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https://github.com/BelfrySCAD/BOSL2.git
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838 lines
32 KiB
OpenSCAD
838 lines
32 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: comparisons.scad
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// Functions for comparisons with lists, ordering and sorting
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// Includes:
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// include <BOSL2/std.scad>
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//////////////////////////////////////////////////////////////////////
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// Section: List comparison operations
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// Function: approx()
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// Usage:
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// test = approx(a, b, [eps])
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// Description:
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// Compares two numbers, vectors, or matrices. Returns true if they are closer than `eps` to each other.
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// Results are undefined if `a` and `b` are of different types, or if vectors or matrices contain non-numbers.
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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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// test1 = approx(-0.3333333333,-1/3); // Returns: true
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// test2 = approx(0.3333333333,1/3); // Returns: true
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// test3 = approx(0.3333,1/3); // Returns: false
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// test4 = approx(0.3333,1/3,eps=1e-3); // Returns: true
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// test5 = approx(PI,3.1415926536); // Returns: true
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// test6 = approx([0,0,sin(45)],[0,0,sqrt(2)/2]); // Returns: true
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function approx(a,b,eps=EPSILON) =
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a == b? is_bool(a) == is_bool(b) :
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is_num(a) && is_num(b)? abs(a-b) <= eps :
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is_list(a) && is_list(b) && len(a) == len(b)? (
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[] == [
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for (i=idx(a))
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let(aa=a[i], bb=b[i])
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if(
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is_num(aa) && is_num(bb)? abs(aa-bb) > eps :
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!approx(aa,bb,eps=eps)
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) 1
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]
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) : false;
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// Function: all_zero()
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// Usage:
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// x = all_zero(x, [eps]);
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// Description:
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// Returns true if the finite number passed to it is approximately zero, to within `eps`.
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// If passed a list returns true if all its entries are approximately zero.
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// Otherwise, returns false.
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// Arguments:
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// x = The value to check.
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// eps = The maximum allowed variance. Default: `EPSILON` (1e-9)
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// Example:
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// a = all_zero(0); // Returns: true.
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// b = all_zero(1e-3); // Returns: false.
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// c = all_zero([0,0,0]); // Returns: true.
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// d = all_zero([0,0,1e-3]); // Returns: false.
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function all_zero(x, eps=EPSILON) =
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is_finite(x)? abs(x)<eps :
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is_vector(x) && [for (xx=x) if(abs(xx)>eps) 1] == [];
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// Function: all_nonzero()
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// Usage:
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// test = all_nonzero(x, [eps]);
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// Description:
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// Returns true if the finite number passed to it is different from zero by `eps`.
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// If passed a list returns true if all the entries of the list are different from zero by `eps`.
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// Otherwise, returns false.
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// Arguments:
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// x = The value to check.
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// eps = The maximum allowed variance. Default: `EPSILON` (1e-9)
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// Example:
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// a = all_nonzero(0); // Returns: false.
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// b = all_nonzero(1e-3); // Returns: true.
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// c = all_nonzero([0,0,0]); // Returns: false.
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// d = all_nonzero([0,0,1e-3]); // Returns: false.
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// e = all_nonzero([1e-3,1e-3,1e-3]); // Returns: true.
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function all_nonzero(x, eps=EPSILON) =
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is_finite(x)? abs(x)>eps :
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is_vector(x) && [for (xx=x) if(abs(xx)<eps) 1] == [];
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// Function: all_positive()
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// Usage:
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// test = all_positive(x,[eps]);
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// Description:
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// Returns true if the finite number passed to it is greater than zero.
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// If passed a list returns true if all the entries are positive.
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// Otherwise, returns false.
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// Arguments:
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// x = The value to check.
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// eps = Tolerance. Default: 0
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// Example:
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// a = all_positive(-2); // Returns: false.
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// b = all_positive(0); // Returns: false.
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// c = all_positive(2); // Returns: true.
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// d = all_positive([0,0,0]); // Returns: false.
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// e = all_positive([0,1,2]); // Returns: false.
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// f = all_positive([3,1,2]); // Returns: true.
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// g = all_positive([3,-1,2]); // Returns: false.
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function all_positive(x,eps=0) =
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is_num(x)? x>eps :
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is_vector(x) && [for (xx=x) if(xx<=0) 1] == [];
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// Function: all_negative()
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// Usage:
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// test = all_negative(x, [eps]);
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// Description:
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// Returns true if the finite number passed to it is less than zero.
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// If passed a list, recursively checks if all items in the list are negative.
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// Otherwise, returns false.
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// Arguments:
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// x = The value to check.
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// eps = tolerance. Default: 0
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// Example:
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// a = all_negative(-2); // Returns: true.
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// b = all_negative(0); // Returns: false.
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// c = all_negative(2); // Returns: false.
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// d = all_negative([0,0,0]); // Returns: false.
