BOSL2/lists.scad
2024-11-27 20:20:56 -05:00

1169 lines
48 KiB
OpenSCAD

//////////////////////////////////////////////////////////////////////
// LibFile: lists.scad
// Functions for operating on generic lists. Provides functiosn for indexing lists, changing list
// structure, and constructing lists by rearranging or modifying another list.
// Includes:
// include <BOSL2/std.scad>
// FileGroup: Data Management
// FileSummary: List indexing, change list structure, rearrange/modify lists
// FileFootnotes: STD=Included in std.scad
//////////////////////////////////////////////////////////////////////
// Terminology:
// **List** = An ordered collection of zero or more arbitrary items. ie: `["a", "b", "c"]`, or `[3, "a", [4,5]]`
// **Vector** = A list of numbers. ie: `[4, 5, 6]`
// **Set** = A list of unique items.
// Section: List Query Operations
// Function: is_homogeneous()
// Alias: is_homogenous()
// Synopsis: Returns true if all members of a list are of the same type.
// Topics: List Handling, Type Checking
// See Also: is_vector(), is_matrix()
// Usage:
// bool = is_homogeneous(list, [depth]);
// Description:
// Returns true when the list has elements of same type up to the depth `depth`.
// Booleans and numbers are not distinguinshed as of distinct types.
// Arguments:
// l = the list to check
// depth = the lowest level the check is done. Default: 10
// Example:
// a = is_homogeneous([[1,["a"]], [2,["b"]]]); // Returns true
// b = is_homogeneous([[1,["a"]], [2,[true]]]); // Returns false
// c = is_homogeneous([[1,["a"]], [2,[true]]], 1); // Returns true
// d = is_homogeneous([[1,["a"]], [2,[true]]], 2); // Returns false
// e = is_homogeneous([[1,["a"]], [true,["b"]]]); // Returns true
function is_homogeneous(l, depth=10) =
!is_list(l) || l==[] ? false :
let( l0=l[0] )
[] == [for(i=[1:1:len(l)-1]) if( ! _same_type(l[i],l0, depth+1) ) 0 ];
function is_homogenous(l, depth=10) = is_homogeneous(l, depth);
function _same_type(a,b, depth) =
(depth==0) ||
(is_undef(a) && is_undef(b)) ||
(is_bool(a) && is_bool(b)) ||
(is_num(a) && is_num(b)) ||
(is_string(a) && is_string(b)) ||
(is_list(a) && is_list(b) && len(a)==len(b)
&& []==[for(i=idx(a)) if( ! _same_type(a[i],b[i],depth-1) ) 0] );
// Function: min_length()
// Synopsis: Given a list of sublists, returns the length of the shortest sublist.
// Topics: List Handling
// See Also: max_length()
// Usage:
// llen = min_length(list);
// Description:
// Returns the length of the shortest sublist in a list of lists.
// Arguments:
// list = A list of lists.
// Example:
// slen = min_length([[3,4,5],[6,7,8,9]]); // Returns: 3
function min_length(list) =
assert(is_list(list), "Invalid input." )
min([for (v = list) len(v)]);
// Function: max_length()
// Synopsis: Given a list of sublists, returns the length of the longest sublist.
// Topics: List Handling
// See Also: min_length()
// Usage:
// llen = max_length(list);
// Description:
// Returns the length of the longest sublist in a list of lists.
// Arguments:
// list = A list of lists.
// Example:
// llen = max_length([[3,4,5],[6,7,8,9]]); // Returns: 4
function max_length(list) =
assert(is_list(list), "Invalid input." )
max([for (v = list) len(v)]);
// Internal. Not exposed.
function _list_shape_recurse(v) =
!is_list(v[0])
? len( [for(entry=v) if(!is_list(entry)) 0] ) == 0 ? [] : [undef]
: let(
firstlen = is_list(v[0]) ? len(v[0]): undef,
first = len( [for(entry = v) if(! is_list(entry) || (len(entry) != firstlen)) 0 ] ) == 0 ? firstlen : undef,
leveldown = flatten(v)
)
is_list(leveldown[0])
? concat([first],_list_shape_recurse(leveldown))
: [first];
function _list_shape_recurse(v) =
let( alen = [for(vi=v) is_list(vi) ? len(vi): -1] )
v==[] || max(alen)==-1 ? [] :
let( add = max(alen)!=min(alen) ? undef : alen[0] )
concat( add, _list_shape_recurse(flatten(v)));
// Function: list_shape()
// Synopsis: Returns the dimensions of an array.
// Topics: Matrices, List Handling
// See Also: is_homogenous()
// Usage:
// dims = list_shape(v, [depth]);
// Description:
// Returns the size of a multi-dimensional array, a list of the lengths at each depth.
// If the returned value has `dims[i] = j` then it means the ith index ranges of j items.
// The return `dims[0]` is equal to the length of v. Then `dims[1]` is equal to the
// length of the lists in v, and in general, `dims[i]` is equal to the length of the items
// nested to depth i in the list v. If the length of items at that depth is inconsistent, then
// `undef` is returned. If no items exist at that depth then `0` is returned. Note that
// for simple vectors or matrices it is faster to compute `len(v)` and `len(v[0])`.
// Arguments:
// v = list to get shape of
// depth = depth to compute the size of. If not given, returns a list of sizes at all depths.
// Example:
// a = list_shape([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]]); // Returns [2,2,3]
// b = list_shape([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]], 0); // Returns 2
// c = list_shape([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]], 2); // Returns 3
// d = list_shape([[[1,2,3],[4,5,6]],[[7,8,9]]]); // Returns [2,undef,3]
function list_shape(v, depth=undef) =
assert( is_undef(depth) || ( is_finite(depth) && depth>=0 ), "Invalid depth.")
! is_list(v) ? 0 :
(depth == undef)
? concat([len(v)], _list_shape_recurse(v))
: (depth == 0)
? len(v)
: let( dimlist = _list_shape_recurse(v))
(depth > len(dimlist))? 0 : dimlist[depth-1] ;
// Function: in_list()
// Synopsis: Returns true if a value is in a list.
// Topics: List Handling
// See Also: select(), slice()
// Usage:
// bool = in_list(val, list, [idx]);
// Description:
// Returns true if value `val` is in list `list`. When `val==NAN` the answer will be false for any list.
