximum integer value to return.
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// N = Number of random integers to return.
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// seed = If given, sets the random number seed.
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// Example:
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// ints = rand_int(0,100,3);
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// int = rand_int(-10,10,1)[0];
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function rand_int(min, max, N, seed=undef) =
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assert(max >= min, "Max value cannot be smaller than min")
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let (rvect = is_def(seed) ? rands(min,max+1,N,seed) : rands(min,max+1,N))
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[for(entry = rvect) floor(entry)];
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// Function: gaussian_rands()
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// Usage:
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// gaussian_rands(mean, stddev, [N], [seed])
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// Description:
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// Returns a random number with a gaussian/normal distribution.
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// Arguments:
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// mean = The average random number returned.
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// stddev = The standard deviation of the numbers to be returned.
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// N = Number of random numbers to return. Default: 1
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// seed = If given, sets the random number seed.
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function gaussian_rands(mean, stddev, N=1, seed=undef) =
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let(nums = is_undef(seed)? rands(0,1,N*2) : rands(0,1,N*2,seed))
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[for (i = list_range(N)) mean + stddev*sqrt(-2*ln(nums[i*2]))*cos(360*nums[i*2+1])];
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// Function: log_rands()
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// Usage:
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// log_rands(minval, maxval, factor, [N], [seed]);
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// Description:
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// Returns a single random number, with a logarithmic distribution.
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// Arguments:
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// minval = Minimum value to return.
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// maxval = Maximum value to return. `minval` <= X < `maxval`.
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// factor = Log factor to use. Values of X are returned `factor` times more often than X+1.
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// N = Number of random numbers to return. Default: 1
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// seed = If given, sets the random number seed.
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function log_rands(minval, maxval, factor, N=1, seed=undef) =
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assert(maxval >= minval, "maxval cannot be smaller than minval")
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let(
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minv = 1-1/pow(factor,minval),
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maxv = 1-1/pow(factor,maxval),
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nums = is_undef(seed)? rands(minv, maxv, N) : rands(minv, maxv, N, seed)
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) [for (num=nums) -ln(1-num)/ln(factor)];
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// Section: GCD/GCF, LCM
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// If argument is a list return it. Otherwise return a singleton list containing the argument.
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function _force_list(x) = is_list(x) ? x : [x];
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// Function: gcd()
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// Usage:
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// gcd(a,b)
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// Description:
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// Computes the Greatest Common Divisor/Factor of `a` and `b`.
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function gcd(a,b) =
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assert(is_int(a) && is_int(b),"Arguments to gcd must be integers")
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b==0 ? abs(a) : gcd(b,a % b);
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// Computes lcm for two scalars
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function _lcm(a,b) =
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assert(is_int(a), "Invalid non-integer parameters to lcm")
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assert(is_int(b), "Invalid non-integer parameters to lcm")
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assert(a!=0 && b!=0, "Arguments to lcm must be nonzero")
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abs(a*b) / gcd(a,b);
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// Computes lcm for a list of values
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function _lcmlist(a) =
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len(a)==1 ? a[0] :
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_lcmlist(concat(slice(a,0,len(a)-2),[lcm(a[len(a)-2],a[len(a)-1])]));
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// Function: lcm()
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// Usage:
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// lcm(a,b)
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// lcm(list)
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// Description:
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// Computes the Least Common Multiple of the two arguments or a list of arguments. Inputs should
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// be non-zero integers. The output is always a positive integer. It is an error to pass zero
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// as an argument.
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function lcm(a,b=[]) =
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!is_list(a) && !is_list(b) ? _lcm(a,b) :
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let(
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arglist = concat(_force_list(a),_force_list(b))
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)
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assert(len(arglist)>0,"invalid call to lcm with empty list(s)")
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_lcmlist(arglist);
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// Section: Sums, Products, Aggregate Functions.
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// Function: sum()
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// Description:
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// Returns the sum of all entries in the given list.
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// If passed an array of vectors, returns a vector of sums of each part.
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// Arguments:
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// v = The list to get the sum of.
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// Example:
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// sum([1,2,3]); // returns 6.
