mirror of
https://github.com/BelfrySCAD/BOSL2.git
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1420 lines
57 KiB
OpenSCAD
1420 lines
57 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: arrays.scad
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// List and Array manipulation functions.
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// To use, add the following lines to the beginning of your file:
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// ```
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// use <BOSL2/std.scad>
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// ```
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//////////////////////////////////////////////////////////////////////
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// Section: Terminology
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// - **List**: An ordered collection of zero or more items. ie: `["a", "b", "c"]`
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// - **Vector**: A list of numbers. ie: `[4, 5, 6]`
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// - **Array**: A nested list of lists, or list of lists of lists, or deeper. ie: `[[2,3], [4,5], [6,7]]`
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// - **Dimension**: The depth of nesting of lists in an array. A List is 1D. A list of lists is 2D. etc.
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// - **Set**: A list of unique items.
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// Section: List Query Operations
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// Function: is_homogeneous()
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// Usage:
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// is_homogeneous(list,depth)
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// Description:
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// Returns true when the list have elements of same type up to the depth `depth`.
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// Booleans and numbers are not distinguinshed as of distinct types.
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// Arguments:
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// list = the list to check
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// depth = the lowest level the check is done
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// Example:
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// is_homogeneous( [[1,["a"]], [2,["b"]]] ) // Returns true
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// is_homogeneous( [[1,["a"]], [2,[true]]] ) // Returns false
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// is_homogeneous( [[1,["a"]], [2,[true]]], 1 ) // Returns true
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// is_homogeneous( [[1,["a"]], [2,[true]]], 2 ) // Returns false
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// is_homogeneous( [[1,["a"]], [true,["b"]]] ) // Returns true
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function is_homogeneous(l, depth=10) =
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!is_list(l) || l==[] ? false :
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let( l0=l[0] )
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[] == [for(i=[1:len(l)-1]) if( ! _same_type(l[i],l0, depth+1) ) 0 ];
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function _same_type(a,b, depth) =
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(depth==0) ||
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(is_undef(a) && is_undef(b)) ||
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(is_bool(a) && is_bool(b)) ||
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(is_num(a) && is_num(b)) ||
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(is_string(a) && is_string(b)) ||
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(is_list(a) && is_list(b) && len(a)==len(b)
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&& []==[for(i=idx(a)) if( ! _same_type(a[i],b[i],depth-1) ) 0] );
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// Function: select()
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// Description:
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// Returns a portion of a list, wrapping around past the beginning, if end<start.
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// The first item is index 0. Negative indexes are counted back from the end.
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// The last item is -1. If only the `start` index is given, returns just the value
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// at that position.
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// Usage:
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// select(list,start)
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// select(list,start,end)
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// Arguments:
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// list = The list to get the portion of.
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// start = The index of the first item.
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// end = The index of the last item.
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// Example:
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// l = [3,4,5,6,7,8,9];
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// select(l, 5, 6); // Returns [8,9]
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// select(l, 5, 8); // Returns [8,9,3,4]
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// select(l, 5, 2); // Returns [8,9,3,4,5]
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// select(l, -3, -1); // Returns [7,8,9]
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// select(l, 3, 3); // Returns [6]
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// select(l, 4); // Returns 7
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// select(l, -2); // Returns 8
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// select(l, [1:3]); // Returns [4,5,6]
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// select(l, [1,3]); // Returns [4,6]
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function select(list, start, end=undef) =
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assert( is_list(list) || is_string(list), "Invalid list.")
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let(l=len(list))
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l==0 ? []
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: end==undef?
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is_num(start)?
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list[ (start%l+l)%l ]
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: assert( is_list(start) || is_range(start), "Invalid start parameter")
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[for (i=start) list[ (i%l+l)%l ] ]
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: assert(is_finite(start), "Invalid start parameter.")
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assert(is_finite(end), "Invalid end parameter.")
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let( s = (start%l+l)%l, e = (end%l+l)%l )
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(s <= e)? [for (i = [s:1:e]) list[i]]
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: concat([for (i = [s:1:l-1]) list[i]], [for (i = [0:1:e]) list[i]]) ;
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// Function: slice()
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// Description:
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// Returns a slice of a list. The first item is index 0.
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// Negative indexes are counted back from the end. The last item is -1.
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// Arguments:
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// list = The array/list to get the slice of.
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// start = The index of the first item to return.
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// end = The index after the last item to return, unless negative, in which case the last item to return.
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// Example:
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// slice([3,4,5,6,7,8,9], 3, 5); // Returns [6,7]
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// slice([3,4,5,6,7,8,9], 2, -1); // Returns [5,6,7,8,9]
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// slice([3,4,5,6,7,8,9], 1, 1); // Returns []
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// slice([3,4,5,6,7,8,9], 6, -1); // Returns [9]
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// slice([3,4,5,6,7,8,9], 2, -2); // Returns [5,6,7,8]
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function slice(list,start,end) =
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assert( is_list(list), "Invalid list" )
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assert( is_finite(start) && is_finite(end), "Invalid number(s)" )
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let( l = len(list) )
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l==0 ? []
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: let(
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s = start<0? (l+start): start,
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e = end<0? (l+end+1): end
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) [for (i=[s:1:e-1]) if (e>s) list[i]];
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// Function: in_list()
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// Description: Returns true if value `val` is in list `list`. When `val==NAN` the answer will be false for any list.
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// Arguments:
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// val = The simple value to search for.
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// list = The list to search.
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// idx = If given, searches the given subindex for matches for `val`.
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// Example:
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// in_list("bar", ["foo", "bar", "baz"]); // Returns true.
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// in_list("bee", ["foo", "bar", "baz"]); // Returns false.
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// in_list("bar", [[2,"foo"], [4,"bar"], [3,"baz"]], idx=1); // Returns true.