// Arguments:
// val = The simple value to search for.
// list = The list to search.
// idx = If given, searches the given columns for matches for `val`.
// Example:
// a = in_list("bar", ["foo", "bar", "baz"]); // Returns true.
// b = in_list("bee", ["foo", "bar", "baz"]); // Returns false.
// c = in_list("bar", [[2,"foo"], [4,"bar"], [3,"baz"]], idx=1); // Returns true.
// Note that a huge complication occurs because OpenSCAD's search() finds
// index i as a hits if the val equals list[i] but also if val equals list[i][0].
// This means every hit needs to be checked to see if it's actually a hit,
// and if the first hit is a mismatch we have to keep searching.
// We assume that the normal case doesn't have mixed data, and try first
// with just one hit, but if this finds a mismatch then we try again
// with all hits, which could be slow for long lists.
function in_list(val,list,idx) =
assert(is_list(list),"Input is not a list")
assert(is_undef(idx) || is_finite(idx), "Invalid idx value.")
let( firsthit = search([val], list, num_returns_per_match=1, index_col_num=idx)[0] )
firsthit==[] ? false
: is_undef(idx) && val==list[firsthit] ? true
: is_def(idx) && val==list[firsthit][idx] ? true
// first hit was found but didn't match, so try again with all hits
: let ( allhits = search([val], list, 0, idx)[0])
is_undef(idx) ? [for(hit=allhits) if (list[hit]==val) 1] != []
: [for(hit=allhits) if (list[hit][idx]==val) 1] != [];
// Section: List Indexing
// Function: select()
// Synopsis: Returns one or more items from a list, with wrapping.
// Topics: List Handling
// See Also: slice(), column(), last()
// Description:
// Returns a portion of a list, wrapping around past the beginning, if end<start.
// The first item is index 0. Negative indexes are counted back from the end.
// The last item is -1. If only the `start` index is given, returns just the value
// at that position when `start` is a number or the selected list of entries when `start` is
// a list of indices or a range.
// Usage:
// item = select(list, start);
// item = select(list, [s:d:e]);
// item = select(list, [i0,i1...,ik]);
// list = select(list, start, end);
// Arguments:
// list = The list to get the portion of.
// start = Either the index of the first item or an index range or a list of indices.
// end = The index of the last item when `start` is a number. When `start` is a list or a range, `end` should not be given.
// Example:
// l = [3,4,5,6,7,8,9];
// a = select(l, 5, 6); // Returns [8,9]
// b = select(l, 5, 8); // Returns [8,9,3,4]
// c = select(l, 5, 2); // Returns [8,9,3,4,5]
// d = select(l, -3, -1); // Returns [7,8,9]
// e = select(l, 3, 3); // Returns [6]
// f = select(l, 4); // Returns 7
// g = select(l, -2); // Returns 8
// h = select(l, [1:3]); // Returns [4,5,6]
// i = select(l, [3,1]); // Returns [6,4]
function select(list, start, end) =
assert( is_list(list) || is_string(list), "Invalid list.")
let(l=len(list))
l==0
? []
: end==undef
? is_num(start)
? list[ (start%l+l)%l ]
: assert( start==[] || is_vector(start) || is_range(start), "Invalid start parameter")
[for (i=start) list[ (i%l+l)%l ] ]
: assert(is_finite(start), "When `end` is given, `start` parameter should be a number.")
assert(is_finite(end), "Invalid end parameter.")
let( s = (start%l+l)%l, e = (end%l+l)%l )
(s <= e)
? [ for (i = [s:1:e]) list[i] ]
: [ for (i = [s:1:l-1]) list[i],
for (i = [0:1:e]) list[i] ] ;
// Function: slice()
// Synopsis: Returns part of a list without wrapping.
// Topics: List Handling
// See Also: select(), column(), last()
// Usage:
// list = slice(list, s, e);
// Description:
// Returns a slice of a list, from the first position `s` up to and including the last position `e`.
// The first item in the list is at index 0. Negative indexes are counted back from the end, with
// -1 referring to the last list item. If `s` is after `e` then the empty list is returned.
// If an index is off the start/end of the list it will refer to the list start/end.
// Arguments:
// list = The list to get the slice of.
// start = The index of the first item to return. Default: 0
// end = The index of the last item to return. Default: -1 (last item)
// Example:
// a = slice([3,4,5,6,7,8,9], 3, 5); // Returns [6,7,8]
// b = slice([3,4,5,6,7,8,9], 2, -1); // Returns [5,6,7,8,9]
// c = slice([3,4,5,6,7,8,9], 1, 1); // Returns [4]
// d = slice([3,4,5,6,7,8,9], 5); // Returns [8,9]
// e = slice([3,4,5,6,7,8,9], 2, -2); // Returns [5,6,7,8]
// f = slice([3,4,5,6,7,8,9], 4, 3; // Returns []
// g = slice([3,4,5], 1, 5; // Returns [4,5]
// h = slice([3,4,5], 5, 7); // Returns []
function slice(list,start=0,end=-1) =
assert(is_list(list))
assert(is_int(start))
assert(is_int(end))
!list? [] :
let(
l = len(list),
start = start+(start<0 ? l : 0),
end = end + (end<0? l : 0)
)
[if (start<=end && end>=0 && start<=l) for (i=[max(start,0):1:min(end,l-1)]) list[i]];
// Function: last()
// Synopsis: Returns the last item of a list.
// Topics: List Handling
// See Also: select(), slice(), column()
// Usage:
// item = last(list);
// Description:
// Returns the last element of a list, or undef if empty.
// Arguments:
// list = The list to get the last element of.
// Example:
// l = [3,4,5,6,7,8,9];
// x = last(l); // Returns 9.
function last(list) =
list[len(list)-1];
// Function: list_head()
// Synopsis: Returns the elements at the beginning of a list.
// Topics: List Handling
// See Also: select(), slice(), list_tail(), last()
// Usage:
// list = list_head(list, [to]);
// Description:
// Returns the head of the given list, from the first item up until the `to` index, inclusive.
// By default returns all but the last element of the list.
