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Reorganize math.scad
This commit is contained in:
Revar Desmera
parent
fe7b87e92d
commit
48d30fc686
54
arrays.scad
54
arrays.scad
@ -806,6 +806,38 @@ function subindex(v, idx) = [
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];
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// Function: min_index()
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// Usage:
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// min_index(vals,[all]);
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// Description:
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// Returns the index of the first occurrence of the minimum value in the given list.
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// If `all` is true then returns a list of all indices where the minimum value occurs.
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// Arguments:
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// vals = vector of values
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// all = set to true to return indices of all occurences of the minimum. Default: false
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// Example:
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// min_index([5,3,9,6,2,7,8,2,1]); // Returns: 4
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// min_index([5,3,9,6,2,7,8,2,1],all=true); // Returns: [4,7]
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function min_index(vals, all=false) =
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all ? search(min(vals),vals,0) : search(min(vals), vals)[0];
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// Function: max_index()
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// Usage:
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// max_index(vals,[all]);
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// Description:
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// Returns the index of the first occurrence of the maximum value in the given list.
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// If `all` is true then returns a list of all indices where the maximum value occurs.
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// Arguments:
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// vals = vector of values
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// all = set to true to return indices of all occurences of the maximum. Default: false
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// Example:
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// max_index([5,3,9,6,2,7,8,9,1]); // Returns: 2
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// max_index([5,3,9,6,2,7,8,9,1],all=true); // Returns: [2,7]
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function max_index(vals, all=false) =
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all ? search(max(vals),vals,0) : search(max(vals), vals)[0];
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// Function: pair()
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// Usage:
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// pair(v)
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@ -858,6 +890,28 @@ function triplet_wrap(v) =
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[for (i=[0:1:len(v)-1]) [v[i],v[(i+1)%len(v)],v[(i+2)%len(v)]]];
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// Function: permute()
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// Usage:
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// list = permute(l, [n]);
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// Description:
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// Returns an ordered list of every unique permutation of `n` items out of the given list `l`.
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// For the list `[1,2,3,4]`, with `n=2`, this will return `[[1,2], [1,3], [1,4], [2,3], [2,4], [3,4]]`.
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// For the list `[1,2,3,4]`, with `n=3`, this will return `[[1,2,3], [1,2,4], [1,3,4], [2,3,4]]`.
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// Arguments:
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// l = The list to provide permutations for.
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// n = The number of items in each permutation. Default: 2
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// Example:
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// pairs = permute([3,4,5,6]); // Returns: [[3,4],[3,5],[3,6],[4,5],[4,6],[5,6]]
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// triplets = permute([3,4,5,6],n=3); // Returns: [[3,4,5],[3,4,6],[3,5,6],[4,5,6]]
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// Example(2D):
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// for (p=permute(regular_ngon(n=7,d=100))) stroke(p);
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function permute(l,n=2,_s=0) =
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assert(is_list(l))
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assert(len(l)-_s >= n)
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n==1? [for (i=[_s:1:len(l)-1]) [l[i]]] :
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[for (i=[_s:1:len(l)-n], p=permute(l,n=n-1,_s=i+1)) concat([l[i]], p)];
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// Function: zip()
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// Usage:
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// zip(v1, v2, v3, [fit], [fill]);
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22
common.scad
22
common.scad
@ -64,6 +64,16 @@ function is_def(x) = !is_undef(x);
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function is_str(x) = is_string(x);
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// Function: is_int()
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// Usage:
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// is_int(n)
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// Description:
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// Returns true if the given value is an integer (it is a number and it rounds to itself).
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function is_int(n) = is_num(n) && n == round(n);
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function is_integer(n) = is_num(n) && n == round(n);
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// Section: Handling `undef`s.
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@ -184,4 +194,16 @@ function scalar_vec3(v, dflt=undef) =
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!is_undef(dflt)? [v,dflt,dflt] : [v,v,v];
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// Function: segs()
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// Usage:
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// sides = segs(r);
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// Description:
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// Calculate the standard number of sides OpenSCAD would give a circle based on `$fn`, `$fa`, and `$fs`.
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// Arguments:
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// r = Radius of circle to get the number of segments for.