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function in_list(val,list,idx=undef) =
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assert( is_list(list) && (is_undef(idx) || is_finite(idx)),
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"Invalid input." )
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let( s = search([val], list, num_returns_per_match=1, index_col_num=idx)[0] )
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s==[] || s==[[]] ? false
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: is_undef(idx) ? val==list[s]
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: val==list[s][idx];
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// Function: min_index()
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// Usage:
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// min_index(vals,[all]);
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// Description:
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// Returns the index of the first occurrence of the minimum value in the given list.
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// If `all` is true then returns a list of all indices where the minimum value occurs.
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// Arguments:
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// vals = vector of values
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// all = set to true to return indices of all occurences of the minimum. Default: false
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// Example:
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// min_index([5,3,9,6,2,7,8,2,1]); // Returns: 8
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// 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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// max_index(vals,[all]);
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// Description:
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// Returns the index of the first occurrence of the maximum value in the given list.
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// If `all` is true then returns a list of all indices where the maximum value occurs.
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// Arguments:
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// vals = vector of values
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// all = set to true to return indices of all occurences of the maximum. Default: false
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// Example:
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// max_index([5,3,9,6,2,7,8,9,1]); // Returns: 2
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// max_index([5,3,9,6,2,7,8,9,1],all=true); // Returns: [2,7]
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function max_index(vals, all=false) =
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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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// Function: list_increasing()
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// Usage:
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// list_increasing(list)
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// Description:
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// Returns true if the list is (non-strictly) increasing
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// Example:
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// list_increasing([1,2,3,4]); // Returns: true
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// list_increasing([1,3,2,4]); // Returns: false
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// list_increasing([4,3,2,1]); // Returns: false
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function list_increasing(list) =
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assert(is_list(list)||is_string(list))
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len([for (p=pair(list)) if(p.x>p.y) true])==0;
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// Function: list_decreasing()
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// Usage:
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// list_decreasing(list)
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// Description:
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// Returns true if the list is (non-strictly) decreasing
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// Example:
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// list_decreasing([1,2,3,4]); // Returns: false
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// list_decreasing([4,2,3,1]); // Returns: false
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// list_decreasing([4,3,2,1]); // Returns: true
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function list_decreasing(list) =
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assert(is_list(list)||is_string(list))
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len([for (p=pair(list)) if(p.x<p.y) true])==0;
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// Section: Basic List Generation
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// Function: repeat()
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// Usage:
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// repeat(val, n)
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// Description:
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// Generates a list or array of `n` copies of the given value `val`.
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// If the count `n` is given as a list of counts, then this creates a
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// multi-dimensional array, filled with `val`.
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// Arguments:
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// val = The value to repeat to make the list or array.
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// n = The number of copies to make of `val`.
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// Example:
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// repeat(1, 4); // Returns [1,1,1,1]
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// repeat(8, [2,3]); // Returns [[8,8,8], [8,8,8]]
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// repeat(0, [2,2,3]); // Returns [[[0,0,0],[0,0,0]], [[0,0,0],[0,0,0]]]
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// repeat([1,2,3],3); // Returns [[1,2,3], [1,2,3], [1,2,3]]
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function repeat(val, n, i=0) =
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is_num(n)? [for(j=[1:1:n]) val] :
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assert( is_list(n), "Invalid count number.")
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(i>=len(n))? val :
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[for (j=[1:1:n[i]]) repeat(val, n, i+1)];
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// Function: list_range()
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// Usage:
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// list_range(n, [s], [e])
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// list_range(n, [s], [step])
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// list_range(e, [step])
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// list_range(s, e, [step])
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// Description:
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// Returns a list, counting up from starting value `s`, by `step` increments,
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// until either `n` values are in the list, or it reaches the end value `e`.
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// If both `n` and `e` are given, returns `n` values evenly spread from `s`
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// to `e`, and `step` is ignored.
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// Arguments:
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// n = Desired number of values in returned list, if given.
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// s = Starting value. Default: 0
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// e = Ending value to stop at, if given.
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// step = Amount to increment each value. Default: 1
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// Example:
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// list_range(4); // Returns [0,1,2,3]
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// list_range(n=4, step=2); // Returns [0,2,4,6]
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// list_range(n=4, s=3, step=3); // Returns [3,6,9,12]
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// list_range(n=5, s=0, e=10); // Returns [0, 2.5, 5, 7.5, 10]
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// list_range(e=3); // Returns [0,1,2,3]
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// list_range(e=7, step=2); // Returns [0,2,4,6]
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// list_range(s=3, e=5); // Returns [3,4,5]
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// list_range(s=3, e=8, step=2); // Returns [3,5,7]
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// list_range(s=4, e=8.3, step=2); // Returns [4,6,8]
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// list_range(n=4, s=[3,4], step=[2,3]); // Returns [[3,4], [5,7], [7,10], [9,13]]
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function list_range(n=undef, s=0, e=undef, step=undef) =
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assert( is_undef(n) || is_finite(n), "Parameter `n` must be a number.")
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assert( is_undef(n) || is_undef(e) || is_undef(step), "At most 2 of n, e, and step can be given.")
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let( step = (n!=undef && e!=undef)? (e-s)/(n-1) : default(step,1) )
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is_undef(e) ?
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assert( is_consistent([s, step]), "Incompatible data.")
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[for (i=[0:1:n-1]) s+step*i ]
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: assert( is_vector([s,step,e]), "Start `s`, step `step` and end `e` must be numbers.")
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[for (v=[s:step:e]) v] ;
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// Section: List Manipulation
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// Function: reverse()
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// Description: Reverses a list/array or string.
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// Arguments:
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// x = The list or string to reverse.
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// Example:
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// reverse([3,4,5,6]); // Returns [6,5,4,3]
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function reverse(x) =
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assert(is_list(x)||is_string(x))
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let (elems = [ for (i = [len(x)-1 : -1 : 0]) x[i] ])
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is_string(x)? str_join(elems) : elems;
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// Function: list_rotate()
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// Usage:
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// rlist = list_rotate(list,n);
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// Description:
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// Rotates the contents of a list by `n` positions left.