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// e = all_negative([0,1,2]); // Returns: false.
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// f = all_negative([3,1,2]); // Returns: false.
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// g = all_negative([3,-1,2]); // Returns: false.
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// h = all_negative([-3,-1,-2]); // Returns: true.
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function all_negative(x, eps=0) =
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is_num(x)? x<-eps :
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is_vector(x) && [for (xx=x) if(xx>=-eps) 1] == [];
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// Function: all_nonpositive()
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// Usage:
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// all_nonpositive(x, [eps]);
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// Description:
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// Returns true if the finite number passed to it is less than or equal to zero.
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// If passed a list, recursively checks if all items in the list are nonpositive.
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// Otherwise, returns false.
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// Arguments:
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// x = The value to check.
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// eps = tolerance. Default: 0
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// Example:
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// a = all_nonpositive(-2); // Returns: true.
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// b = all_nonpositive(0); // Returns: true.
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// c = all_nonpositive(2); // Returns: false.
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// d = all_nonpositive([0,0,0]); // Returns: true.
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// e = all_nonpositive([0,1,2]); // Returns: false.
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// f = all_nonpositive([3,1,2]); // Returns: false.
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// g = all_nonpositive([3,-1,2]); // Returns: false.
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// h = all_nonpositive([-3,-1,-2]); // Returns: true.
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function all_nonpositive(x,eps=0) =
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is_num(x)? x<=eps :
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is_vector(x) && [for (xx=x) if(xx>eps) 1] == [];
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// Function: all_nonnegative()
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// Usage:
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// all_nonnegative(x, [eps]);
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// Description:
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// Returns true if the finite number passed to it is greater than or equal to zero.
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// If passed a list, recursively checks if all items in the list are nonnegative.
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// Otherwise, returns false.
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// Arguments:
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// x = The value to check.
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// eps = tolerance. Default: 0
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// Example:
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// a = all_nonnegative(-2); // Returns: false.
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// b = all_nonnegative(0); // Returns: true.
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// c = all_nonnegative(2); // Returns: true.
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// d = all_nonnegative([0,0,0]); // Returns: true.
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// e = all_nonnegative([0,1,2]); // Returns: true.
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// f = all_nonnegative([0,-1,-2]); // Returns: false.
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// g = all_nonnegative([3,1,2]); // Returns: true.
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// h = all_nonnegative([3,-1,2]); // Returns: false.
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// i = all_nonnegative([-3,-1,-2]); // Returns: false.
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function all_nonnegative(x,eps=0) =
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is_num(x)? x>=-eps :
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is_vector(x) && [for (xx=x) if(xx<-eps) 1] == [];
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// Function: all_equal()
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// Usage:
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// b = all_equal(vec, [eps]);
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// Description:
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// Returns true if all of the entries in vec are equal to each other, or approximately equal to each other if eps is set.
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// Arguments:
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// vec = vector to check
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// eps = Set to tolerance for approximate equality. Default: 0
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function all_equal(vec,eps=0) =
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eps==0 ? [for(v=vec) if (v!=vec[0]) v] == []
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: [for(v=vec) if (!approx(v,vec[0],eps)) v] == [];
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// Function: is_increasing()
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// Usage:
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// bool = is_increasing(list);
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// Topics: List Handling
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// See Also: max_index(), min_index(), is_decreasing()
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// Description:
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// Returns true if the list is (non-strictly) increasing, or strictly increasing if strict is set to true.
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// The list can be a list of any items that OpenSCAD can compare, or it can be a string which will be
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// evaluated character by character.
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// Arguments:
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// list = list (or string) to check
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// strict = set to true to test that list is strictly increasing
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// Example:
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// a = is_increasing([1,2,3,4]); // Returns: true
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// b = is_increasing([1,3,2,4]); // Returns: false
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// c = is_increasing([1,3,3,4]); // Returns: true
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// d = is_increasing([1,3,3,4],strict=true); // Returns: false
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// e = is_increasing([4,3,2,1]); // Returns: false
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function is_increasing(list,strict=false) =
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assert(is_list(list)||is_string(list))
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strict ? len([for (p=pair(list)) if(p.x>=p.y) true])==0
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: len([for (p=pair(list)) if(p.x>p.y) true])==0;
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// Function: is_decreasing()
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// Usage:
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// bool = is_decreasing(list);
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// Topics: List Handling
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// See Also: max_index(), min_index(), is_increasing()
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// Description:
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// Returns true if the list is (non-strictly) decreasing, or strictly decreasing if strict is set to true.
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// The list can be a list of any items that OpenSCAD can compare, or it can be a string which will be
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// evaluated character by character.