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// sum([[1,2,3], [3,4,5], [5,6,7]]); // returns [9, 12, 15]
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function sum(v, _i=0, _acc) =
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_i>=len(v)? _acc :
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sum(v, _i=_i+1, _acc=is_undef(_acc)? v[_i] : _acc+v[_i]);
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// Function: cumsum()
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// Description:
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// Returns a list where each item is the cumulative sum of all items up to and including the corresponding entry in the input list.
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// If passed an array of vectors, returns a list of cumulative vectors sums.
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// Arguments:
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|
// v = The list to get the sum of.
|
|
// Example:
|
|
// cumsum([1,1,1]); // returns [1,2,3]
|
|
// cumsum([2,2,2]); // returns [2,4,6]
|
|
// cumsum([1,2,3]); // returns [1,3,6]
|
|
// cumsum([[1,2,3], [3,4,5], [5,6,7]]); // returns [[1,2,3], [4,6,8], [9,12,15]]
|
|
function cumsum(v,_i=0,_acc=[]) =
|
|
_i==len(v) ? _acc :
|
|
cumsum(
|
|
v, _i+1,
|
|
concat(
|
|
_acc,
|
|
[_i==0 ? v[_i] : select(_acc,-1)+v[_i]]
|
|
)
|
|
);
|
|
|
|
|
|
// Function: sum_of_squares()
|
|
// Description:
|
|
// Returns the sum of the square of each element of a vector.
|
|
// Arguments:
|
|
// v = The vector to get the sum of.
|
|
// Example:
|
|
// sum_of_squares([1,2,3]); // Returns: 14.
|
|
// sum_of_squares([1,2,4]); // Returns: 21
|
|
// sum_of_squares([-3,-2,-1]); // Returns: 14
|
|
function sum_of_squares(v, i=0, tot=0) = sum(vmul(v,v));
|
|
|
|
|
|
// Function: sum_of_sines()
|
|
// Usage:
|
|
// sum_of_sines(a,sines)
|
|
// Description:
|
|
// Gives the sum of a series of sines, at a given angle.
|
|
// Arguments:
|
|
// a = Angle to get the value for.
|
|
// sines = List of [amplitude, frequency, offset] items, where the frequency is the number of times the cycle repeats around the circle.
|
|
// Examples:
|
|
// v = sum_of_sines(30, [[10,3,0], [5,5.5,60]]);
|
|
function sum_of_sines(a, sines) =
|
|
sum([
|
|
for (s = sines) let(
|
|
ss=point3d(s),
|
|
v=ss.x*sin(a*ss.y+ss.z)
|
|
) v
|
|
]);
|
|
|
|
|
|
// Function: deltas()
|
|
// Description:
|
|
// Returns a list with the deltas of adjacent entries in the given list.
|
|
// Given [a,b,c,d], returns [b-a,c-b,d-c].
|
|
// Arguments:
|
|
// v = The list to get the deltas of.
|
|
// Example:
|
|
// deltas([2,5,9,17]); // returns [3,4,8].
|
|
// deltas([[1,2,3], [3,6,8], [4,8,11]]); // returns [[2,4,5], [1,2,3]]
|
|
function deltas(v) = [for (p=pair(v)) p.y-p.x];
|
|
|
|
|
|
// Function: product()
|
|
// Description:
|
|
// Returns the product of all entries in the given list.
|
|
// If passed an array of vectors, returns a vector of products of each part.
|
|
// If passed an array of matrices, returns a the resulting product matrix.
|
|
// Arguments:
|
|
// v = The list to get the product of.
|
|
// Example:
|
|
// product([2,3,4]); // returns 24.
|
|
// product([[1,2,3], [3,4,5], [5,6,7]]); // returns [15, 48, 105]
|
|
function product(v, i=0, tot=undef) = i>=len(v)? tot : product(v, i+1, ((tot==undef)? v[i] : is_vector(v[i])? vmul(tot,v[i]) : tot*v[i]));
|
|
|
|
|
|
// Function: mean()
|
|
// Description:
|
|
// Returns the mean of all entries in the given array.
|
|
// If passed an array of vectors, returns a vector of mean of each part.
|
|
// Arguments:
|
|
// v = The list of values to get the mean of.
|
|
// Example:
|
|
// mean([2,3,4]); // returns 3.