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// If `n` is negative, then the rotation is `abs(n)` positions to the right.
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// If `list` is a string, then a string is returned with the characters rotates within the string.
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// Arguments:
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// list = The list to rotate.
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// n = The number of positions to rotate by. If negative, rotated to the right. Positive rotates to the left. Default: 1
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// Example:
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// l1 = list_rotate([1,2,3,4,5],-2); // Returns: [4,5,1,2,3]
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// l2 = list_rotate([1,2,3,4,5],-1); // Returns: [5,1,2,3,4]
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// l3 = list_rotate([1,2,3,4,5],0); // Returns: [1,2,3,4,5]
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// l4 = list_rotate([1,2,3,4,5],1); // Returns: [2,3,4,5,1]
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// l5 = list_rotate([1,2,3,4,5],2); // Returns: [3,4,5,1,2]
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// l6 = list_rotate([1,2,3,4,5],3); // Returns: [4,5,1,2,3]
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// l7 = list_rotate([1,2,3,4,5],4); // Returns: [5,1,2,3,4]
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// l8 = list_rotate([1,2,3,4,5],5); // Returns: [1,2,3,4,5]
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// l9 = list_rotate([1,2,3,4,5],6); // Returns: [2,3,4,5,1]
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function list_rotate(list,n=1) =
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assert(is_list(list)||is_string(list), "Invalid list or string.")
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assert(is_finite(n), "Invalid number")
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let (elems = select(list,n,n+len(list)-1))
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is_string(list)? str_join(elems) : elems;
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// Function: deduplicate()
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// Usage:
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// deduplicate(list,[close],[eps]);
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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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// This is different from `unique()` in that 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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// Examples:
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// deduplicate([8,3,4,4,4,8,2,3,3,8,8]); // Returns: [8,3,4,8,2,3,8]
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// 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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// deduplicate("Hello"); // Returns: "Helo"
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// deduplicate([[3,4],[7,2],[7,1.99],[1,4]],eps=0.1); // Returns: [[3,4],[7,2],[1,4]]
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// 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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// Description:
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// Given a list, and indices into it, removes consecutive indices that
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// index to the same values in the list.
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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 what they index matches what the first index indexes.
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// eps = The maximum difference to allow between numbers or vectors.
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// Examples:
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// 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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// 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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// deduplicate_indexed([[7,undef],[7,undef],[1,4],[1,4],[1,4+1e-12]],eps=0); // Returns: [0,2,4]
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function deduplicate_indexed(list, indices, closed=false, eps=EPSILON) =
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assert(is_list(list)||is_string(list), "Improper list or string.")
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indices==[]? [] :
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assert(is_vector(indices), "Indices must be a list of numbers.")
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let( l = len(indices),
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end = l-(closed?0:1) )
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[ for (i = [0:1:l-1])
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let(
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a = list[indices[i]],
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b = list[indices[(i+1)%l]],
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eq = (a == b)? true :
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(a*0 != b*0) || (eps==0)? false :
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is_num(a) || is_vector(a) ? approx(a, b, eps=eps)
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: false
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)
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if (i==end || !eq) indices[i]
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];
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// Function: repeat_entries()
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// Usage:
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// newlist = repeat_entries(list, N)
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// Description:
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// Takes a list as input and duplicates some of its entries to produce a list
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// with length `N`. If the requested `N` is not a multiple of the list length then
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// the entries will be duplicated as uniformly as possible. You can also set `N` to a vector,
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// in which case len(N) must equal len(list) and the output repeats the ith entry N[i] times.
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// 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
|
|
// Examples:
|
|
// list = [0,1,2,3];
|
|
// echo(repeat_entries(list, 6)); // Outputs [0,0,1,2,2,3]
|
|
// echo(repeat_entries(list, 6, exact=false)); // Outputs [0,0,1,1,2,2,3,3]
|
|
// echo(repeat_entries(list, [1,1,2,1], exact=false)); // Outputs [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_set()
|
|
// Usage:
|
|
// 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
|
|
// beyond the length of the list then the list is extended and filled in with the `dflt` value.
|
|
// 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.
|
|
// Examples:
|
|
// list_set([2,3,4,5], 2, 21); // Returns: [2,3,21,5]
|
|
// 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)? (
|
|
(is_finite(indices) && indices<len(list))?
|
|
[for (i=idx(list)) i==indices? values : list[i]]
|
|
: list_set(list,[indices],[values],dflt) )
|
|
: assert(is_vector(indices) && is_list(values) && len(values)==len(indices) ,
|
|
"Index list and value list must have the same length")
|
|
let( midx = max(len(list)-1, max(indices)) )
|
|
[ for(i=[0:midx] )
|
|
let( j = search(i,indices,0),
|
|
k = j[0] )
|
|
assert( len(j)<2, "Repeated indices are not acceptable." )
|
|
k!=undef ? values[k] :
|
|
i<len(list) ? list[i]:
|
|
dflt ,
|
|
each repeat(dflt, minlen-max(indices))
|
|
];
|
|
|
|
|
|
// Function: list_insert()
|
|
// Usage:
|
|
// list_insert(list, indices, values);
|
|
// Description:
|
|
// Insert `values` into `list` before position `indices`.
|
|
// Example:
|
|
// list_insert([3,6,9,12],1,5); // Returns [3,5,6,9,12]
|
|
// list_insert([3,6,9,12],[1,3],[5,11]); // Returns [3,5,6,9,11,12]
|
|
function list_insert(list, indices, values, _i=0) =
|
|
assert(is_list(list))
|
|
! is_list(indices)?
|
|
assert( is_finite(indices) && is_finite(values), "Invalid indices/values." )
|
|
assert( indices<=len(list), "Indices must be <= len(list) ." )
|
|
[for (i=idx(list)) each ( i==indices? [ values, list[i] ] : [ list[i] ] ) ]
|
|
: 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( maxidx = max(indices),
|
|
minidx = min(indices) )
|
|
[ 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 acceptable." )
|
|
)
|
|
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()
|
|
// Usage:
|
|
// list_remove(list, indices)
|
|
// Description:
|
|
// Remove all items from `list` whose indexes are in `indices`.