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function segs(r) =
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$fn>0? ($fn>3? $fn : 3) :
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ceil(max(5, min(360/$fa, abs(r)*2*PI/$fs)));
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// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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372
math.scad
372
math.scad
@ -15,7 +15,138 @@ 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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// Section: Simple Calculations
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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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@ -104,6 +235,8 @@ function quantup(x,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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@ -122,55 +255,6 @@ function quantup(x,y) =
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function constrain(v, minval, maxval) = min(maxval, max(minval, v));
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// Function: approx()
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// Usage:
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// approx(a,b,[eps])
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// Description:
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// Compares two numbers or vectors, and returns true if they are closer than `eps` to each other.
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// Arguments:
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// a = First value.
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// b = Second value.
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// eps = The maximum allowed difference between `a` and `b` that will return true.
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// Example:
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// approx(-0.3333333333,-1/3); // Returns: true
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// approx(0.3333333333,1/3); // Returns: true
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// approx(0.3333,1/3); // Returns: false
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// approx(0.3333,1/3,eps=1e-3); // Returns: true
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// approx(PI,3.1415926536); // Returns: true
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function approx(a,b,eps=EPSILON) = let(c=a-b) (is_num(c)? abs(c) : norm(c)) <= eps;
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// Function: min_index()
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// Usage:
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// min_index(vals,[all]);
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// Description:
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// Returns the index of the first occurrence of the mainimum value in the given list.
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// If `all` is true then returns a list of all indices where the minimum value occurs.
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// Arguments:
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// vals = vector of values
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// all = set to true to return indices of all occurences of the minimum. Default: false
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// Example:
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// min_index([5,3,9,6,2,7,8,2,1]); // Returns: 4
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// min_index([5,3,9,6,2,7,8,2,1],all=true); // Returns: [4,7]
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function min_index(vals, all=false) =
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all ? search(min(vals),vals,0) : search(min(vals), vals)[0];
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// Function: max_index()
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// Usage:
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// max_index(vals,[all]);
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// Description:
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// Returns the index of the first occurrence of the maximum value in the given list.
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// If `all` is true then returns a list of all indices where the maximum value occurs.
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// Arguments:
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// vals = vector of values
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// all = set to true to return indices of all occurences of the maximum. Default: false
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// Example:
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// max_index([5,3,9,6,2,7,8,9,1]); // Returns: 2
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// max_index([5,3,9,6,2,7,8,9,1],all=true); // Returns: [2,7]
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function max_index(vals, all=false) =
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all ? search(max(vals),vals,0) : search(max(vals), vals)[0];
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// Function: posmod()
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// Usage:
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// posmod(x,m)
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@ -229,26 +313,8 @@ function modrange(x, y, m, step=1) =
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) [for (i=[a:step:c]) (i%m+m)%m];
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// Function: sqr()
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// Usage:
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// sqr(x);
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// Description: 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: Returns the logarith base 10 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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// Section: Random Number Generation
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// Function: rand_int()
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// Usage:
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@ -304,72 +370,55 @@ function log_rands(minval, maxval, factor, N=1, seed=undef) =
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) [for (num=nums) -ln(1-num)/ln(factor)];
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// Function: segs()
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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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// Calculate the standard number of sides OpenSCAD would give a circle based on `$fn`, `$fa`, and `$fs`.
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// Arguments:
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// r = Radius of circle to get the number of segments for.
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function segs(r) =
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$fn>0? ($fn>3? $fn : 3) :
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ceil(max(5, min(360/$fa, abs(r)*2*PI/$fs)));
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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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// Function: lerp()
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// Description: Interpolate between two values or vectors.
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// Arguments:
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// a = First value.
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// b = Second value.
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// u = The proportion from `a` to `b` to calculate. Valid 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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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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// 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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// Function: hypot()
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// Description: 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.
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function hypot(x,y,z=0) =
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norm([x,y,z]);
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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: 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: 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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// 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);
|
||||
|
||||
|
||||
// Function: asinh()
|
||||
// Description: Takes a value `x`, and returns the inverse hyperbolic sine of it.
|
||||
function asinh(x) =
|
||||
ln(x+sqrt(x*x+1));
|
||||
|
||||
|
||||
// Function: acosh()
|
||||
// Description: Takes a value `x`, and returns the inverse hyperbolic cosine of it.
|
||||
function acosh(x) =
|
||||
ln(x+sqrt(x*x-1));
|
||||
|
||||
|
||||
// Function: atanh()
|
||||
// Description: Takes a value `x`, and returns the inverse hyperbolic tangent of it.