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// Arguments:
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// list = list (or string) to check
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// strict = set to true to test that list is strictly decreasing
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// Example:
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// a = is_decreasing([1,2,3,4]); // Returns: false
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// b = is_decreasing([4,2,3,1]); // Returns: false
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// c = is_decreasing([4,3,2,1]); // Returns: true
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function is_decreasing(list,strict=false) =
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assert(is_list(list)||is_string(list))
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strict ? len([for (p=pair(list)) if(p.x<=p.y) true])==0
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: len([for (p=pair(list)) if(p.x<p.y) true])==0;
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function _type_num(x) =
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is_undef(x)? 0 :
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is_bool(x)? 1 :
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is_num(x)? 2 :
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is_nan(x)? 3 :
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is_string(x)? 4 :
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is_list(x)? 5 : 6;
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// Function: compare_vals()
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// Usage:
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// test = compare_vals(a, b);
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// Description:
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// Compares two values. Lists are compared recursively.
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// Returns <0 if a<b. Returns >0 if a>b. Returns 0 if a==b.
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// If types are not the same, then undef < bool < nan < num < str < list < range.
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// Arguments:
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// a = First value to compare.
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// b = Second value to compare.
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function compare_vals(a, b) =
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(a==b)? 0 :
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let(t1=_type_num(a), t2=_type_num(b)) (t1!=t2)? (t1-t2) :
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is_list(a)? compare_lists(a,b) :
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is_nan(a)? 0 :
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(a<b)? -1 : (a>b)? 1 : 0;
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// Function: compare_lists()
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// Usage:
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// test = compare_lists(a, b)
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// Description:
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// Compare contents of two lists using `compare_vals()`.
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// Returns <0 if `a`<`b`.
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// Returns 0 if `a`==`b`.
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// Returns >0 if `a`>`b`.
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// Arguments:
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// a = First list to compare.
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// b = Second list to compare.
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function compare_lists(a, b) =
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a==b? 0 :
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let(
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cmps = [
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for (i = [0:1:min(len(a),len(b))-1])
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let( cmp = compare_vals(a[i],b[i]) )
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if (cmp!=0) cmp
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]
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)
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cmps==[]? (len(a)-len(b)) : cmps[0];
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// Section: Finding the index of the minimum or maximum of a list
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// Function: min_index()
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// Usage:
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// idx = min_index(vals);
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// idxlist = min_index(vals, all=true);
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// Topics: List Handling
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// See Also: max_index(), is_increasing(), is_decreasing()
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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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// a = min_index([5,3,9,6,2,7,8,2,1]); // Returns: 8
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// b = min_index([5,3,9,6,2,7,8,2,7],all=true); // Returns: [4,7]
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function min_index(vals, all=false) =
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assert( is_vector(vals) && len(vals)>0 , "Invalid or empty list of numbers.")
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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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// idx = max_index(vals);
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// idxlist = max_index(vals, all=true);
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// Topics: List Handling
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// See Also: min_index(), is_increasing(), is_decreasing()
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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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assert( is_vector(vals) && len(vals)>0 , "Invalid or empty list of numbers.")
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all ? search(max(vals),vals,0) : search(max(vals), vals)[0];
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// Section: Dealing with duplicate list entries
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// Function: find_approx()
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// Topics: List Handling
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// See Also: in_list()
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// Usage:
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// idx = find_approx(val, list, [start=], [eps=]);
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// indices = find_approx(val, list, all=true, [start=], [eps=]);
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// Description:
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// Finds the first item in `list` that matches `val`, returning the index. Returns `undef` if there is no match.
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// Arguments:
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// val = The value to search for.
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// list = The list to search through.
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// ---
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// start = The index to start searching from. Default: 0
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// all = If true, returns a list of all matching item indices.
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// eps = The maximum allowed floating point rounding error for numeric comparisons.
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function find_approx(val, list, start=0, all=false, eps=EPSILON) =
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all ? [for (i=[start:1:len(list)-1]) if (approx(val, list[i], eps=eps)) i]
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: __find_approx(val, list, eps=eps, i=start);
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function __find_approx(val, list, eps, i=0) =
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i >= len(list)? undef :
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approx(val, list[i], eps=eps)
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? i
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: __find_approx(val, list, eps=eps, i=i+1);
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// Function: deduplicate()
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// Usage:
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// list = deduplicate(list, [close], [eps]);
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// Topics: List Handling
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// See Also: deduplicate_indexed()
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// Description:
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// Removes consecutive duplicate items in a list.
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// When `eps` is zero, the comparison between consecutive items is exact.
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// Otherwise, when all list items and subitems are numbers, the comparison is within the tolerance `eps`.
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// Unlike `unique()` only consecutive duplicates are removed and the list is *not* sorted.
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// Arguments:
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// list = The list to deduplicate.
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// closed = If true, drops trailing items if they match the first list item.
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// eps = The maximum tolerance between items.
