User:LABoyd2/Vector to manual 150928

Vectors

A vector is a sequence of zero or more OpenSCAD values. Vectors are a collection (or list or table) of numeric or boolean values, variables, vectors, strings or any combination thereof. They can also be expressions which evaluate to one of these. A vector has square brackets, [] enclosing zero or more items (elements or members), separated by commas. A vector can contain vectors, which contain vectors, etc. The information here also applies to lists and tables which use vectors for their data.

examples

   [1,2,3]
   [a,5,b]
   []
   [5.643]
   ["a","b","string"]
   [[1,r],[x,y,z,4,5]]
   [3, 5, [6,7], [[8,9],[10,[11,12],13], c, "string"]
   [4/3, 6*1.5, cos(60)]

use in OpenSCAD:

  cube( [width,depth,height] )           // optional spaces shown for clarity
  translate( [x,y,z] )
  polygon( [ [x0,y0],  [x1,y1],  [x2,y2] ] )

creation

Vectors are created by writing the list of elements, separated by commas, and enclosed in square brackets. Variables are replaced by their values.

  cube([10,15,20]);
  a1 = [1,2,3];
  a2 = [4,5];
  a3 = [6,7,8,9];
  b  = [a1,a2,a3];    // [ [1,2,3], [4,5], [5,7,8,9] ]  note increased nesting depth

elements within vectors

Elements within vectors are numbered from 0 to n-1 where n is the length returned by len(). Address elements within vectors with the following notation:

e[5]           // element no 5 (sixth) at   1st nesting level
e[5][2]        // element 2 of element 5    2nd nesting level
e[5][2][0]     // element 0 of 2 of 5       3rd nesting level
e[5][2][0][1]  // element 1 of 0 of 2 of 5  4th nesting level

example elements with lengths

e = [ [1], [], [3,4,5], "string", "x", [[10,11],[12,13,14],[[15,16],[17]]] ];  // length 6

address       length  element
e[0]          1       [1]
e[1]          0       []
e[5]          3       [ [10,11], [12,13,14], [[15,16],[17]] ]
e[5][1]       3       [ 12, 13, 14 ]
e[5][2]       2       [ [15,16], [17] ]
e[5][2][0]    2       [ 15, 16 ]
e[5][2][0][1] undef   16
    
e[3]          6       "string"
e[3 ][2]      1       "r"
  
s = [2,0,5]; a = 2;
e[s[a]]       3       [ [10,11], [12,13,14], [[15,16],[17]] ]

vector operators

concat

[Note: Requires version 2015.03 or later]

concat() combines the elements of 2 or more vectors into a single vector. No change in nesting level is made.

 vector1 = [1,2,3]; vector2 = [4]; vector3 = [5,6];
 new_vector = concat(vector1, vector2, vector3) // [1,2,3,4,5,6]
  
 string_vector = concat("abc","def");                 // ["abc", "def"]
 one_string = str(string_vector[0],string_vector[1]); // "abcdef"

len

len() is a function which return the length of vectors or strings. Indices of elements are from [0] to [length-1].

vector

Returns the number of elements at this level.

Single values, which are not vectors, return undef.

string

Returns the number of characters in string.

See example elements with lengths

select

select() performs selection and reordering of elements into a new vector. NOTE: To use, copy this function into your script.

 function select(source_vector,select_vector)=
   [ for (i = [0 : len(select_vector) - 1]) source_vector[select_vector[i]] ];
  
 vector1 =   [[0,0],[1,1],[2,2],[3,3],[4,4]];
 selector1 = [4,0,3];
 vector2 =   select(vector1,selector1);   //  [[4, 4], [0, 0], [3, 3]]
 vector3 =   select(vector1,[0,2,4]);     //  [[0, 0], [2, 2], [4, 4]]