|
|
// mean([[1,2,3], [3,4,5], [5,6,7]]); // returns [3, 4, 5]
|
|
function mean(v) = sum(v)/len(v);
|
|
|
|
|
|
|
|
// Section: Determinants
|
|
|
|
// Function: det2()
|
|
// Description:
|
|
// Optimized function that returns the determinant for the given 2x2 square matrix.
|
|
// Arguments:
|
|
// M = The 2x2 square matrix to get the determinant of.
|
|
// Example:
|
|
// M = [ [6,-2], [1,8] ];
|
|
// det = det2(M); // Returns: 50
|
|
function det2(M) = M[0][0] * M[1][1] - M[0][1]*M[1][0];
|
|
|
|
|
|
// Function: det3()
|
|
// Description:
|
|
// Optimized function that returns the determinant for the given 3x3 square matrix.
|
|
// Arguments:
|
|
// M = The 3x3 square matrix to get the determinant of.
|
|
// Example:
|
|
// M = [ [6,4,-2], [1,-2,8], [1,5,7] ];
|
|
// det = det3(M); // Returns: -334
|
|
function det3(M) =
|
|
M[0][0] * (M[1][1]*M[2][2]-M[2][1]*M[1][2]) -
|
|
M[1][0] * (M[0][1]*M[2][2]-M[2][1]*M[0][2]) +
|
|
M[2][0] * (M[0][1]*M[1][2]-M[1][1]*M[0][2]);
|
|
|
|
|
|
// Function: determinant()
|
|
// Description:
|
|
// Returns the determinant for the given square matrix.
|
|
// Arguments:
|
|
// M = The NxN square matrix to get the determinant of.
|
|
// Example:
|
|
// M = [ [6,4,-2,9], [1,-2,8,3], [1,5,7,6], [4,2,5,1] ];
|
|
// det = determinant(M); // Returns: 2267
|
|
function determinant(M) =
|
|
assert(len(M)==len(M[0]))
|
|
len(M)==1? M[0][0] :
|
|
len(M)==2? det2(M) :
|
|
len(M)==3? det3(M) :
|
|
sum(
|
|
[for (col=[0:1:len(M)-1])
|
|
((col%2==0)? 1 : -1) *
|
|
M[col][0] *
|
|
determinant(
|
|
[for (r=[1:1:len(M)-1])
|
|
[for (c=[0:1:len(M)-1])
|
|
if (c!=col) M[c][r]
|
|
]
|
|
]
|
|
)
|
|
]
|
|
);
|
|
|
|
|
|
|
|
// Section: Comparisons and Logic
|
|
|
|
// Function: approx()
|
|
// Usage:
|
|
// approx(a,b,[eps])
|
|
// Description:
|
|
// Compares two numbers or vectors, and returns true if they are closer than `eps` to each other.
|
|
// Arguments:
|
|
// a = First value.
|
|
// b = Second value.
|
|
// eps = The maximum allowed difference between `a` and `b` that will return true.
|
|
// Example:
|
|
// approx(-0.3333333333,-1/3); // Returns: true
|
|
// approx(0.3333333333,1/3); // Returns: true
|
|
// approx(0.3333,1/3); // Returns: false
|
|
// approx(0.3333,1/3,eps=1e-3); // Returns: true
|
|
// approx(PI,3.1415926536); // Returns: true
|
|
function approx(a,b,eps=EPSILON) = let(c=a-b) (is_num(c)? abs(c) : norm(c)) <= eps;
|
|
|
|
|
|
function _type_num(x) =
|
|
is_undef(x)? 0 :
|
|
is_bool(x)? 1 :
|
|
is_num(x)? 2 :
|
|
is_string(x)? 3 :
|
|
is_list(x)? 4 : 5;
|
|
|
|
|
|
// Function: compare_vals()
|
|
// Usage:
|
|
// compare_vals(a, b);
|
|
// Description:
|
|
// Compares two values. Lists are compared recursively.
|
|
// If types are not the same, then undef < bool < num < str < list < range.
|
|
// Arguments:
|
|
// a = First value to compare.
|
|
// b = Second value to compare.
|
|
function compare_vals(a, b) =
|
|
(a==b)? 0 :
|
|
let(t1=_type_num(a), t2=_type_num(b)) (t1!=t2)? (t1-t2) :
|
|
is_list(a)? compare_lists(a,b) :
|
|
(a<b)? -1 : (a>b)? 1 : 0;
|
|
|
|
|
|
// Function: compare_lists()
|
|
// Usage:
|
|
// compare_lists(a, b)
|
|
// Description:
|
|
// Compare contents of two lists using `compare_vals()`.