|
|
// Arguments:
|
|
// list = The list to remove items from.
|
|
// indices = The list of indexes of items to remove.
|
|
// Example:
|
|
// list_insert([3,6,9,12],1); // Returns: [3,9,12]
|
|
// list_insert([3,6,9,12],[1,3]); // Returns: [3,9]
|
|
function list_remove(list, indices) =
|
|
assert(is_list(list))
|
|
is_finite(indices) ?
|
|
[
|
|
for (i=[0:1:min(indices, len(list)-1)-1]) list[i],
|
|
for (i=[min(indices, len(list)-1)+1:1:len(list)-1]) list[i]
|
|
]
|
|
: indices==[] ? list
|
|
: assert( is_vector(indices), "Invalid list `indices`." )
|
|
[
|
|
for(i=[0:len(list)-1])
|
|
if ( []==search(i,indices,1) )
|
|
list[i]
|
|
];
|
|
|
|
|
|
// Function: list_remove_values()
|
|
// Usage:
|
|
// list_remove_values(list,values,all=false) =
|
|
// Description:
|
|
// Removes the first, or all instances of the given `values` from the `list`.
|
|
// Returns the modified list.
|
|
// Arguments:
|
|
// list = The list to modify.
|
|
// values = The 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:
|
|
// 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) =
|
|
assert(is_list(list))
|
|
!is_list(values)? list_remove_values(list, values=[values], all=all) :
|
|
let(
|
|
idxs = all? flatten(search(values,list,0)) : search(values,list,1),
|
|
uidxs = unique(idxs)
|
|
) list_remove(list,uidxs);
|
|
|
|
|
|
// Function: bselect()
|
|
// Usage:
|
|
// bselect(array,index);
|
|
// Description:
|
|
// Returns the items in `array` whose matching element in `index` is true.
|
|
// Arguments:
|
|
// array = Initial list to extract items from.
|
|
// index = List of booleans.
|
|
// Example:
|
|
// bselect([3,4,5,6,7], [false,true,true,false,true]); // Returns: [4,5,7]
|
|
function bselect(array,index) =
|
|
assert(is_list(array)||is_string(array), "Improper array." )
|
|
assert(is_list(index) && len(index)>=len(array) , "Improper index list." )
|
|
is_string(array)? str_join(bselect( [for (x=array) x], index)) :
|
|
[for(i=[0:len(array)-1]) if (index[i]) array[i]];
|
|
|
|
|
|
// Function: list_bset()
|
|
// Usage:
|
|
// 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.
|
|
// Example:
|
|
// list_bset([false,true,false,true,false], [3,4]); // Returns: [0,3,0,4,0]
|
|
// 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
|
|
);
|
|
|
|
|
|
// Section: List Length Manipulation
|
|
|
|
// Function: list_shortest()
|
|
// Description:
|
|
// Returns the length of the shortest sublist in a list of lists.
|
|
// Arguments:
|
|
// array = A list of lists.
|
|
function list_shortest(array) =
|
|
assert(is_list(array), "Invalid input." )
|
|
min([for (v = array) len(v)]);
|
|
|
|
|
|
// Function: list_longest()
|
|
// Description:
|
|
// Returns the length of the longest sublist in a list of lists.
|
|
// Arguments:
|
|
// array = A list of lists.
|
|
function list_longest(array) =
|
|
assert(is_list(array), "Invalid input." )
|
|
max([for (v = array) len(v)]);
|
|
|
|
|
|
// Function: list_pad()
|
|
// Description:
|
|
// If the list `array` is shorter than `minlen` length, pad it to length with the value given in `fill`.
|
|
// Arguments:
|
|
// array = A list.
|
|
// minlen = The minimum length to pad the list to.
|
|
// fill = The value to pad the list with.
|
|
function list_pad(array, minlen, fill=undef) =
|
|
assert(is_list(array), "Invalid input." )
|
|
concat(array,repeat(fill,minlen-len(array)));
|
|
|
|
|
|
// Function: list_trim()
|
|
// Description:
|
|
// If the list `array` is longer than `maxlen` length, truncates it to be `maxlen` items long.
|
|
// Arguments:
|
|
// array = A list.
|
|
// minlen = The minimum length to pad the list to.
|
|
function list_trim(array, maxlen) =
|
|
assert(is_list(array), "Invalid input." )
|
|
[for (i=[0:1:min(len(array),maxlen)-1]) array[i]];
|
|
|
|
|
|
// Function: list_fit()
|
|
// Description:
|
|
// If the list `array` is longer than `length` items long, truncates it to be exactly `length` items long.
|
|
// If the list `array` is shorter than `length` items long, pad it to length with the value given in `fill`.
|
|
// Arguments:
|
|
// array = A list.
|
|
// minlen = The minimum length to pad the list to.
|
|
// fill = The value to pad the list with.
|
|
function list_fit(array, length, fill) =
|
|
assert(is_list(array), "Invalid input." )
|
|
let(l=len(array))
|
|
l==length ? array :
|
|
l> length ? list_trim(array,length)
|
|
: list_pad(array,length,fill);
|
|
|
|
|
|
// Section: List Shuffling and 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 ) ) );
|
|
|
|
|
|
// Function: shuffle()
|
|
// Description:
|
|
// Shuffles the input list into random order.
|
|
// If given a string, shuffles the characters within the string.
|
|
function shuffle(list) =
|
|
assert(is_list(list)||is_string(list), "Invalid input." )
|
|
is_string(list)? str_join(shuffle([for (x = list) x])) :
|
|
len(list)<=1 ? list :
|
|
let (
|
|
rval = 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));
|
|
|
|
|
|
// 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( arrind = _indexed_sort(enumerate(arr,idx)) )
|
|
indexed
|
|
? arrind
|
|
: [for(i=arrind) arr[i]];
|
|
|
|
// lexical sort using compare_vals()
|
|
function _lexical_sort(arr) =
|
|
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:
|
|
// sort(list, [idx])
|
|
// 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 = array_dim(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()
|
|
// 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.