// If the `to` index is negative, then the length of the list is added to it, such that
// `-1` is the last list item. `-2` is the second from last. `-3` is third from last, etc.
// If the list is shorter than the given index, then the full list is returned.
// Arguments:
// list = The list to get the head of.
// to = The last index to include. If negative, adds the list length to it. ie: -1 is the last list item. Default: -2
// Example:
// hlist1 = list_head(["foo", "bar", "baz"]); // Returns: ["foo", "bar"]
// hlist2 = list_head(["foo", "bar", "baz"], -3); // Returns: ["foo"]
// hlist3 = list_head(["foo", "bar", "baz"], 1); // Returns: ["foo","bar"]
// hlist4 = list_head(["foo", "bar", "baz"], -5); // Returns: []
// hlist5 = list_head(["foo", "bar", "baz"], 5); // Returns: ["foo","bar","baz"]
function list_head(list, to=-2) =
assert(is_list(list))
assert(is_finite(to))
to<0? [for (i=[0:1:len(list)+to]) list[i]] :
to<len(list)? [for (i=[0:1:to]) list[i]] :
list;
// Function: list_tail()
// Synopsis: Returns the elements at the end of a list.
// Topics: List Handling
// See Also: select(), slice(), list_tail(), last()
// Usage:
// list = list_tail(list, [from]);
// Description:
// Returns the tail of the given list, from the `from` index up until the end of the list, inclusive.
// By default returns all but the first item.
// If the `from` index is negative, then the length of the list is added to it, such that
// `-1` is the last list item. `-2` is the second from last. `-3` is third from last, etc.
// If you want it to return the last three items of the list, use `from=-3`.
// Arguments:
// list = The list to get the tail of.
// from = The first index to include. If negative, adds the list length to it. ie: -1 is the last list item. Default: 1.
// Example:
// tlist1 = list_tail(["foo", "bar", "baz"]); // Returns: ["bar", "baz"]
// tlist2 = list_tail(["foo", "bar", "baz"], -1); // Returns: ["baz"]
// tlist3 = list_tail(["foo", "bar", "baz"], 2); // Returns: ["baz"]
// tlist4 = list_tail(["foo", "bar", "baz"], -5); // Returns: ["foo","bar","baz"]
// tlist5 = list_tail(["foo", "bar", "baz"], 5); // Returns: []
function list_tail(list, from=1) =
assert(is_list(list))
assert(is_finite(from))
from>=0? [for (i=[from:1:len(list)-1]) list[i]] :
let(from = from + len(list))
from>=0? [for (i=[from:1:len(list)-1]) list[i]] :
list;
// Function: bselect()
// Synopsis: Select list items using boolean index list.
// Topics: List Handling
// See Also: list_bset()
// Usage:
// sublist = bselect(list, index);
// Description:
// Returns the items in `list` whose matching element in `index` evaluates as true.
// Arguments:
// list = Initial list (or string) to extract items from.
// index = List of values that will be evaluated as boolean, same length as `list`.
// Example:
// a = bselect([3,4,5,6,7], [false,true,true,false,true]); // Returns: [4,5,7]
function bselect(list,index) =
assert(is_list(list)||is_string(list), "First argument must be a list or string." )
assert(is_list(index) && len(index)==len(list) , "Second argument must have same length as the first." )
is_string(list)? str_join(bselect( [for (x=list) x], index)) :
[for(i=idx(list)) if (index[i]) list[i]];
// Section: List Construction
// Function: repeat()
// Synopsis: Returns a list of repeated copies of a value.
// Topics: List Handling
// See Also: count(), lerpn()
// Usage:
// list = repeat(val, n);
// Description:
// Generates a list of `n` copies of the given value `val`.
// If the count `n` is given as a list of counts, then this creates a
// multi-dimensional array, filled with `val`. If `n` is negative, returns the empty list.
// Arguments:
// val = The value to repeat to make the list or array.
// n = The number of copies to make of `val`. Can be a list to make an array of copies.
// Example:
// a = repeat(1, 4); // Returns [1,1,1,1]
// b = repeat(8, [2,3]); // Returns [[8,8,8], [8,8,8]]
// c = repeat(0, [2,2,3]); // Returns [[[0,0,0],[0,0,0]], [[0,0,0],[0,0,0]]]
// d = repeat([1,2,3],3); // Returns [[1,2,3], [1,2,3], [1,2,3]]
// e = repeat(4, -1); // Returns []
function repeat(val, n, i=0) =
is_num(n)? [for(j=[1:1:n]) val] :
assert( is_list(n), "Invalid count number.")
(i>=len(n))? val :
[for (j=[1:1:n[i]]) repeat(val, n, i+1)];
// Function: list_bset()
// Synopsis: Returns a list where values are spread to locations indicated by a boolean index list.
// Topics: List Handling
// See Also: bselect()
// Usage:
// arr = list_bset(indexset, valuelist, [dflt]);
// Description:
// Opposite of `bselect()`. Returns a list the same length as `indexlist`, where each item will
// either be 0 if the corresponding item in `indexset` is false, or the next sequential value
// from `valuelist` if the item is true. The number of `true` values in `indexset` must be equal
// to the length of `valuelist`.
// Arguments:
// indexset = A list of boolean values.
// valuelist = The list of values to set into the returned list.
// dflt = Default value to store when the indexset item is false. Default: 0
// Example:
// a = list_bset([false,true,false,true,false], [3,4]); // Returns: [0,3,0,4,0]
// b = list_bset([false,true,false,true,false], [3,4], dflt=1); // Returns: [1,3,1,4,1]
function list_bset(indexset, valuelist, dflt=0) =
assert(is_list(indexset), "The index set is not a list." )
assert(is_list(valuelist), "The `valuelist` is not a list." )
let( trueind = search([true], indexset,0)[0] )
assert( !(len(trueind)>len(valuelist)), str("List `valuelist` too short; its length should be ",len(trueind)) )
assert( !(len(trueind)<len(valuelist)), str("List `valuelist` too long; its length should be ",len(trueind)) )
concat(
list_set([],trueind, valuelist, dflt=dflt), // Fill in all of the values
repeat(dflt,len(indexset)-max(trueind)-1) // Add trailing values so length matches indexset
);
// Function: list()
// Synopsis: Expands a range into a full list.