|
|
// Returns <0 if `a`<`b`.
|
|
// Returns 0 if `a`==`b`.
|
|
// Returns >0 if `a`>`b`.
|
|
// Arguments:
|
|
// a = First list to compare.
|
|
// b = Second list to compare.
|
|
function compare_lists(a, b) =
|
|
a==b? 0 : let(
|
|
cmps = [
|
|
for(i=[0:1:min(len(a),len(b))-1]) let(
|
|
cmp = compare_vals(a[i],b[i])
|
|
) if(cmp!=0) cmp
|
|
]
|
|
) cmps==[]? (len(a)-len(b)) : cmps[0];
|
|
|
|
|
|
// Function: any()
|
|
// Description:
|
|
// Returns true if any item in list `l` evaluates as true.
|
|
// If `l` is a lists of lists, `any()` is applied recursively to each sublist.
|
|
// Arguments:
|
|
// l = The list to test for true items.
|
|
// Example:
|
|
// any([0,false,undef]); // Returns false.
|
|
// any([1,false,undef]); // Returns true.
|
|
// any([1,5,true]); // Returns true.
|
|
// any([[0,0], [0,0]]); // Returns false.
|
|
// any([[0,0], [1,0]]); // Returns true.
|
|
function any(l, i=0, succ=false) =
|
|
(i>=len(l) || succ)? succ :
|
|
any(
|
|
l, i=i+1, succ=(
|
|
is_list(l[i])? any(l[i]) :
|
|
!(!l[i])
|
|
)
|
|
);
|
|
|
|
|
|
// Function: all()
|
|
// Description:
|
|
// Returns true if all items in list `l` evaluate as true.
|
|
// If `l` is a lists of lists, `all()` is applied recursively to each sublist.
|
|
// Arguments:
|
|
// l = The list to test for true items.
|
|
// Example:
|
|
// all([0,false,undef]); // Returns false.
|
|
// all([1,false,undef]); // Returns false.
|
|
// all([1,5,true]); // Returns true.
|
|
// all([[0,0], [0,0]]); // Returns false.
|
|
// all([[0,0], [1,0]]); // Returns false.
|
|
// all([[1,1], [1,1]]); // Returns true.
|
|
function all(l, i=0, fail=false) =
|
|
(i>=len(l) || fail)? (!fail) :
|
|
all(
|
|
l, i=i+1, fail=(
|
|
is_list(l[i])? !all(l[i]) :
|
|
!l[i]
|
|
)
|
|
);
|
|
|
|
|
|
// Function: count_true()
|
|
// Usage:
|
|
// count_true(l)
|
|
// Description:
|
|
// Returns the number of items in `l` that evaluate as true.
|
|
// If `l` is a lists of lists, this is applied recursively to each
|
|
// sublist. Returns the total count of items that evaluate as true
|
|
// in all recursive sublists.
|
|
// Arguments:
|
|
// l = The list to test for true items.
|
|
// nmax = If given, stop counting if `nmax` items evaluate as true.
|
|
// Example:
|
|
// count_true([0,false,undef]); // Returns 0.
|
|
// count_true([1,false,undef]); // Returns 1.
|
|
// count_true([1,5,false]); // Returns 2.
|
|
// count_true([1,5,true]); // Returns 3.
|
|
// count_true([[0,0], [0,0]]); // Returns 0.
|
|
// count_true([[0,0], [1,0]]); // Returns 1.
|
|
// count_true([[1,1], [1,1]]); // Returns 4.
|
|
// count_true([[1,1], [1,1]], nmax=3); // Returns 3.
|
|
function count_true(l, nmax=undef, i=0, cnt=0) =
|
|
(i>=len(l) || (nmax!=undef && cnt>=nmax))? cnt :
|
|
count_true(
|
|
l=l, nmax=nmax, i=i+1, cnt=cnt+(
|
|
is_list(l[i])? count_true(l[i], nmax=nmax-cnt) :
|
|
(l[i]? 1 : 0)
|
|
)
|
|
);
|
|
|
|
|
|
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|