|
|
// 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 = array_dim(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: unique()
|
|
// Usage:
|
|
// l = unique(list);
|
|
// Description:
|
|
// Returns a sorted list with all repeated items removed.
|
|
// Arguments:
|
|
// list = The list to uniquify.
|
|
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 :
|
|
let( sorted = sort(list))
|
|
[ for (i=[0:1:len(sorted)-1])
|
|
if (i==0 || (sorted[i] != sorted[i-1]))
|
|
sorted[i]
|
|
];
|
|
|
|
|
|
// Function: unique_count()
|
|
// Usage:
|
|
// counts = unique_count(list);
|
|
// 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.
|
|
function unique_count(list) =
|
|
assert(is_list(list) || is_string(list), "Invalid input." )
|
|
list == [] ? [[],[]] :
|
|
let( list=sort(list) )
|
|
let( 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: List Iteration Helpers
|
|
|
|
// Function: idx()
|
|
// Usage:
|
|
// i = idx(list);
|
|
// for(i=idx(list)) ...
|
|
// Description:
|
|
// Returns the range of indexes for the given list.
|
|
// Arguments:
|
|
// list = The list to returns the index range of.
|
|
// step = The step size to stride through the list. Default: 1
|
|
// end = The delta from the end of the list. Default: -1
|
|
// start = The starting index. Default: 0
|
|
// Example(2D):
|
|
// colors = ["red", "green", "blue"];
|
|
// for (i=idx(colors)) right(20*i) color(colors[i]) circle(d=10);
|
|
function idx(list, step=1, end=-1,start=0) =
|
|
assert(is_list(list)||is_string(list), "Invalid input." )
|
|
[start : step : len(list)+end];
|
|
|
|
|
|
// Function: enumerate()
|
|
// Description:
|
|
// Returns a list, with each item of the given list `l` numbered in a sublist.
|
|
// Something like: `[[0,l[0]], [1,l[1]], [2,l[2]], ...]`
|
|
// Arguments:
|
|
// l = List to enumerate.
|
|
// idx = If given, enumerates just the given subindex items of `l`.
|
|
// Example:
|
|
// enumerate(["a","b","c"]); // Returns: [[0,"a"], [1,"b"], [2,"c"]]
|
|
// enumerate([[88,"a"],[76,"b"],[21,"c"]], idx=1); // Returns: [[0,"a"], [1,"b"], [2,"c"]]
|
|
// enumerate([["cat","a",12],["dog","b",10],["log","c",14]], idx=[1:2]); // Returns: [[0,"a",12], [1,"b",10], [2,"c",14]]
|
|
// Example(2D):
|
|
// colors = ["red", "green", "blue"];
|
|
// for (p=enumerate(colors)) right(20*p[0]) color(p[1]) circle(d=10);
|
|
function enumerate(l,idx=undef) =
|
|
assert(is_list(l)||is_string(list), "Invalid input." )
|
|
assert( _valid_idx(idx,0,len(l)), "Invalid index/indices." )
|
|
(idx==undef)
|
|
? [for (i=[0:1:len(l)-1]) [i,l[i]]]
|
|
: [for (i=[0:1:len(l)-1]) [ i, for (j=idx) l[i][j]] ];
|
|
|
|
|
|
// Function: force_list()
|
|
// 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`)
|
|
// Examples:
|
|
// 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];
|
|
|
|
|
|
// Function: pair()
|
|
// Usage:
|
|
// pair(v)
|
|
// Description:
|
|
// Takes a list, and returns a list of adjacent pairs from it.
|
|
// Example(2D): Note that the last point and first point do NOT get paired together.
|
|
// for (p = pair(circle(d=20, $fn=12)))
|
|
// move(p[0])
|
|
// rot(from=BACK, to=p[1]-p[0])
|
|
// trapezoid(w1=1, w2=0, h=norm(p[1]-p[0]), anchor=FRONT);
|
|
// Example:
|
|
// l = ["A","B","C","D"];
|
|
// echo([for (p=pair(l)) str(p.y,p.x)]); // Outputs: ["BA", "CB", "DC"]
|
|
function pair(v) =
|
|
assert(is_list(v)||is_string(v), "Invalid input." )
|
|
[for (i=[0:1:len(v)-2]) [v[i],v[i+1]]];
|
|
|
|
|
|
// Function: pair_wrap()
|
|
// Usage:
|
|
// pair_wrap(v)
|
|
// Description:
|
|
// Takes a list, and returns a list of adjacent pairs from it, wrapping around from the end to the start of the list.
|
|
// Example(2D):
|
|
// for (p = pair_wrap(circle(d=20, $fn=12)))
|
|
// move(p[0])
|
|
// rot(from=BACK, to=p[1]-p[0])
|
|
// trapezoid(w1=1, w2=0, h=norm(p[1]-p[0]), anchor=FRONT);
|
|
// Example:
|
|
// l = ["A","B","C","D"];
|
|
// echo([for (p=pair_wrap(l)) str(p.y,p.x)]); // Outputs: ["BA", "CB", "DC", "AD"]
|
|
function pair_wrap(v) =
|
|
assert(is_list(v)||is_string(v), "Invalid input." )
|
|
[for (i=[0:1:len(v)-1]) [v[i],v[(i+1)%len(v)]]];
|
|
|
|
|
|
// Function: triplet()
|
|
// Usage:
|
|
// triplet(v)
|
|
// Description:
|
|
// Takes a list, and returns a list of adjacent triplets from it.
