OpenSCAD Functional Programming Utilities

This library is a collection of OpenSCAD functions for use with OpenSCAD function-literals.

It is meant to provide algorithms and tools to help build efficient scripts using functional programming techniques in OpenSCAD.

This was started as somewhat of an experiment or coding exercise to see how well various general algorithms could be implemented and built upon in the OpenSCAD language. The C++ standard algorithms library was chosen as a model for most of funcutils API. An attempt was made to support as much of the C++ API as possible, although due to language differences some of these functions may be decidedly less useful or practical within OpenSCAD.

In addition to std_algorithm.scad, various other utilities have been provided which the authors felt were particularly useful for OpenSCAD.

⚠️ - Only OpenSCAD Release 2021.01 or later has builtin support for function-literals.

ℹ️ - Prior to release 2021.01, function-literals were available as an experimental feature, accessible from Development Snapshots and Nightly Builds.

• Such builds must be newer than Oct. 23 2019 when function-literals was merged into OpenSCAD master.
• If build is from sources between 2019.10.23 and 2021.01 Release, then the feature must be enabled within OpenSCAD by checking the option under Preferences -> Features -> function-literals.
• If built from sources from the above date range, then experimental features must be enabled in the build config e.g.: cmake -DEXPERIMENTAL=ON [...] (pre-built Development Snapshots and Nightlies from OpenSCAD all have this configuration enabled)

General Usage

In order to pass functions as values, function literals are declared slightly differently than "traditional" OpenSCAD functions, so that they exist as an assignment in OpenSCAD's variable namespace.

• function literal: foo = function(x) x + 1337;
• vs traditional function: function foo(x) = x + 1337;

⚠️ Important note for including files which define function literals:

• function literal declarations are variable assignments, and use <filename> does not evaluate assignments.
• Therefore include <filename> should be used instead, for files from this library.

Currently OpenSCAD's builtin functions are not available directly as literals (this might change in future), but can be wrapped in anonymous functions for passing into higher-order functions.

Example:

echo(filter([1,[],2,3,4,5,undef,"no"], function(x) is_num(x))); // result: [1,2,3,4,5]

API Reference

Library Files

• funcutils.scad
  • Main file to include all other files in this library
• func.scad
  • Minimal collection of common higher-order functions: map, filter, fold
• ops.scad
  • Elementary function literals for comparison, arithmetic and boolean value operations.
• std_algorithm.scad
  • Functions modeled after C++ Algorithms standard library, mostly operating on ranges of sequences (lists/vectors or strings)
• list.scad
  • Various list-based functions which are not directly modeled after C++ STL algorithms.
• math.scad
  • Mathematical functions which are not directly modeled after C++ STL algorithms.
• string.scad
  • String specific functions
• types.scad
  • Extra type checking functions for which no OpenSCAD buitin exists.

Dependency / Include Tree

⚠️ - Individual library files already include <...> their own dependencies. To avoid duplicate definitions, do not manually include any more-deeply-nested dependencies than the outermost one(s) you choose. So, if including top-level functils.scad, then do not include any others.

• funcutils.scad
  • list.scad
    • types.scad
    • std_algorithm.scad
      • ops.scad
    • math.scad
  • func.scad
  • string.scad

funcutils.scad

Top level file, existing only to include all others. No function definitions in itself.

ops.scad

Elementary Operators

Comparators

• eq (x, y)
  • Equal
• ne (x, y)
  • Not Equal
• lt (x, y)
  • Less Than
• gt (x, y)
  • Greater Than
• le (x, y)
  • Less than or Equal
• ge (x, y)
  • Greater than or Equal

Arithmetic unary ops

• ident (x)
  • Identity function (returns x unchanged)
• neg (x)
  • Negation

Arithmetic binary ops

• add (x, y)
  • Addition
• sub (x, y)
  • Subtraction
• mul (x, y)
  • Multiplication
• div (x, y)
  • Division
• rem (x, y)
  • Remainder (x % y)
• mod (x, y)
  • Modulo operator. Unlike remainder, always returns non-negative value in range: [0,y)

Boolean unary op

• not (x)
  • NOT

Boolean binary ops

• and (x, y)
  • AND
• or (x, y)
  • OR
• xor (x, y)
  • XOR
• nand (x, y)
  • NAND
• nor (x, y)
  • NOR
• xnor (x, y)
  • XNOR

list.scad

Various list-based functions which are not directly modeled after C++ STL algorithms.