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// Example:
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// a = deduplicate([8,3,4,4,4,8,2,3,3,8,8]); // Returns: [8,3,4,8,2,3,8]
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// b = deduplicate(closed=true, [8,3,4,4,4,8,2,3,3,8,8]); // Returns: [8,3,4,8,2,3]
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// c = deduplicate("Hello"); // Returns: "Helo"
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// d = deduplicate([[3,4],[7,2],[7,1.99],[1,4]],eps=0.1); // Returns: [[3,4],[7,2],[1,4]]
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// e = deduplicate([[7,undef],[7,undef],[1,4],[1,4+1e-12]],eps=0); // Returns: [[7,undef],[1,4],[1,4+1e-12]]
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function deduplicate(list, closed=false, eps=EPSILON) =
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assert(is_list(list)||is_string(list))
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let(
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l = len(list),
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end = l-(closed?0:1)
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)
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is_string(list) ? str_join([for (i=[0:1:l-1]) if (i==end || list[i] != list[(i+1)%l]) list[i]]) :
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eps==0 ? [for (i=[0:1:l-1]) if (i==end || list[i] != list[(i+1)%l]) list[i]] :
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[for (i=[0:1:l-1]) if (i==end || !approx(list[i], list[(i+1)%l], eps)) list[i]];
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// Function: deduplicate_indexed()
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// Usage:
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// new_idxs = deduplicate_indexed(list, indices, [closed], [eps]);
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// Topics: List Handling
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// See Also: deduplicate()
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// Description:
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// Given a list, and a list of indices, removes consecutive indices corresponding to list values that are equal
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// or approximately equal.
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// Arguments:
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// list = The list that the indices index into.
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// indices = The list of indices to deduplicate.
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// closed = If true, drops trailing indices if their list value matches the list value corresponding to the first index.
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// eps = The maximum difference to allow between numbers or vectors.
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// Example:
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// a = deduplicate_indexed([8,6,4,6,3], [1,4,3,1,2,2,0,1]); // Returns: [1,4,3,2,0,1]
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// b = deduplicate_indexed([8,6,4,6,3], [1,4,3,1,2,2,0,1], closed=true); // Returns: [1,4,3,2,0]
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// c = deduplicate_indexed([[7,undef],[7,undef],[1,4],[1,4],[1,4+1e-12]],eps=0); // Returns: [0,2,4]
|
|
function deduplicate_indexed(list, indices, closed=false, eps=EPSILON) =
|
|
assert(is_list(list)||is_string(list), "Improper list or string.")
|
|
indices==[]? [] :
|
|
assert(is_vector(indices), "Indices must be a list of numbers.")
|
|
let(
|
|
ll = len(list),
|
|
l = len(indices),
|
|
end = l-(closed?0:1)
|
|
) [
|
|
for (i = [0:1:l-1]) let(
|
|
idx1 = indices[i],
|
|
idx2 = indices[(i+1)%l],
|
|
a = assert(idx1>=0,"Bad index.")
|
|
assert(idx1<len(list),"Bad index in indices.")
|
|
list[idx1],
|
|
b = assert(idx2>=0,"Bad index.")
|
|
assert(idx2<len(list),"Bad index in indices.")
|
|
list[idx2],
|
|
eq = (a == b)? true :
|
|
(a*0 != b*0) || (eps==0)? false :
|
|
is_num(a) || is_vector(a) ? approx(a, b, eps=eps)
|
|
: false
|
|
)
|
|
if (i==end || !eq) indices[i]
|
|
];
|
|
|
|
|
|
|
|
|
|
// Function: unique()
|
|
// Usage:
|
|
// ulist = unique(list);
|
|
// Topics: List Handling
|
|
// See Also: shuffle(), sort(), sortidx(), unique_count()
|
|
// Description:
|
|
// Given a string or a list returns the sorted string or the sorted list with all repeated items removed.
|
|
// The sorting order of non homogeneous lists is the function `sort` order.
|
|
// Arguments:
|
|
// list = The list to uniquify.
|
|
// Example:
|
|
// sorted = unique([5,2,8,3,1,3,8,7,5]); // Returns: [1,2,3,5,7,8]
|
|
// sorted = unique("axdbxxc"); // Returns: "abcdx"
|
|
// sorted = unique([true,2,"xba",[1,0],true,[0,0],3,"a",[0,0],2]); // Returns: [true,2,3,"a","xba",[0,0],[1,0]]
|
|
function unique(list) =
|
|
assert(is_list(list)||is_string(list), "Invalid input." )
|
|
is_string(list)? str_join(unique([for (x = list) x])) :
|
|
len(list)<=1? list :
|
|
is_homogeneous(list,1) && ! is_list(list[0])
|
|
? _unique_sort(list)
|
|
: let( sorted = sort(list))
|
|
[
|
|
for (i=[0:1:len(sorted)-1])
|
|
if (i==0 || (sorted[i] != sorted[i-1]))
|
|
sorted[i]
|
|
];
|
|
|
|
function _unique_sort(l) =
|
|
len(l) <= 1 ? l :
|
|
let(
|
|
pivot = l[floor(len(l)/2)],
|
|
equal = [ for(li=l) if( li==pivot) li ],
|
|
lesser = [ for(li=l) if( li<pivot ) li ],
|
|
greater = [ for(li=l) if( li>pivot) li ]
|
|
)
|
|
concat(
|
|
_unique_sort(lesser),
|
|
equal[0],
|
|
_unique_sort(greater)
|
|
);
|
|
|
|
|
|
// Function: unique_count()
|
|
// Usage:
|
|
// counts = unique_count(list);
|
|
// Topics: List Handling
|
|
// See Also: shuffle(), sort(), sortidx(), unique()
|
|
// Description:
|
|
// Returns `[sorted,counts]` where `sorted` is a sorted list of the unique items in `list` and `counts` is a list such
|
|
// that `count[i]` gives the number of times that `sorted[i]` appears in `list`.