// Topics: List Handling, Type Conversion
// See Also: scalar_vec3(), force_list()
// Usage:
// list = list(l)
// Description:
// Expands a range into a full list. If given a list, returns it verbatim.
// If given a string, explodes it into a list of single letters.
// Arguments:
// l = The value to expand.
// Example:
// l1 = list([3:2:9]); // Returns: [3,5,7,9]
// l2 = list([3,4,5]); // Returns: [3,4,5]
// l3 = list("Foo"); // Returns: ["F","o","o"]
// l4 = list(23); // Returns: [23]
function list(l) = is_list(l)? l : [for (x=l) x];
// Function: force_list()
// Synopsis: Coerces non-list values into a list.
// Topics: List Handling
// See Also: scalar_vec3()
// Usage:
// list = force_list(value, [n], [fill]);
// Description:
// Coerces non-list values into a list. Makes it easy to treat a scalar input
// consistently as a singleton list, as well as list inputs.
// - If `value` is a list, then that list is returned verbatim.
// - If `value` is not a list, and `fill` is not given, then a list of `n` copies of `value` will be returned.
// - If `value` is not a list, and `fill` is given, then a list `n` items long will be returned where `value` will be the first item, and the rest will contain the value of `fill`.
// Arguments:
// value = The value or list to coerce into a list.
// n = The number of items in the coerced list. Default: 1
// fill = The value to pad the coerced list with, after the firt value. Default: undef (pad with copies of `value`)
// Example:
// x = force_list([3,4,5]); // Returns: [3,4,5]
// y = force_list(5); // Returns: [5]
// z = force_list(7, n=3); // Returns: [7,7,7]
// w = force_list(4, n=3, fill=1); // Returns: [4,1,1]
function force_list(value, n=1, fill) =
is_list(value) ? value :
is_undef(fill)? [for (i=[1:1:n]) value] : [value, for (i=[2:1:n]) fill];
// Section: List Modification
// Function: reverse()
// Synopsis: Reverses the elements of a list.
// Topics: List Handling
// See Also: select(), list_rotate()
// Usage:
// rlist = reverse(list);
// Description:
// Reverses a list or string.
// Arguments:
// list = The list or string to reverse.
// Example:
// reverse([3,4,5,6]); // Returns [6,5,4,3]
function reverse(list) =
assert(is_list(list)||is_string(list), str("Input to reverse must be a list or string. Got: ",list))
let (elems = [ for (i = [len(list)-1 : -1 : 0]) list[i] ])
is_string(list)? str_join(elems) : elems;
// Function: list_rotate()
// Synopsis: Rotates the ordering of a list.
// Topics: List Handling
// See Also: select(), reverse()
// Usage:
// rlist = list_rotate(list, [n]);
// Description:
// Rotates the contents of a list by `n` positions left, so that list[n] becomes the first entry of the list.
// If `n` is negative, then the rotation is `abs(n)` positions to the right.
// If `list` is a string, then a string is returned with the characters rotates within the string.
// Arguments:
// list = The list to rotate.
// n = The number of positions to rotate by. If negative, rotated to the right. Positive rotates to the left. Default: 1
// Example:
// l1 = list_rotate([1,2,3,4,5],-2); // Returns: [4,5,1,2,3]
// l2 = list_rotate([1,2,3,4,5],-1); // Returns: [5,1,2,3,4]
// l3 = list_rotate([1,2,3,4,5],0); // Returns: [1,2,3,4,5]
// l4 = list_rotate([1,2,3,4,5],1); // Returns: [2,3,4,5,1]
// l5 = list_rotate([1,2,3,4,5],2); // Returns: [3,4,5,1,2]
// l6 = list_rotate([1,2,3,4,5],3); // Returns: [4,5,1,2,3]
// l7 = list_rotate([1,2,3,4,5],4); // Returns: [5,1,2,3,4]
// l8 = list_rotate([1,2,3,4,5],5); // Returns: [1,2,3,4,5]
// l9 = list_rotate([1,2,3,4,5],6); // Returns: [2,3,4,5,1]
function list_rotate(list,n=1) =
assert(is_list(list)||is_string(list), "Invalid list or string.")
assert(is_int(n), "The rotation number should be integer")
let (
ll = len(list),
n = ((n % ll) + ll) % ll,
elems = [
for (i=[n:1:ll-1]) list[i],
for (i=[0:1:n-1]) list[i]
]
)
is_string(list)? str_join(elems) : elems;
// Function: shuffle()
// Synopsis: Randomizes the order of a list.
// Topics: List Handling
// See Also: sort(), sortidx(), unique(), unique_count()
// Usage:
// shuffled = shuffle(list, [seed]);
// Description:
// Shuffles the input list into random order.
// If given a string, shuffles the characters within the string.
// If you give a numeric seed value then the permutation
// will be repeatable.
// Arguments:
// list = The list to shuffle.
// seed = Optional random number seed for the shuffling.
// Example:
// // Spades Hearts Diamonds Clubs
// suits = ["\u2660", "\u2661", "\u2662", "\u2663"];
// ranks = [2,3,4,5,6,7,8,9,10,"J","Q","K","A"];
// cards = [for (suit=suits, rank=ranks) str(rank,suit)];
// deck = shuffle(cards);
function shuffle(list,seed) =
assert(is_list(list)||is_string(list), "Invalid input." )
is_string(list)? str_join(shuffle([for (x = list) x],seed=seed)) :
len(list)<=1 ? list :
let(
rval = is_num(seed) ? rands(0,1,len(list),seed_value=seed)
: rands(0,1,len(list)),
left = [for (i=[0:len(list)-1]) if (rval[i]< 0.5) list[i]],
right = [for (i=[0:len(list)-1]) if (rval[i]>=0.5) list[i]]
)
concat(shuffle(left), shuffle(right));
// Function: repeat_entries()
// Synopsis: Repeats list entries (as uniformly as possible) to make list of specified length.
// Topics: List Handling
// See Also: repeat()
// Usage:
// newlist = repeat_entries(list, N, [exact]);
// Description:
// Takes a list as input and duplicates some of its entries to produce a list
// with length `N`. If the requested `N` is not a multiple of the list length then
// the entries will be duplicated as uniformly as possible. You can also set `N` to a vector,
// in which case len(N) must equal len(list) and the output repeats the ith entry N[i] times.