• clamp_range (v, begin, step, end)
  • Return a range with begin (inclusive) and end (exclusive) clamped between 0 and len(v).
  • Allows negative values to wrap but only once (-1 becomes index of last element, and values less than -len(v) clamp to 0).
  • mainly for use by slice function
• def (x, default)
  • return x, or default if x undefined
• get (v, i)
  • get element from v with wrapping, using index mod(i,len(v))
• insert (v, x, i)
  • insert element x into v at index i
• insertv (v, i, xs)
  • insert vector of elements xs into v at index i
• insert_sorted (v, x, cmp=lt)
  • insert x into sorted vector v
• insertv_sorted (v, xs, cmp=lt)
  • insert vector xs into sorted vector v
  • xs does not need to be sorted

echo(insertv_sorted([1,2,3,5,5,8,12],[6,4,7,-8,4,3,5,-6,5,3,2,1,10,0,-1]));
echo(insertv_sorted([],[for (x=rands(0,10000,10000)) floor(x)]));

• replace_range (v, range, xs)
  • replace elements of v in range with elements from vector xs
  • range is vec2 containing [begin,end) indices.
  • xs does not need to be same length as range
• rotl (v, l=1)
  • Rotate elements in vector v, by l positions to the left.
• rotr (v, l=1)
  • Rotate elements in vector v, by l positions to the right.
• sublist (s, b=0, e)
  • Extract sub-list given begin (inclusive) and end (exclusive). If end not specified, go to end of list
• slice (v, begin, step, end, range)
  • slice vector v, similar to Python's builtin slice function or extended indexing syntax.
  • all params after v are optional
  • range param overrides others
  • unnamed range may be optionally positioned in place of begin

std_algorithm.scad

Functions modeled after C++ STL Algorithms (incomplete, see std algorithm status for details)

ℹ️ Where C++ uses first and last iterators for most of the following functions, OpenSCAD uses indices of the same name. This results in some differences between function signatures including:

• v (for "vector", but may also be a string) is always the first parameter for such OpenSCAD functions
• first=0 is default when omitted
• last=len(v) is default when omitted
  • default parameter values cannot depend on previous parameters being initialized in order, so documented function signatures don't explicitely show last=len(v), but it is set within the function body via end (v, last)
• In some cases, the OpenSCAD version of functions have parameters in a different order than C++
  • For example C++'s std::find(first, last, value); is find(v, value, first, last) in OpenSCAD. value comes before first and last since they can be reasonably defaulted, when value can't.

Non-modifying sequence operations

• end (v,last) (ref: std::end, loosely based)
  • return last, OR length of v if last not defined.
• find_if (v, first=0, last, p) (ref: std::find_if)
• return index of first element in range [first,last) which matches predicate p, or last if none found.
• find_if_not (v, first=0, last, p) (ref: std::find_if_not)
• return index of first element in range [first,last) which does not match predicate p, or last if none found.
• find (v, value, first=0, last, cmp=eq) (ref: std::find)
  • return index of first element in range [first,last) equivalent to value, or last if none found.

v=[6,4,7,-8,4,3,5,-6,5,3,2,1,10,0,-1];
echo(find(v,-8));
echo(find(v,-1));
echo(find(v,undef));
echo(find([0],0));
echo(find([0],1));
echo(find([],undef));

• all_of (v, first=0, last, p) (ref: std::all_of)
  • Checks if unary predicate p returns true for all elements in the range [first, last).
• any_of (v, first=0, last, p) (ref: std::any_of)
  • Checks if unary predicate p returns true for at least one element in the range [first, last).
• none_of (v,first=0,last,p) (ref: std::none_of)
  • Checks if unary predicate p returns true for no elements in the range [first, last).

for(v=[ [], [0,1,2,3], [0,1,2,3,0/0], [[],false,true,"ok"] ]) let(p=function(x)is_num(x)) {
  if (all_of(v,p=p)) echo(str("all_of(",v,",is_num) = true"));
  if (any_of(v,p=p)) echo(str("any_of(",v,",is_num) = true"));
  if (none_of(v,p=p)) echo(str("none_of(",v,",is_num) = true"));
}

• contains (v, value, first, last, cmp=eq)
  • No direct analogue in C++ STL, but a variation of std::find returning bool, or loosely based on std::map::contains
  • return true if any element in range [first,last) is equivalent to value

echo(contains([6,4,7,-8,4,3,5,-6,5,3,2,1,10,0,-1],3.14));
echo(contains([6,4,7,-8,4,3,5,-6,5,3,2,1,10,0,-1],-1));