|
|
// Arguments:
|
|
// list = The list to analyze.
|
|
// Example:
|
|
// sorted = unique([5,2,8,3,1,3,8,3,5]); // Returns: [ [1,2,3,5,8], [1,1,3,2,2] ]
|
|
function unique_count(list) =
|
|
assert(is_list(list) || is_string(list), "Invalid input." )
|
|
list == [] ? [[],[]] :
|
|
is_homogeneous(list,1) && ! is_list(list[0])
|
|
? let( sorted = _group_sort(list) )
|
|
[ [for(s=sorted) s[0] ], [for(s=sorted) len(s) ] ]
|
|
: let(
|
|
list = sort(list),
|
|
ind = [0, for(i=[1:1:len(list)-1]) if (list[i]!=list[i-1]) i]
|
|
)
|
|
[ select(list,ind), deltas( concat(ind,[len(list)]) ) ];
|
|
|
|
|
|
|
|
// Section: Sorting
|
|
|
|
|
|
// returns true for valid index specifications idx in the interval [imin, imax)
|
|
// note that idx can't have any value greater or EQUAL to imax
|
|
// this allows imax=INF as a bound to numerical lists
|
|
function _valid_idx(idx,imin,imax) =
|
|
is_undef(idx)
|
|
|| ( is_finite(idx)
|
|
&& ( is_undef(imin) || idx>=imin )
|
|
&& ( is_undef(imax) || idx< imax ) )
|
|
|| ( is_list(idx)
|
|
&& ( is_undef(imin) || min(idx)>=imin )
|
|
&& ( is_undef(imax) || max(idx)< imax ) )
|
|
|| ( is_range(idx)
|
|
&& ( is_undef(imin) || (idx[1]>0 && idx[0]>=imin ) || (idx[1]<0 && idx[0]<=imax ) )
|
|
&& ( is_undef(imax) || (idx[1]>0 && idx[2]<=imax ) || (idx[1]<0 && idx[2]>=imin ) ) );
|
|
|
|
// idx should be an index of the arrays l[i]
|
|
function _group_sort_by_index(l,idx) =
|
|
len(l) == 0 ? [] :
|
|
len(l) == 1 ? [l] :
|
|
let(
|
|
pivot = l[floor(len(l)/2)][idx],
|
|
equal = [ for(li=l) if( li[idx]==pivot) li ],
|
|
lesser = [ for(li=l) if( li[idx]< pivot) li ],
|
|
greater = [ for(li=l) if( li[idx]> pivot) li ]
|
|
)
|
|
concat(
|
|
_group_sort_by_index(lesser,idx),
|
|
[equal],
|
|
_group_sort_by_index(greater,idx)
|
|
);
|
|
|
|
|
|
function _group_sort(l) =
|
|
len(l) == 0 ? [] :
|
|
len(l) == 1 ? [l] :
|
|
let(
|
|
pivot = l[floor(len(l)/2)],
|
|
equal = [ for(li=l) if( li==pivot) li ],
|
|
lesser = [ for(li=l) if( li< pivot) li ],
|
|
greater = [ for(li=l) if( li> pivot) li ]
|
|
)
|
|
concat(
|
|
_group_sort(lesser),
|
|
[equal],
|
|
_group_sort(greater)
|
|
);
|
|
|
|
|
|
// Sort a vector of scalar values with the native comparison operator
|
|
// all elements should have the same type.