// In either case, the result will be a list of length `N`. The `exact` option requires
// that the final length is exactly as requested. If you set it to `false` then the
// algorithm will favor uniformity and the output list may have a different number of
// entries due to rounding.
// .
// When applied to a path the output path is the same geometrical shape but has some vertices
// repeated. This can be useful when you need to align paths with a different number of points.
// (See also subdivide_path for a different way to do that.)
// Arguments:
// list = list whose entries will be repeated
// N = scalar total number of points desired or vector requesting N[i] copies of vertex i.
// exact = if true return exactly the requested number of points, possibly sacrificing uniformity. If false, return uniform points that may not match the number of points requested. Default: True
// Example:
// list = [0,1,2,3];
// a = repeat_entries(list, 6); // Returns: [0,0,1,2,2,3]
// b = repeat_entries(list, 6, exact=false); // Returns: [0,0,1,1,2,2,3,3]
// c = repeat_entries(list, [1,1,2,1], exact=false); // Returns: [0,1,2,2,3]
function repeat_entries(list, N, exact=true) =
assert(is_list(list) && len(list)>0, "The list cannot be void.")
assert((is_finite(N) && N>0) || is_vector(N,len(list)),
"Parameter N must be a number greater than zero or vector with the same length of `list`")
let(
length = len(list),
reps_guess = is_list(N)? N : repeat(N/length,length),
reps = exact ?
_sum_preserving_round(reps_guess)
: [for (val=reps_guess) round(val)]
)
[for(i=[0:length-1]) each repeat(list[i],reps[i])];
// Function: list_pad()
// Synopsis: Extend list to specified length.
// Topics: List Handling
// See Also: force_list(), scalar_vec3()
// Usage:
// newlist = list_pad(list, minlen, [fill]);
// Description:
// If the list `list` is shorter than `minlen` length, pad it to length with the value given in `fill`.
// Arguments:
// list = A list.
// minlen = The minimum length to pad the list to.
// fill = The value to pad the list with. Default: `undef`
// Example:
// list = [3,4,5];
// nlist = list_pad(list,5,23); // Returns: [3,4,5,23,23]
function list_pad(list, minlen, fill) =
assert(is_list(list), "Invalid input." )
concat(list,repeat(fill,minlen-len(list)));
// Function: list_set()
// Synopsis: Sets the value of specific list items.
// Topics: List Handling
// See Also: list_insert(), list_remove(), list_remove_values()
// Usage:
// list = list_set(list, indices, values, [dflt], [minlen]);
// Description:
// Takes the input list and returns a new list such that `list[indices[i]] = values[i]` for all of
// the (index,value) pairs supplied and unchanged for other indices. If you supply `indices` that are
// larger that the length of the list then the list is extended and filled in with the `dflt` value.
// If you specify indices smaller than zero then they index from the end, with -1 being the last element.
// Negative indexing does not wrap around: an error occurs if you give a value smaller than `-len(list)`.
// If you set `minlen` then the list is lengthed, if necessary, by padding with `dflt` to that length.
// Repetitions in `indices` are not allowed. The lists `indices` and `values` must have the same length.
// If `indices` is given as a scalar, then that index of the given `list` will be set to the scalar value of `values`.
// Arguments:
// list = List to set items in. Default: []
// indices = List of indices into `list` to set.
// values = List of values to set.
// dflt = Default value to store in sparse skipped indices.
// minlen = Minimum length to expand list to.
// Example:
// a = list_set([2,3,4,5], 2, 21); // Returns: [2,3,21,5]
// b = list_set([2,3,4,5], [1,3], [81,47]); // Returns: [2,81,4,47]
function list_set(list=[],indices,values,dflt=0,minlen=0) =
assert(is_list(list))
!is_list(indices)?
assert(is_finite(indices))
let(
index = indices<0 ? indices+len(list) : indices
)
assert(index>=0, str("Index ",indices," is smaller than negative list length"))
(
index<len(list) ?
[
for(i=[0:1:index-1]) list[i],
values,
for(i=[index+1:1:len(list)-1]) list[i],
for(i=[len(list):1:minlen-1]) dflt
]
: concat(list, repeat(dflt, index-len(list)), [values], repeat(dflt, minlen-index-1))
)
: indices==[] && values==[]
? concat(list, repeat(dflt, minlen-len(list)))
: assert(is_vector(indices) && is_list(values) && len(values)==len(indices),
"Index list and value list must have the same length")
let( indices = [for(ind=indices) ind<0 ? ind+len(list) : ind],
midx = max(len(list)-1, max(indices))
)
assert(min(indices)>=0, "Index list contains value smaller than negative list length")
[
for (i=[0:1:midx])
let(
j = search(i,indices,0),
k = j[0]
)
assert( len(j)<2, "Repeated indices are not allowed." )
k!=undef ? values[k]
: i<len(list) ? list[i]
: dflt,
each repeat(dflt, minlen-max(len(list),max(indices)+1))
];
// Function: list_insert()
// Synopsis: Inserts values into the middle of a list.
// Topics: List Handling
// See Also: list_set(), list_remove(), list_remove_values()
// Usage:
// list = list_insert(list, indices, values);
// Description:
// Insert `values` into `list` before position `indices`. The indices for insertion
// are based on the original list, before any insertions have occurred.
// You can use negative indices to count from the end of the list. Note that -1 refers
// to the last element, so the insertion will be *before* the last element.