• count (v, value, first=0, last, cmp=eq) ref: std::count
  • return the number of elements in the range [first, last) equal to value
• count_if (v, p, first=0, last) ref: std::count_if
  • return the number of elements in the range [first, last) for which predicate p returns true
• mismatch (v1, first1=0, last1, v2, first2=0, last2, cmp=eq) ref: std::mismatch
  • return pair of indices [i1,i2] to the first two non-equal elements.
  • if no mismatches are found when the comparison reaches last1 or last2, whichever happens first, the pair holds the end index and the corresponding index from the other range.

echo(count("this is a test","t"));
echo(count_if([1,2,3,4,5,6,7,8,9,10],p=function(x)x>3));
echo(mismatch(v1="oh! hi, how are you?",first1=4,v2="hi, how's it going?"));// [11, 7]
echo(mismatch(v1="Hello World",v2="Hello World"));// [11, 11]
echo(mismatch(v1="Hello!",v2="Hello"));           // [5, 5]
echo(mismatch(v1="l",v2="Hello",first2=3));       // [1, 4]

Modifying sequence operations

• remove(v,first=0,last) ref: std::remove
  • remove range of elements [first,last) from list
• remove_if(v,first=0,last,p) ref: std::remove_if
  • remove elements from range which match predicate

echo(remove([0,1,2,3,4,5,6,7,8,9],3,7));
echo(remove([0,1,2,3,4,5,6,7,8,9]));
echo(remove_if([0,1,2,3,4,5,6,7,8,9],p=function(x)x%3==0));

• replace (v, old_value, new_value, first=0, last, cmp=eq) ref: std::replace
  • Replaces all elements that are equivalent to old_value with new_value, in the range [first, last).
• replace_if (v, new_value, first=0, last, p) ref: std::replace_if
  • Replaces all elements for which predicate p returns true, with new_value, in the range [first, last).

echo(replace([0,1,2,3,1,4,5,6,1,7,8,1,9],1,[]));
echo(replace_if([0,1,2,3,1,4,5,6,1,7,8,1,9],0,p=function(x)x<5));

• reverse (v, first=0, last) ref: std::reverse
  • Reverse a range of elements

echo(reverse([0,1,2,3,4,5,6,7,8,9]));
echo(reverse([0,1,2,3,4,5,6,7,8,9],3,7));

• std_rotate (v, first=0, first_n, last) ref: std::rotate
  • Reorders elements in the range [first,last) such that sub-ranges:
    • [first_n, last) moves to the beginning of the range, and
    • [first, first_n) moves to end of the range.

// move elements [3,7) to position 12: https://www.youtube.com/watch?v=W2tWOdzgXHA&feature=youtu.be&t=630
echo(std_rotate([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],3,7,12)); 
// move elements [8,12) to position 3: https://www.youtube.com/watch?v=W2tWOdzgXHA&feature=youtu.be&t=645
echo(std_rotate([0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],3,8,12)); 

• unique (v, first=0, last, cmp=eq) ref: std::unique
  • Removes all but the first element from every group of consecutive equivalent elements in range [first,last).
  • v should be pre-sorted if uniqueness across entire vector is desired.

echo(unique(insertv_sorted([],[1,2,3,1,2,3,3,4,5,4,5,6,7])));

Partitioning operations

• stable_partition (v, first=0, last, p) ref: std::stable_partition
  • Reorders the elements in the range [first, last) in such a way that all elements for which the predicate p returns true precede the elements for which predicate p returns false.
  • Relative order of the elements is preserved.

is_even = function(x)x%2==0;
echo(stable_partition([0,1,2,3,4,5,6,7,8,9],p=is_even));

Sorting operations

• None yet implemented

Binary search operations (on sorted ranges)

• upper_bound (v, value, first=0, last=undef, cmp=lt) ref: std::upper_bound
  • return index of first element in range [first,last) which is greater than value.
• lower_bound (v, value, first=0, last=undef, cmp=lt) ref: std::lower_bound
  • return index of first element in range [first,last) which is not less than value.
• binary_search (v, value, first=0, last=undef, cmp=lt) ref: std::binary_search
  • return true if range [first,last) contains value.

v = [1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6];
echo(sublist(v,lower_bound(v,4),upper_bound(v,4)));
echo(binary_search([1,2,3,5,5,8,12],3));