|
|
function _sort_scalars(arr) =
|
|
len(arr)<=1 ? arr :
|
|
let(
|
|
pivot = arr[floor(len(arr)/2)],
|
|
lesser = [ for (y = arr) if (y < pivot) y ],
|
|
equal = [ for (y = arr) if (y == pivot) y ],
|
|
greater = [ for (y = arr) if (y > pivot) y ]
|
|
)
|
|
concat( _sort_scalars(lesser), equal, _sort_scalars(greater) );
|
|
|
|
|
|
// lexical sort of a homogeneous list of vectors
|
|
// uses native comparison operator
|
|
function _sort_vectors(arr, _i=0) =
|
|
len(arr)<=1 || _i>=len(arr[0]) ? arr :
|
|
let(
|
|
pivot = arr[floor(len(arr)/2)][_i],
|
|
lesser = [ for (entry=arr) if (entry[_i] < pivot ) entry ],
|
|
equal = [ for (entry=arr) if (entry[_i] == pivot ) entry ],
|
|
greater = [ for (entry=arr) if (entry[_i] > pivot ) entry ]
|
|
)
|
|
concat(
|
|
_sort_vectors(lesser, _i ),
|
|
_sort_vectors(equal, _i+1 ),
|
|
_sort_vectors(greater, _i ) );
|
|
|
|
|
|
// lexical sort of a homogeneous list of vectors by the vector components with indices in idxlist
|
|
// all idxlist indices should be in the range of the vector dimensions
|
|
// idxlist must be undef or a simple list of numbers
|
|
// uses native comparison operator
|
|
function _sort_vectors(arr, idxlist, _i=0) =
|
|
len(arr)<=1 || ( is_list(idxlist) && _i>=len(idxlist) ) || _i>=len(arr[0]) ? arr :
|
|
let(
|
|
k = is_list(idxlist) ? idxlist[_i] : _i,
|
|
pivot = arr[floor(len(arr)/2)][k],
|
|
lesser = [ for (entry=arr) if (entry[k] < pivot ) entry ],
|
|
equal = [ for (entry=arr) if (entry[k] == pivot ) entry ],
|
|
greater = [ for (entry=arr) if (entry[k] > pivot ) entry ]
|
|
)
|
|
concat(
|
|
_sort_vectors(lesser, idxlist, _i ),
|
|
_sort_vectors(equal, idxlist, _i+1),
|
|
_sort_vectors(greater, idxlist, _i ) );
|
|
|
|
|
|
// sorting using compare_vals(); returns indexed list when `indexed==true`
|
|
function _sort_general(arr, idx=undef, indexed=false) =
|
|
(len(arr)<=1) ? arr :
|
|
! indexed && is_undef(idx)
|
|
? _lexical_sort(arr)
|
|
: let( labeled = is_undef(idx) ? [for(i=idx(arr)) [i,arr[i]]]
|
|
: [for(i=idx(arr)) [i, for(j=idx) arr[i][j]]],
|
|
arrind = _indexed_sort(labeled))
|
|
indexed
|
|
? arrind
|
|
: [for(i=arrind) arr[i]];
|
|
|
|
// lexical sort using compare_vals()
|
|
function _lexical_sort(arr) =
|
|
len(arr)<=1? arr :
|
|
let( pivot = arr[floor(len(arr)/2)] )
|
|
let(
|
|
lesser = [ for (entry=arr) if (compare_vals(entry, pivot) <0 ) entry ],
|
|
equal = [ for (entry=arr) if (compare_vals(entry, pivot)==0 ) entry ],
|
|
greater = [ for (entry=arr) if (compare_vals(entry, pivot) >0 ) entry ]
|
|
)
|
|
concat(_lexical_sort(lesser), equal, _lexical_sort(greater));
|
|
|
|
|
|
// given a list of pairs, return the first element of each pair of the list sorted by the second element of the pair
|
|
// the sorting is done using compare_vals()
|
|
function _indexed_sort(arrind) =
|
|
arrind==[] ? [] : len(arrind)==1? [arrind[0][0]] :
|
|
let( pivot = arrind[floor(len(arrind)/2)][1] )
|
|
let(
|
|
lesser = [ for (entry=arrind) if (compare_vals(entry[1], pivot) <0 ) entry ],
|
|
equal = [ for (entry=arrind) if (compare_vals(entry[1], pivot)==0 ) entry[0] ],
|
|
greater = [ for (entry=arrind) if (compare_vals(entry[1], pivot) >0 ) entry ]
|
|
)
|
|
concat(_indexed_sort(lesser), equal, _indexed_sort(greater));
|
|
|
|
|
|
// Function: sort()
|
|
// Usage:
|
|
// slist = sort(list, [idx]);
|
|
// Topics: List Handling
|
|
// See Also: shuffle(), sortidx(), unique(), unique_count(), group_sort()
|
|
// Description:
|
|
// Sorts the given list in lexicographic order. If the input is a homogeneous simple list or a homogeneous
|
|
// list of vectors (see function is_homogeneous), the sorting method uses the native comparison operator and is faster.
|
|
// When sorting non homogeneous list the elements are compared with `compare_vals`, with types ordered according to
|
|
// `undef < boolean < number < string < list`. Comparison of lists is recursive.
|
|
// When comparing vectors, homogeneous or not, the parameter `idx` may be used to select the components to compare.