|
|
// Example:
|
|
// l = ["A","B","C","D","E"];
|
|
// echo([for (p=triplet(l)) str(p.z,p.y,p.x)]); // Outputs: ["CBA", "DCB", "EDC"]
|
|
function triplet(v) =
|
|
assert(is_list(v)||is_string(v), "Invalid input." )
|
|
[for (i=[0:1:len(v)-3]) [v[i],v[i+1],v[i+2]]];
|
|
|
|
|
|
// Function: triplet_wrap()
|
|
// Usage:
|
|
// triplet_wrap(v)
|
|
// Description:
|
|
// Takes a list, and returns a list of adjacent triplets from it, wrapping around from the end to the start of the list.
|
|
// Example:
|
|
// l = ["A","B","C","D"];
|
|
// echo([for (p=triplet_wrap(l)) str(p.z,p.y,p.x)]); // Outputs: ["CBA", "DCB", "ADC", "BAD"]
|
|
function triplet_wrap(v) =
|
|
assert(is_list(v)||is_string(v), "Invalid input." )
|
|
[for (i=[0:1:len(v)-1]) [v[i],v[(i+1)%len(v)],v[(i+2)%len(v)]]];
|
|
|
|
|
|
// Function: permute()
|
|
// Usage:
|
|
// list = permute(l, [n]);
|
|
// Description:
|
|
// Returns an ordered list of every unique permutation 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 permutation. Default: 2
|
|
// Example:
|
|
// pairs = permute([3,4,5,6]); // Returns: [[3,4],[3,5],[3,6],[4,5],[4,6],[5,6]]
|
|
// triplets = permute([3,4,5,6],n=3); // Returns: [[3,4,5],[3,4,6],[3,5,6],[4,5,6]]
|
|
// Example(2D):
|
|
// for (p=permute(regular_ngon(n=7,d=100))) stroke(p);
|
|
function permute(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=permute(l,n=n-1,_s=i+1)) concat([l[i]], p)];
|
|
|
|
|
|
|
|
// Section: Set Manipulation
|
|
|
|
// Function: set_union()
|
|
// 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()
|
|
// 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()
|
|
// 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] ];
|
|
|
|
|
|
|
|
// Section: Array Manipulation
|
|
|
|
// Function: add_scalar()
|
|
// Usage:
|
|
// add_scalar(v,s);
|
|
// Description:
|
|
// Given an array and a scalar, returns the array with the scalar added to each item in it.
|
|
// If given a list of arrays, recursively adds the scalar to the each array.
|
|
// Arguments:
|
|
// v = The initial array.
|
|
// s = A scalar value to add to every item in the array.
|
|
// Example:
|
|
// add_scalar([1,2,3],3); // Returns: [4,5,6]
|
|
// add_scalar([[1,2,3],[3,4,5]],3); // Returns: [[4,5,6],[6,7,8]]
|
|
function add_scalar(v,s) =
|
|
is_finite(s) ? [for (x=v) is_list(x)? add_scalar(x,s) : is_finite(x) ? x+s: x] : v;
|
|
|
|
|
|
// Function: subindex()
|
|
// Usage:
|
|
// subindex(M, idx)
|
|
// Description:
|
|
// Extracts the entries listed in idx from each entry in M. For a matrix this means
|
|
// selecting a specified set of columns. If idx is a number the return is a vector,
|
|
// otherwise it is a list of lists (the submatrix).
|
|
// This function will return `undef` at all entry positions indexed by idx not found in the input list M.
|
|
// Arguments:
|
|
// M = The given list of lists.
|
|
// idx = The index, list of indices, or range of indices to fetch.
|
|
// Example:
|
|
// M = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]];
|
|
// subindex(M,2); // Returns [3, 7, 11, 15]
|
|
// subindex(M,[2]); // Returns [[3], [7], [11], [15]]
|
|
// subindex(M,[2,1]); // Returns [[3, 2], [7, 6], [11, 10], [15, 14]]
|
|
// subindex(M,[1:3]); // Returns [[2, 3, 4], [6, 7, 8], [10, 11, 12], [14, 15, 16]]
|
|
// N = [ [1,2], [3], [4,5], [6,7,8] ];
|
|
// subindex(N,[0,1]); // Returns [ [1,2], [3,undef], [4,5], [6,7] ]
|
|
function subindex(M, idx) =
|
|
assert( is_list(M), "The input is not a list." )
|
|
assert( !is_undef(idx) && _valid_idx(idx,0,1/0), "Invalid index input." )
|
|
is_finite(idx)
|
|
? [for(row=M) row[idx]]
|
|
: [for(row=M) [for(i=idx) row[i]]];
|
|
|
|
|
|
// Function: submatrix()
|
|
// Usage:
|
|
// mat = submatrix(M, idx1, idx2)
|
|
// Description:
|
|
// The input must be a list of lists (a matrix or 2d array). Returns a submatrix by selecting the rows listed in idx1 and columns listed in idx2.
|
|
// Arguments:
|
|
// M = Given list of lists
|
|
// idx1 = rows index list or range
|
|
// idx2 = column index list or range
|
|
// Example:
|
|
// M = [[ 1, 2, 3, 4, 5],
|
|
// [ 6, 7, 8, 9,10],
|
|
// [11,12,13,14,15],
|
|
// [16,17,18,19,20],
|
|
// [21,22,23,24,25]];
|
|
// submatrix(M,[1:2],[3:4]); // Returns [[9, 10], [14, 15]]
|
|
// submatrix(M,[1], [3,4])); // Returns [[9,10]]
|
|
// submatrix(M,1, [3,4])); // Returns [[9,10]]
|
|
// submatrix(M,1,3)); // Returns [[9]]
|
|
// submatrix(M, [3,4],1); // Returns [[17],[22]]);
|
|
// submatrix(M, [1,3],[2,4]); // Returns [[8,10],[18,20]]);
|
|
// A = [[true, 17, "test"],
|
|
// [[4,2], 91, false],
|
|
// [6, [3,4], undef]];
|
|
// submatrix(A,[0,2],[1,2]); // Returns [[17, "test"], [[3, 4], undef]]
|
|
|
|
function submatrix(M,idx1,idx2) =
|
|
[for(i=idx1) [for(j=idx2) M[i][j] ] ];
|
|
|
|
|
|
// Function: zip()
|
|
// Usage:
|
|
// zip(v1, v2, v3, [fit], [fill]);
|
|
// zip(vecs, [fit], [fill]);
|
|
// Description:
|
|
// Zips together corresponding items from two or more lists.