|
||||
function atanh(x) =
|
||||
ln((1+x)/(1-x))/2;
|
||||
|
||||
// Section: Sums, Products, Aggregate Functions.
|
||||
|
||||
// Function: sum()
|
||||
// Description:
|
||||
@ -380,7 +429,12 @@ function atanh(x) =
|
||||
// Example:
|
||||
// sum([1,2,3]); // returns 6.
|
||||
// sum([[1,2,3], [3,4,5], [5,6,7]]); // returns [9, 12, 15]
|
||||
function sum(v, _i=0, _acc=undef) = _i>=len(v)? _acc : sum(v, _i+1, ((_acc==undef)? v[_i] : _acc+v[_i]));
|
||||
function sum(v, _i=0, _acc=undef) =
|
||||
_i>=len(v)? _acc :
|
||||
sum(
|
||||
v, _i=_i+1,
|
||||
_acc=v[_i] + (is_undef(_acc)? 0 : _acc)
|
||||
);
|
||||
|
||||
|
||||
// Function: cumsum()
|
||||
@ -473,6 +527,9 @@ function product(v, i=0, tot=undef) = i>=len(v)? tot : product(v, i+1, ((tot==un
|
||||
function mean(v) = sum(v)/len(v);
|
||||
|
||||
|
||||
|
||||
// Section: Determinants
|
||||
|
||||
// Function: det2()
|
||||
// Description:
|
||||
// Optimized function that returns the determinant for the given 2x2 square matrix.
|
||||
@ -526,8 +583,26 @@ function determinant(M) =
|
||||
);
|
||||
|
||||
|
||||
|
||||
// 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 :
|
||||
@ -648,50 +723,5 @@ function count_true(l, nmax=undef, i=0, cnt=0) =
|
||||
)
|
||||
);
|
||||
|
||||
// If argument is a list return it. Otherwise return a singleton list containing the argument.
|
||||
function _force_list(x) = is_list(x) ? x : [x];
|
||||
|
||||
// Function: gcd()
|
||||
// Usage:
|
||||
// gcd(a,b)
|
||||
// Description:
|
||||
// Computes the greatest common divisor of `a` and `b`.
|
||||
function gcd(a,b) =
|
||||
assert(is_integer(a) && is_integer(b),"Arguments to gcd must be integers")
|
||||
b==0 ? abs(a) : gcd(b,a % b);
|
||||
|
||||
// Computes lcm for two scalars
|
||||
function _lcm(a,b) =
|
||||
let(
|
||||
parmok = is_integer(a) && is_integer(b),
|
||||
dummy=assert(parmok,"Invalid non-integer parameters to lcm")
|
||||
assert(a!=0 && b!=0, "Arguments to lcm must be nonzero")
|
||||
)
|
||||
abs(a*b) / gcd(a,b);
|
||||
|
||||
// Computes lcm for a list of values
|
||||
function _lcmlist(a) =
|
||||
len(a)==1 ? a[0] : _lcmlist(concat(slice(a,0,len(a)-2),[lcm(a[len(a)-2],a[len(a)-1])]));
|
||||
|
||||
// Function: lcm()
|
||||
// Usage:
|
||||
// lcm(a,b)
|
||||
// lcm(list)
|
||||
// Description: Computes the least common multiple of the two arguments or a list of arguments. Inputs should be
|
||||
// nonzero integers. The output is always a positive integer. It is an error to pass zero as an argument.
|
||||
function lcm(a,b=[]) =
|
||||
!is_list(a) && !is_list(b) ? _lcm(a,b) :
|
||||
let(
|
||||
arglist = concat(_force_list(a),_force_list(b))
|
||||
)
|
||||
assert(len(arglist)>0,"invalid call to lcm with empty list(s)")
|
||||
_lcmlist(arglist);
|
||||
|
||||
// Function: is_integer()
|
||||
// Usage:
|
||||
// is_integer(n)
|
||||
// Description: returns true if the given value is an integer (it is a number and it rounds to itself).
|
||||
function is_integer(n) = is_num(n) && n == round(n);
|
||||
|
||||
|
||||
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|
||||
|
||||
@ -8,7 +8,7 @@
|
||||
//////////////////////////////////////////////////////////////////////
|
||||
|
||||
|
||||
BOSL_VERSION = [2,0,74];
|
||||
BOSL_VERSION = [2,0,75];
|
||||
|
||||
|
||||
// Section: BOSL Library Version Functions
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user