|
|
// Note that homogeneous lists of vectors may contain mixed types provided that for any two list elements
|
|
// list[i] and list[j] satisfies type(list[i][k])==type(list[j][k]) for all k.
|
|
// Strings are allowed as any list element and are compared with the native operators although no substring
|
|
// comparison is possible.
|
|
// Arguments:
|
|
// list = The list to sort.
|
|
// idx = If given, do the comparison based just on the specified index, range or list of indices.
|
|
// Example:
|
|
// // Homogeneous lists
|
|
// l1 = [45,2,16,37,8,3,9,23,89,12,34];
|
|
// sorted1 = sort(l1); // Returns [2,3,8,9,12,16,23,34,37,45,89]
|
|
// l2 = [["oat",0], ["cat",1], ["bat",3], ["bat",2], ["fat",3]];
|
|
// sorted2 = sort(l2); // Returns: [["bat",2],["bat",3],["cat",1],["fat",3],["oat",0]]
|
|
// // Non-homegenous list
|
|
// l3 = [[4,0],[7],[3,9],20,[4],[3,1],[8]];
|
|
// sorted3 = sort(l3); // Returns: [20,[3,1],[3,9],[4],[4,0],[7],[8]]
|
|
function sort(list, idx=undef) =
|
|
assert(is_list(list)||is_string(list), "Invalid input." )
|
|
is_string(list)? str_join(sort([for (x = list) x],idx)) :
|
|
!is_list(list) || len(list)<=1 ? list :
|
|
is_homogeneous(list,1)
|
|
? let(size = list_shape(list[0]))
|
|
size==0 ? _sort_scalars(list)
|
|
: len(size)!=1 ? _sort_general(list,idx)
|
|
: is_undef(idx) ? _sort_vectors(list)
|
|
: assert( _valid_idx(idx) , "Invalid indices.")
|
|
_sort_vectors(list,[for(i=idx) i])
|
|
: _sort_general(list,idx);
|
|
|
|
|
|
// Function: sortidx()
|
|
// Usage:
|
|
// idxlist = sortidx(list, [idx]);
|
|
// Topics: List Handling
|
|
// See Also: shuffle(), sort(), group_sort(), unique(), unique_count()
|
|
// Description:
|
|
// Given a list, sort it as function `sort()`, and returns
|
|
// a list of indexes into the original list in that sorted order.
|
|
// If you iterate the returned list in order, and use the list items
|
|
// to index into the original list, you will be iterating the original
|
|
// values in sorted order.
|
|
// Arguments:
|
|
// list = The list to sort.
|
|
// idx = If given, do the comparison based just on the specified index, range or list of indices.
|
|
// Example:
|
|
// lst = ["d","b","e","c"];
|
|
// idxs = sortidx(lst); // Returns: [1,3,0,2]
|
|
// ordered = select(lst, idxs); // Returns: ["b", "c", "d", "e"]
|
|
// Example:
|
|
// lst = [
|
|
// ["foo", 88, [0,0,1], false],
|
|
// ["bar", 90, [0,1,0], true],
|
|
// ["baz", 89, [1,0,0], false],
|
|
// ["qux", 23, [1,1,1], true]
|
|
// ];
|
|
// idxs1 = sortidx(lst, idx=1); // Returns: [3,0,2,1]
|
|
// idxs2 = sortidx(lst, idx=0); // Returns: [1,2,0,3]
|
|
// idxs3 = sortidx(lst, idx=[1,3]); // Returns: [3,0,2,1]
|
|
function sortidx(list, idx=undef) =
|
|
assert(is_list(list)||is_string(list), "Invalid input." )
|
|
!is_list(list) || len(list)<=1 ? list :
|
|
is_homogeneous(list,1)
|
|
? let(
|
|
size = list_shape(list[0]),
|
|
aug = ! (size==0 || len(size)==1) ? 0 // for general sorting
|
|
: [for(i=[0:len(list)-1]) concat(i,list[i])], // for scalar or vector sorting
|
|
lidx = size==0? [1] : // scalar sorting
|
|
len(size)==1
|
|
? is_undef(idx) ? [for(i=[0:len(list[0])-1]) i+1] // vector sorting
|
|
: [for(i=idx) i+1] // vector sorting
|
|
: 0 // just to signal
|
|
)
|
|
assert( ! ( size==0 && is_def(idx) ),
|
|
"The specification of `idx` is incompatible with scalar sorting." )
|
|
assert( _valid_idx(idx) , "Invalid indices." )
|
|
lidx!=0
|
|
? let( lsort = _sort_vectors(aug,lidx) )
|
|
[for(li=lsort) li[0] ]
|
|
: _sort_general(list,idx,indexed=true)
|
|
: _sort_general(list,idx,indexed=true);
|
|
|
|
|
|
|
|
|
|
// Function: group_sort()
|
|
// Usage:
|
|
// ulist = group_sort(list);
|
|
// Topics: List Handling
|
|
// See Also: shuffle(), sort(), sortidx(), unique(), unique_count()
|
|
// Description:
|
|
// Given a list of values, returns the sorted list with all repeated items grouped in a list.