|
|
// Returns a list of lists, where each sublist contains corresponding
|
|
// items from each of the input lists. `[[A1, B1, C1], [A2, B2, C2], ...]`
|
|
// Arguments:
|
|
// vecs = A list of two or more lists to zipper together.
|
|
// fit = If `fit=="short"`, the zips together up to the length of the shortest list in vecs. If `fit=="long"`, then pads all lists to the length of the longest, using the value in `fill`. If `fit==false`, then requires all lists to be the same length. Default: false.
|
|
// fill = The default value to fill in with if one or more lists if short. Default: undef
|
|
// Example:
|
|
// v1 = [1,2,3,4];
|
|
// v2 = [5,6,7];
|
|
// v3 = [8,9,10,11];
|
|
// zip(v1,v3); // returns [[1,8], [2,9], [3,10], [4,11]]
|
|
// zip([v1,v3]); // returns [[1,8], [2,9], [3,10], [4,11]]
|
|
// zip([v1,v2], fit="short"); // returns [[1,5], [2,6], [3,7]]
|
|
// zip([v1,v2], fit="long"); // returns [[1,5], [2,6], [3,7], [4,undef]]
|
|
// zip([v1,v2], fit="long, fill=0); // returns [[1,5], [2,6], [3,7], [4,0]]
|
|
// zip([v1,v2,v3], fit="long"); // returns [[1,5,8], [2,6,9], [3,7,10], [4,undef,11]]
|
|
// Example:
|
|
// v1 = [[1,2,3], [4,5,6], [7,8,9]];
|
|
// v2 = [[20,19,18], [17,16,15], [14,13,12]];
|
|
// zip(v1,v2); // Returns [[1,2,3,20,19,18], [4,5,6,17,16,15], [7,8,9,14,13,12]]
|
|
function zip(vecs, v2, v3, fit=false, fill=undef) =
|
|
(v3!=undef)? zip([vecs,v2,v3], fit=fit, fill=fill) :
|
|
(v2!=undef)? zip([vecs,v2], fit=fit, fill=fill) :
|
|
assert(in_list(fit, [false, "short", "long"]), "Invalid fit value." )
|
|
assert(all([for(v=vecs) is_list(v)]), "One of the inputs to zip is not a list")
|
|
let(
|
|
minlen = list_shortest(vecs),
|
|
maxlen = list_longest(vecs)
|
|
)
|
|
assert(fit!=false || minlen==maxlen, "Input vectors to zip must have the same length")
|
|
(fit == "long")
|
|
? [for(i=[0:1:maxlen-1]) [for(v=vecs) for(x=(i<len(v)? v[i] : (fill==undef)? [fill] : fill)) x] ]
|
|
: [for(i=[0:1:minlen-1]) [for(v=vecs) for(x=v[i]) x] ];
|
|
|
|
|
|
// Function: block_matrix()
|
|
// Usage:
|
|
// block_matrix([[M11, M12,...],[M21, M22,...], ... ])
|
|
// Description:
|
|
// Create a block matrix by supplying a matrix of matrices, which will
|
|
// be combined into one unified matrix. Every matrix in one row
|
|
// must have the same height, and the combined width of the matrices
|
|
// in each row must be equal.
|
|
function block_matrix(M) =
|
|
let(
|
|
bigM = [for(bigrow = M) each zip(bigrow)],
|
|
len0=len(bigM[0]),
|
|
badrows = [for(row=bigM) if (len(row)!=len0) 1]
|
|
)
|
|
assert(badrows==[], "Inconsistent or invalid input")
|
|
bigM;
|
|
|
|
// Function: diagonal_matrix()
|
|
// Usage:
|
|
// diagonal_matrix(diag, [offdiag])
|
|
// Description:
|
|
// Creates a square matrix with the items in the list `diag` on
|
|
// its diagonal. The off diagonal entries are set to offdiag,
|
|
// which is zero by default.
|
|
function diagonal_matrix(diag,offdiag=0) =
|
|
assert(is_list(diag) && len(diag)>0)
|
|
[for(i=[0:1:len(diag)-1]) [for(j=[0:len(diag)-1]) i==j?diag[i] : offdiag]];
|
|
|
|
|
|
// Function: submatrix_set()
|
|
// Usage:
|
|
// mat = submatrix_set(M,A,[m],[n])
|
|
// Description:
|
|
// Sets a submatrix of M equal to the matrix A. By default the top left corner of M is set to A, but
|
|
// you can specify offset coordinates m and n. If A (as adjusted by m and n) extends beyond the bounds
|
|
// of M then the extra entries are ignored. You can pass in A=[[]], a null matrix, and M will be
|
|
// returned unchanged. Note that the input M need not be rectangular in shape.
|
|
function submatrix_set(M,A,m=0,n=0) =
|
|
assert(is_list(M))
|
|
assert(is_list(A))
|
|
assert(is_int(m))
|
|
assert(is_int(n))
|
|
let( badrows = [for(i=idx(A)) if (!is_list(A[i])) i])
|
|
assert(badrows==[], str("Input submatrix malformed rows: ",badrows))
|
|
[for(i=[0:1:len(M)-1])
|
|
assert(is_list(M[i]), str("Row ",i," of input matrix is not a list"))
|
|
[for(j=[0:1:len(M[i])-1])
|
|
i>=m && i <len(A)+m && j>=n && j<len(A[0])+n ? A[i-m][j-n] : M[i][j]]];
|
|
|
|
|
|
// Function: array_group()
|
|
// Description:
|
|
// Takes a flat array 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 is the list is not a multiple of `cnt` items long.