// Arguments:
// list = list to insert items into
// indices = index or list of indices where values are inserted
// values = value or list of values to insert
// Example:
// a = list_insert([3,6,9,12],1,5); // Returns [3,5,6,9,12]
// b = list_insert([3,6,9,12],[1,3],[5,11]); // Returns [3,5,6,9,11,12]
function list_insert(list, indices, values) =
assert(is_list(list))
!is_list(indices) ?
assert(is_finite(indices), "Invalid indices." )
let(indices = indices<0 ? indices+len(list) : indices)
assert(indices>=0, "Index is too small, must be >= len(list)")
assert( indices<=len(list), "Indices must be <= len(list) ." )
[
for (i=idx(list)) each ( i==indices? [ values, list[i] ] : [ list[i] ] ),
if (indices==len(list)) values
] :
indices==[] && values==[] ? list :
assert( is_vector(indices) && is_list(values) && len(values)==len(indices),
"Index list and value list must have the same length")
assert( max(indices)<=len(list), "Indices must be <= len(list)." )
let(
indices = [for(ind=indices) ind<0 ? ind+len(list) : ind],
maxidx = max(indices),
minidx = min(indices)
)
assert(minidx>=0, "Index list contains values that are too small")
assert(maxidx<=len(list), "Index list contains values that are too large")
[
for (i=[0:1:minidx-1] ) list[i],
for (i=[minidx : min(maxidx, len(list)-1)] )
let(
j = search(i,indices,0),
k = j[0],
x = assert( len(j)<2, "Repeated indices are not allowed." )
) each ( k != undef ? [ values[k], list[i] ] : [ list[i] ] ),
for ( i = [min(maxidx, len(list)-1)+1 : 1 : len(list)-1] ) list[i],
if (maxidx == len(list)) values[max_index(indices)]
];
// Function: list_remove()
// Synopsis: Removes items by index from a list.
// Topics: List Handling
// See Also: list_set(), list_insert(), list_remove_values()
// Usage:
// list = list_remove(list, ind);
// Description:
// If `ind` is a number remove `list[ind]` from the list. If `ind` is a list of indices
// remove from the list the item all items whose indices appear in `ind`. If you give
// indices that are not in the list they are ignored.
// Arguments:
// list = The list to remove items from.
// ind = index or list of indices of items to remove.
// Example:
// a = list_remove([3,6,9,12],1); // Returns: [3,9,12]
// b = list_remove([3,6,9,12],[1,3]); // Returns: [3,9]
// c = list_remove([3,6],3); // Returns: [3,6]
function list_remove(list, ind) =
assert(is_list(list), "Invalid list in list_remove")
is_finite(ind) ?
(
(ind<0 || ind>=len(list)) ? list
:
[
for (i=[0:1:ind-1]) list[i],
for (i=[ind+1:1:len(list)-1]) list[i]
]
)
: ind==[] ? list
: assert( is_vector(ind), "Invalid index list in list_remove")
let(sres = search(count(list),ind,1))
[
for(i=idx(list))
if (sres[i] == [])
list[i]
];
// This method is faster for long lists with few values to remove
// let( rem = list_set([], indices, repeat(1,len(indices)), minlen=len(list)))
// [for(i=idx(list)) if (rem[i]==0) list[i]];
// Function: list_remove_values()
// Synopsis: Removes items by value from a list.
// Topics: List Handling
// See Also: list_set(), list_insert(), list_remove()
// Usage:
// list = list_remove_values(list, values, [all]);
// Description:
// Removes the first, or all instances of the given value or list of values from the list.
// If you specify `all=false` and list a value twice then the first two instances will be removed.
// Note that if you want to remove a list value such as `[3,4]` then you must give it as
// a singleton list, or it will be interpreted as a list of two scalars to remove.
// Arguments:
// list = The list to modify.
// values = The value or list of values to remove from the list.
// all = If true, remove all instances of the value `value` from the list `list`. If false, remove only the first. Default: false
// Example:
// test = [3,4,[5,6],7,5,[5,6],4,[6,5],7,[4,4]];
// a=list_remove_values(test,4); // Returns: [3, [5, 6], 7, 5, [5, 6], 4, [6, 5], 7, [4, 4]]
// b=list_remove_values(test,[4,4]); // Returns: [3, [5, 6], 7, 5, [5, 6], [6, 5], 7, [4, 4]]
// c=list_remove_values(test,[4,7]); // Returns: [3, [5, 6], 5, [5, 6], 4, [6, 5], 7, [4, 4]]
// d=list_remove_values(test,[5,6]); // Returns: [3, 4, [5, 6], 7, [5, 6], 4, [6, 5], 7, [4, 4]]
// e=list_remove_values(test,[[5,6]]); // Returns: [3,4,7,5,[5,6],4,[6,5],7,[4,4]]
// f=list_remove_values(test,[[5,6]],all=true); // Returns: [3,4,7,5,4,[6,5],7,[4,4]]
// animals = ["bat", "cat", "rat", "dog", "bat", "rat"];
// animals2 = list_remove_values(animals, "rat"); // Returns: ["bat","cat","dog","bat","rat"]
// nonflying = list_remove_values(animals, "bat", all=true); // Returns: ["cat","rat","dog","rat"]
// animals3 = list_remove_values(animals, ["bat","rat"]); // Returns: ["cat","dog","bat","rat"]
// domestic = list_remove_values(animals, ["bat","rat"], all=true); // Returns: ["cat","dog"]
// animals4 = list_remove_values(animals, ["tucan","rat"], all=true); // Returns: ["bat","cat","dog","bat"]
function list_remove_values(list,values=[],all=false) =
!is_list(values)? list_remove_values(list, values=[values], all=all) :
assert(is_list(list), "Invalid list")
len(values)==0 ? list :
len(values)==1 ?
(
!all ?
(
let(firsthit = search(values,list,1)[0])
firsthit==[] ? list
: list[firsthit]==values[0] ? list_remove(list,firsthit)
: let(allhits = search(values,list,0)[0],
allind = [for(i=allhits) if (list[i]==values[0]) i]
)
allind==[] ? list : list_remove(list,min(allind))
)
:
(
let(allhits = search(values,list,0)[0],
allind = [for(i=allhits) if (list[i]==values[0]) i]
)
allind==[] ? list : list_remove(list,allind)
)
)
:!all ? list_remove_values(list_remove_values(list, values[0],all=all), list_tail(values),all=all)
:
[
for(i=idx(list))
let(hit=search([list[i]],values,0)[0])
if (hit==[]) list[i]
else
let(check = [for(j=hit) if (values[j]==list[i]) 1])
if (check==[]) list[i]
];
// Section: List Iteration Index Helper
// Function: idx()
// Synopsis: Returns a range useful for iterating over a list.
// Topics: List Handling, Iteration
// See Also: count()
// Usage:
// range = idx(list, [s=], [e=], [step=]);
// for(i=idx(list, [s=], [e=], [step=])) ...