Mininum/maximum operations

• max (a, b, cmp=lt) ref: std::max
  • return the greater of the two values. if equivalent, return a
  • overrides max builtin function, but with customizable comparator
• max_element (v, first=0, last, cmp=lt) ref: std::max_element
  • return index of maximum value in range [first,last), or last if empty range
• min (a, b, cmp=lt) ref: std::min
  • return the lesser of the two values. if equivalent, return a
  • overrides min builtin function, but with customizable comparator
• min_element (v, first=0, last, cmp=lt) ref: std::min_element
  • return index of minimum value in range [first,last), or last if empty range
• minmax (a, b, cmp=lt) ref: std::minmax
  • return [a,b] when a <= b or [b,a] when a > b
• minmax_element (v, first=0, last, cmp=lt) ref: std::minmax_element
  • return pair of indices [i,j] where v[i] is minimum element and v[j] is maximum in range [first,last), OR [last,last] if empty range
  • if multiple elements are equivalent to the minimum, return first such index for i
  • if multiple elements are equivalent to the maximum, return last such index for j
• clamp(x,lo,hi,cmp=lt) ref std::clamp
  • return lo if x is less than lo, or to hi if hi is less than x, otherwise x

// Example compare by index
echo(max([100,1],[-100,2],function(a,b) a[0]<b[0])); // [100,1]
echo(max([100,1],[-100,2],function(a,b) a[1]<b[1])); // [-100,2]
echo(min([100,1],[-100,2],function(a,b) a[0]<b[0])); // [-100,2]
echo(min([100,1],[-100,2],function(a,b) a[1]<b[1])); // [100,1]
// return first when "equivalent"
echo(max([1,2,3],[3,2,1],function(a,b) a[1]<b[1])); // [1,2,3] 
echo(min([1,2,3],[3,2,1],function(a,b) a[1]<b[1])); // [1,2,3]

v= [0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,0,9];
echo(min_element(v));    // 0
echo(min_element(v,10)); // 18
echo(max_element(v));    // 9
echo(max_element(v,10)); // 19

lencmp = function (a,b) len(a) < len(b);
echo(minmax("World!","Hello",lencmp)); // ["Hello", "World!"]
echo(minmax("Hello","World!",lencmp)); // ["Hello", "World!"]
// [a,b] stay in-order when equivalent
echo(minmax("Hello","World",lencmp));  // ["Hello", "World"]
echo(minmax("world","Hello",lencmp));  // ["World", "Hello"]
s = "The quick brown fox jumps over the lazy dog";
x = minmax_element(s);
echo(x,s[x[0]],s[x[1]]); // [3, 37], " ", "z"

Numeric operations

• accumulate (v, first=0, last=undef, init=0, op=add) ref: std::accumulate
  • same as "fold" but with optional params for first, last, op (default addition)

echo(accumulate([1,2,3,4,5]));
echo(accumulate([1,2,3,4,5],init=1,op=function(x,y)x*y));

string.scad

String specific functions

Strings may be iterated over character by character, and many of the same functions/algorithsm that work on vectors will also "work" on strings. However the value returned is typically a vector of single-character strings, when what is expected is a single string. This is why string-specific functions have their own place here.

• substr (s, b, e)
  • extract substring given begin(inclusive) and end(exclusive)
  • if end not specified, go to end of string
• join (strs, delimiter="")
  • converts a vector of values into a single string, with optional delimiter between elements
  • uses efficient binary tree based join, where depth of recursion is log_2(len(strs)).
• fixed (x, w, p, sp="0")
  • format number x as string with fixed width w and precision p.

types.scad

Extra type checking functions for which no OpenSCAD buitin exists.

• is_range (x)
  • return true only if x is a range object
• is_nan (x)
  • return true only if x is the nan value
• has_nan (x)
  • return true only if x is a list containing nan, or is itself nan
• has_function (v)
  • return true only if x is a list containing a function

for (
  x=[undef,1/0,-1/0,0/0,[],[1,2,3],[1,0/0,2],[1,function(x)x,2],[1,function(x)x,0/0,2],
    "hi!","",function(x)x,true,false,0,1,-1,[0:-10],[0:1:10],[0:0:0],[0:1:2]]
  ) {
  if (is_nan(x)) echo(str("is_nan(",x,") = true"));
  if (has_nan(x)) echo(str("has_nan(",x,") = true"));
  if (has_function(x)) echo(str("has_function(",x,") = true"));
  if (is_range(x)) echo(str("is_range(",x,") = true"));
}