|
|
// Example:
|
|
// v = [1,2,3,4,5,6];
|
|
// array_group(v,2) returns [[1,2], [3,4], [5,6]]
|
|
// array_group(v,3) returns [[1,2,3], [4,5,6]]
|
|
// array_group(v,4,0) returns [[1,2,3,4], [5,6,0,0]]
|
|
function array_group(v, cnt=2, dflt=0) = [for (i = [0:cnt:len(v)-1]) [for (j = [0:1:cnt-1]) default(v[i+j], dflt)]];
|
|
|
|
|
|
// Function: flatten()
|
|
// Description: Takes a list of lists and flattens it by one level.
|
|
// Arguments:
|
|
// l = List to flatten.
|
|
// Example:
|
|
// flatten([[1,2,3], [4,5,[6,7,8]]]) returns [1,2,3,4,5,[6,7,8]]
|
|
function flatten(l) = [for (a = l) each a];
|
|
|
|
|
|
// Function: full_flatten()
|
|
// 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:
|
|
// full_flatten([[1,2,3], [4,5,[6,7,8]]]) returns [1,2,3,4,5,6,7,8]
|
|
function full_flatten(l) = [for(a=l) if(is_list(a)) (each full_flatten(a)) else a ];
|
|
|
|
|
|
// Internal. Not exposed.
|
|
function _array_dim_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],_array_dim_recurse(leveldown))
|
|
: [first];
|
|
|
|
function _array_dim_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, _array_dim_recurse(flatten(v)));
|
|
|
|
|
|
// Function: array_dim()
|
|
// Usage:
|
|
// array_dim(v, [depth])
|
|
// Description:
|
|
// Returns the size of a multi-dimensional array. Returns a list of
|
|
// dimension lengths. The length of `v` is the dimension `0`. The
|
|
// length of the items in `v` is dimension `1`. The length of the
|
|
// items in the items in `v` is dimension `2`, etc. For each dimension,
|
|
// if the length of items at that depth is inconsistent, `undef` will
|
|
// be returned. If no items of that dimension depth exist, `0` is
|
|
// returned. Otherwise, the consistent length of items in that
|
|
// dimensional depth is returned.
|
|
// Arguments:
|
|
// v = Array to get dimensions of.
|
|
// depth = Dimension to get size of. If not given, returns a list of dimension lengths.
|
|
// Examples:
|
|
// array_dim([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]]); // Returns [2,2,3]
|
|
// array_dim([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]], 0); // Returns 2
|
|
// array_dim([[[1,2,3],[4,5,6]],[[7,8,9],[10,11,12]]], 2); // Returns 3
|
|
// array_dim([[[1,2,3],[4,5,6]],[[7,8,9]]]); // Returns [2,undef,3]
|
|
function array_dim(v, depth=undef) =
|
|
assert( is_undef(depth) || ( is_finite(depth) && depth>=0 ), "Invalid depth.")
|
|
! is_list(v) ? 0 :
|
|
(depth == undef)
|
|
? concat([len(v)], _array_dim_recurse(v))
|
|
: (depth == 0)
|
|
? len(v)
|
|
: let( dimlist = _array_dim_recurse(v))
|
|
(depth > len(dimlist))? 0 : dimlist[depth-1] ;
|
|
|
|
|
|
|
|
|
|
// Function: transpose()
|
|
// Usage:
|
|
// transpose(arr, [reverse])
|
|
// Description:
|
|
// Returns the transpose of the given input array. The input should be a list of lists that are
|
|
// all the same length. If you give a vector then transpose returns it unchanged.
|
|
// When reverse=true, the transpose is done across to the secondary diagonal. (See example below.)
|
|
// By default, reverse=false.
|
|
// Example:
|
|
// arr = [
|
|
// ["a", "b", "c"],
|
|
// ["d", "e", "f"],
|
|
// ["g", "h", "i"]
|
|
// ];
|
|
// t = transpose(arr);
|
|
// // Returns:
|
|
// // [
|
|
// // ["a", "d", "g"],
|
|
// // ["b", "e", "h"],
|
|
// // ["c", "f", "i"],
|
|
// // ]
|
|
// Example:
|
|
// arr = [
|
|
// ["a", "b", "c"],
|
|
// ["d", "e", "f"]
|
|
// ];
|
|
// t = transpose(arr);
|
|
// // Returns:
|
|
// // [
|
|
// // ["a", "d"],
|
|
// // ["b", "e"],
|
|
// // ["c", "f"],
|
|
// // ]
|
|
// Example:
|
|
// arr = [
|
|
// ["a", "b", "c"],
|
|
// ["d", "e", "f"],
|
|
// ["g", "h", "i"]
|
|
// ];
|
|
// t = transpose(arr, reverse=true);
|
|
// // Returns:
|
|
// // [
|
|
// // ["i", "f", "c"],
|
|
// // ["h", "e", "b"],
|
|
// // ["g", "d", "a"]
|
|
// // ]
|
|
// Example: Transpose on a list of numbers returns the list unchanged
|
|
// transpose([3,4,5]); // Returns: [3,4,5]
|
|
function transpose(arr, reverse=false) =
|
|
assert( is_list(arr) && len(arr)>0, "Input to transpose must be a nonempty list.")
|
|
is_list(arr[0])
|
|
? let( len0 = len(arr[0]) )
|
|
assert([for(a=arr) if(!is_list(a) || len(a)!=len0) 1 ]==[], "Input to transpose has inconsistent row lengths." )
|
|
reverse
|
|
? [for (i=[0:1:len0-1])
|
|
[ for (j=[0:1:len(arr)-1]) arr[len(arr)-1-j][len0-1-i] ] ]
|
|
: [for (i=[0:1:len0-1])
|
|
[ for (j=[0:1:len(arr)-1]) arr[j][i] ] ]
|
|
: assert( is_vector(arr), "Input to transpose must be a vector or list of lists.")
|
|
arr;
|
|
|
|
|
|
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|