// Description:
// Returns the range that gives the indices for a given list. This makes is a little bit
// easier to loop over a list by index, when you need the index numbers and looping of list values isn't enough.
// Note that the return is a **range** not a list.
// Arguments:
// list = The list to returns the index range of.
// ---
// s = The starting index. Default: 0
// e = The delta from the end of the list. Default: -1 (end of list)
// step = The step size to stride through the list. Default: 1
// Example(2D):
// colors = ["red", "green", "blue"];
// for (i=idx(colors)) right(20*i) color(colors[i]) circle(d=10);
function idx(list, s=0, e=-1, step=1) =
assert(is_list(list)||is_string(list), "Invalid input." )
let( ll = len(list) )
ll == 0 ? [0:1:ll-1] :
let(
_s = posmod(s,ll),
_e = posmod(e,ll)
) [_s : step : _e];
// Section: Lists of Subsets
// Function: pair()
// Synopsis: Returns a list of overlapping consecutive pairs in a list.
// Topics: List Handling, Iteration
// See Also: idx(), triplet(), combinations(), permutations()
// Usage:
// p = pair(list, [wrap]);
// for (p = pair(list, [wrap])) ... // On each iteration, p contains a list of two adjacent items.
// Description:
// Returns a list of all of the pairs of adjacent items from a list, optionally wrapping back to the front. The pairs overlap, and
// are returned in order starting with the first two entries in the list. If the list has less than two elements, the empty list is returned.
// Arguments:
// list = The list to use for making pairs
// wrap = If true, wrap back to the start from the end. ie: return the last and first items as the last pair. Default: false
// Example(2D): Does NOT wrap from end to start,
// for (p = pair(circle(d=40, $fn=12)))
// stroke(p, endcap2="arrow2");
// Example(2D): Wraps around from end to start.
// for (p = pair(circle(d=40, $fn=12), wrap=true))
// stroke(p, endcap2="arrow2");
// Example:
// l = ["A","B","C","D"];
// echo([for (p=pair(l)) str(p.y,p.x)]); // Outputs: ["BA", "CB", "DC"]
function pair(list, wrap=false) =
assert(is_list(list)||is_string(list), "Invalid input." )
assert(is_bool(wrap))
let( L = len(list)-1)
L<1 ? [] :
[
for (i=[0:1:L-1]) [list[i], list[i+1]],
if(wrap) [list[L], list[0]]
];
// Function: triplet()
// Synopsis: Returns a list of overlapping consecutive triplets in a list.
// Topics: List Handling, Iteration
// See Also: idx(), pair(), combinations(), permutations()
// Usage:
// list = triplet(list, [wrap]);
// for (t = triplet(list, [wrap])) ...
// Description:
// Returns a list of all adjacent triplets from a list, optionally wrapping back to the front.
// If you set `wrap` to true then the first triplet is the one centered on the first list element, so it includes
// the last element and the first two elements. If the list has fewer than three elements then the empty list is returned.
// Arguments:
// list = list to produce triplets from
// wrap = if true, wrap triplets around the list. Default: false
// Example:
// list = [0,1,2,3,4];
// a = triplet(list); // Returns [[0,1,2],[1,2,3],[2,3,4]]
// b = triplet(list,wrap=true); // Returns [[4,0,1],[0,1,2],[1,2,3],[2,3,4],[3,4,0]]
// letters = ["A","B","C","D","E"];
// [for (p=triplet(letters)) str(p.z,p.y,p.x)]; // Returns: ["CBA", "DCB", "EDC"]
// Example(2D):
// path = [for (i=[0:24]) polar_to_xy(i*2, i*360/12)];
// for (t = triplet(path)) {
// a = t[0]; b = t[1]; c = t[2];
// v = unit(unit(a-b) + unit(c-b));
// translate(b) rot(from=FWD,to=v) anchor_arrow2d();
// }
// stroke(path);
function triplet(list, wrap=false) =
assert(is_list(list)||is_string(list), "Invalid input." )
assert(is_bool(wrap))
let(L=len(list))
L<3 ? [] :
[
if(wrap) [list[L-1], list[0], list[1]],
for (i=[0:1:L-3]) [list[i],list[i+1],list[i+2]],
if(wrap) [list[L-2], list[L-1], list[0]]
];
// Function: combinations()
// Synopsis: Returns a list of all combinations of the list entries.
// Topics: List Handling, Iteration
// See Also: idx(), pair(), triplet(), permutations()
// Usage:
// list = combinations(l, [n]);
// Description:
// Returns a list of all of the (unordered) combinations of `n` items out of the given list `l`.
// 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]]`.
// 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]]`.
// Arguments:
// l = The list to provide permutations for.
// n = The number of items in each combination. Default: 2
// Example:
// pairs = combinations([3,4,5,6]); // Returns: [[3,4],[3,5],[3,6],[4,5],[4,6],[5,6]]
// triplets = combinations([3,4,5,6],n=3); // Returns: [[3,4,5],[3,4,6],[3,5,6],[4,5,6]]
// Example(2D):
// for (p=combinations(regular_ngon(n=7,d=100))) stroke(p);
function combinations(l,n=2,_s=0) =
assert(is_list(l), "Invalid list." )
assert( is_finite(n) && n>=1 && n<=len(l), "Invalid number `n`." )
n==1
? [for (i=[_s:1:len(l)-1]) [l[i]]]
: [for (i=[_s:1:len(l)-n], p=combinations(l,n=n-1,_s=i+1)) concat([l[i]], p)];
// Function: permutations()
// Synopsis: Returns a list of all permutations of the list entries.
// Topics: List Handling, Iteration
// See Also: idx(), pair(), triplet(), combinations()
// Usage:
// list = permutations(l, [n]);
// Description:
// Returns a list of all of the (ordered) permutation `n` items out of the given list `l`.
// For the list `[1,2,3]`, with `n=2`, this will return `[[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]]`
// For the list `[1,2,3]`, with `n=3`, this will return `[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]`
// Arguments:
// l = The list to provide permutations for.