|
|
// When the list entries are themselves lists, the sorting may be done based on the `idx` entry
|
|
// of those entries, that should be numbers.
|
|
// The result is always a list of lists.
|
|
// Arguments:
|
|
// list = The list to sort.
|
|
// idx = If given, do the comparison based just on the specified index. Default: zero.
|
|
// Example:
|
|
// sorted = group_sort([5,2,8,3,1,3,8,7,5]); // Returns: [[1],[2],[3,3],[5,5],[7],[8,8]]
|
|
// sorted2 = group_sort([[5,"a"],[2,"b"], [5,"c"], [3,"d"], [2,"e"] ], idx=0); // Returns: [[[2,"b"],[2,"e"]], [[5,"a"],[5,"c"]], [[3,"d"]] ]
|
|
function group_sort(list, idx) =
|
|
assert(is_list(list), "Input should be a list." )
|
|
assert(is_undef(idx) || (is_finite(idx) && idx>=0) , "Invalid index." )
|
|
len(list)<=1 ? [list] :
|
|
is_vector(list)? _group_sort(list) :
|
|
let( idx = is_undef(idx) ? 0 : idx )
|
|
assert( [for(entry=list) if(!is_list(entry) || len(entry)<idx || !is_num(entry[idx]) ) 1]==[],
|
|
"Some entry of the list is a list shorter than `idx` or the indexed entry of it is not a number.")
|
|
_group_sort_by_index(list,idx);
|
|
|
|
|
|
|
|
// Function: group_data()
|
|
// Usage:
|
|
// groupings = group_data(groups, values);
|
|
// Topics: List Handling
|
|
// See Also: zip()
|
|
// Description:
|
|
// Given a list of integer group numbers, and an equal-length list of values,
|
|
// returns a list of groups with the values sorted into the corresponding groups.
|
|
// Ie: if you have a groups index list of [2,3,2] and values of ["A","B","C"], then
|
|
// the values "A" and "C" will be put in group 2, and "B" will be in group 3.
|
|
// Groups that have no values grouped into them will be an empty list. So the
|
|
// above would return [[], [], ["A","C"], ["B"]]
|
|
// Arguments:
|
|
// groups = A list of integer group index numbers.
|
|
// values = A list of values to sort into groups.
|
|
// Example:
|
|
// groups = group_data([1,2,0], ["A","B","C"]); // Returns [["B"],["C"],["A"]]
|
|
// Example:
|
|
// groups = group_data([1,3,1], ["A","B","C"]); // Returns [[],["A","C"],[],["B"]]
|
|
function group_data(groups, values) =
|
|
assert(all_integer(groups) && all_nonnegative(groups))
|
|
assert(is_list(values))
|
|
assert(len(groups)==len(values),
|
|
"The groups and values arguments should be lists of matching length.")
|
|
let( sorted = _group_sort_by_index([for(i=idx(groups))[groups[i],values[i]]],0) )
|
|
// retrieve values and insert []
|
|
[
|
|
for (i = idx(sorted))
|
|
let(
|
|
a = i==0? 0 : sorted[i-1][0][0]+1,
|
|
g0 = sorted[i]
|
|
)
|
|
each [
|
|
for (j = [a:1:g0[0][0]-1]) [],
|
|
[for (g1 = g0) g1[1]]
|
|
]
|
|
];
|
|
|
|
|
|
// Function: list_smallest()
|
|
// Usage:
|
|
// small = list_smallest(list, k)
|
|
// Description:
|
|
// Returns a set of the k smallest items in list in arbitrary order. The items must be
|
|
// mutually comparable with native OpenSCAD comparison operations. You will get "undefined operation"
|
|
// errors if you provide invalid input.
|
|
// Arguments:
|
|
// list = list to process
|
|
// k = number of items to return
|
|
function list_smallest(list, k) =
|
|
assert(is_list(list))
|
|
assert(is_finite(k) && k>=0, "k must be nonnegative")
|
|
let(
|
|
v = list[rand_int(0,len(list)-1,1)[0]],
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smaller = [for(li=list) if(li<v) li ],
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equal = [for(li=list) if(li==v) li ]
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)
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len(smaller) == k ? smaller :
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len(smaller)<k && len(smaller)+len(equal) >= k ? [ each smaller, for(i=[1:k-len(smaller)]) v ] :
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len(smaller) > k ? list_smallest(smaller, k) :
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let( bigger = [for(li=list) if(li>v) li ] )
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concat(smaller, equal, list_smallest(bigger, k-len(smaller) -len(equal)));
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// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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