// n = The number of items in each permutation. Default: 2
// Example:
// pairs = permutations([3,4,5,6]); // // Returns: [[3,4],[3,5],[3,6],[4,3],[4,5],[4,6],[5,3],[5,4],[5,6],[6,3],[6,4],[6,5]]
function permutations(l,n=2) =
assert(is_list(l), "Invalid list." )
assert( is_finite(n) && n>=1 && n<=len(l), "Invalid number `n`." )
n==1
? [for (i=[0:1:len(l)-1]) [l[i]]]
: [for (i=idx(l), p=permutations([for (j=idx(l)) if (i!=j) l[j]], n=n-1)) concat([l[i]], p)];
// Section: Changing List Structure
// Function: list_to_matrix()
// Synopsis: Groups items in a list into sublists.
// Topics: Matrices, List Handling
// See Also: column(), submatrix(), hstack(), flatten(), full_flatten()
// Usage:
// groups = list_to_matrix(v, cnt, [dflt]);
// Description:
// Takes a flat list of values, and groups items in sets of `cnt` length.
// The opposite of this is `flatten()`.
// Arguments:
// v = The list of items to group.
// cnt = The number of items to put in each grouping.
// dflt = The default value to fill in with if the list is not a multiple of `cnt` items long. Default: undef
// Example:
// v = [1,2,3,4,5,6];
// a = list_to_matrix(v,2) // returns [[1,2], [3,4], [5,6]]
// b = list_to_matrix(v,3) // returns [[1,2,3], [4,5,6]]
// c = list_to_matrix(v,4,0) // returns [[1,2,3,4], [5,6,0,0]]
function list_to_matrix(v, cnt, dflt=undef) =
[for (i = [0:cnt:len(v)-1]) [for (j = [0:1:cnt-1]) default(v[i+j], dflt)]];
// Function: flatten()
// Synopsis: Flattens a list of sublists into a single list.
// Topics: Matrices, List Handling
// See Also: column(), submatrix(), hstack(), full_flatten()
// Usage:
// list = flatten(l);
// Description:
// Takes a list of lists and flattens it by one level.
// Arguments:
// l = List to flatten.
// Example:
// l = flatten([[1,2,3], [4,5,[6,7,8]]]); // returns [1,2,3,4,5,[6,7,8]]
function flatten(l) =
!is_list(l)? l :
[for (a=l) if (is_list(a)) (each a) else a];
// Function: full_flatten()
// Synopsis: Recursively flattens nested sublists into a single list of non-list values.
// Topics: Matrices, List Handling
// See Also: column(), submatrix(), hstack(), flatten()
// Usage:
// list = full_flatten(l);
// Description:
// Collects in a list all elements recursively found in any level of the given list.
// The output list is ordered in depth first order.
// Arguments:
// l = List to flatten.
// Example:
// l = full_flatten([[1,2,3], [4,5,[6,7,8]]]); // returns [1,2,3,4,5,6,7,8]
function full_flatten(l) =
!is_list(l)? l :
[for (a=l) if (is_list(a)) (each full_flatten(a)) else a];
// Section: Set Manipulation
// Function: set_union()
// Synopsis: Merges two lists, returning a list of unique items.
// Topics: Set Handling, List Handling
// See Also: set_difference(), set_intersection()
// Usage:
// s = set_union(a, b, [get_indices]);
// Description:
// Given two sets (lists with unique items), returns the set of unique items that are in either `a` or `b`.
// If `get_indices` is true, a list of indices into the new union set are returned for each item in `b`,
// in addition to returning the new union set. In this case, a 2-item list is returned, `[INDICES, NEWSET]`,
// where INDICES is the list of indices for items in `b`, and NEWSET is the new union set.
// Arguments:
// a = One of the two sets to merge.
// b = The other of the two sets to merge.
// get_indices = If true, indices into the new union set are also returned for each item in `b`. Returns `[INDICES, NEWSET]`. Default: false
// Example:
// set_a = [2,3,5,7,11];
// set_b = [1,2,3,5,8];
// set_u = set_union(set_a, set_b);
// // set_u now equals [2,3,5,7,11,1,8]
// set_v = set_union(set_a, set_b, get_indices=true);
// // set_v now equals [[5,0,1,2,6], [2,3,5,7,11,1,8]]
function set_union(a, b, get_indices=false) =
assert( is_list(a) && is_list(b), "Invalid sets." )
let(
found1 = search(b, a),
found2 = search(b, b),
c = [ for (i=idx(b))
if (found1[i] == [] && found2[i] == i)
b[i]
],
nset = concat(a, c)
)
! get_indices ? nset :
let(
la = len(a),
found3 = search(b, c),
idxs = [ for (i=idx(b))
(found1[i] != [])? found1[i] : la + found3[i]
]
) [idxs, nset];
// Function: set_difference()
// Synopsis: Returns a list of unique items that are in list A, but not in list B.
// Topics: Set Handling, List Handling
// See Also: set_union(), set_intersection()
// Usage:
// s = set_difference(a, b);
// Description:
// Given two sets (lists with unique items), returns the set of items that are in `a`, but not `b`.
// Arguments:
// a = The starting set.
// b = The set of items to remove from set `a`.
// Example:
// set_a = [2,3,5,7,11];
// set_b = [1,2,3,5,8];
// set_d = set_difference(set_a, set_b);
// // set_d now equals [7,11]
function set_difference(a, b) =
assert( is_list(a) && is_list(b), "Invalid sets." )
let( found = search(a, b, num_returns_per_match=1) )
[ for (i=idx(a)) if(found[i]==[]) a[i] ];
// Function: set_intersection()
// Synopsis: Returns a list of unique items that are in both given lists.
// Topics: Set Handling, List Handling
// See Also: set_union(), set_difference()
// Usage:
// s = set_intersection(a, b);
// Description:
// Given two sets (lists with unique items), returns the set of items that are in both sets.
// Arguments:
// a = The starting set.
// b = The set of items to intersect with set `a`.
// Example:
// set_a = [2,3,5,7,11];
// set_b = [1,2,3,5,8];
// set_i = set_intersection(set_a, set_b);
// // set_i now equals [2,3,5]
function set_intersection(a, b) =
assert( is_list(a) && is_list(b), "Invalid sets." )
let( found = search(a, b, num_returns_per_match=1) )
[ for (i=idx(a)) if(found[i]!=[]) a[i] ];
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap