User:LABoyd2/Vector stand alone page 150927

= Vectors = Vectors in OpenSCAD are a collection (or list or table) of numeric values, 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 ]

= Operators =

concat
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.
 * vector
 * Returns the number of elements at this level.
 * Indices of elements are from [0] to [length-1].
 * Single values, which are not vectors, return undef.
 * string
 * Returns the number of characters in string.

See example elements with lengths

= Vector Math Operators =

The vector-number operators take a vector and a number as operands and produce a new vector.

Vector Operators
The vector operators take vectors as operands and produce a new vector.

The "-" can also be used as prefix operator to element-wise negate a vector.

Vector Dot-Product Operator
The vector dot-product operator takes two vectors as operands and produces a scalar.

Matrix Multiplication
Multiplying a matrix by a vector, vector by matrix and matrix by matrix

= notes = https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/List_Comprehensions

Flatten a nested list

 * input : nested list
 * output : list with the outer level nesting removed

a=0,0],[0,10],[10,0],[0,-10],[-10,0],[8,15],[15,8],[-8,15],[15,-8],[8,-15],[8,8],[8,-8;
 * from polygon.scad

PlotPoints(a,"green");

module PlotPoints(PointList,Color){ color(Color){ for ( i = [0 : len(PointList)-1] ){ translate(PointList[i]){ text(str(i),size=2); cube(size=0.5); } } } }

// generate a list with all values defined by a range list1 = [ for (i = [0 : 2 : 10]) i ]; echo(list1); // ECHO: [0, 2, 4, 6, 8, 10]

list1 = [ for (i = [0 : 10]) [i*2,[i,i]] ]; echo(list1); // ECHO: ECHO: 0, [0, 0, [2, [1, 1]], [4, [2, 2]], [6, [3, 3]], [8, [4, 4]], [10, [5, 5]], [12, [6, 6]], [14, [7, 7]], [16, [8, 8]], [18, [9, 9]], [20, [10, 10]]]

// map input list to output list list = [ for (i = [2, 3, 5, 7, 11]) i * i ]; echo(list); // ECHO: [4, 9, 25, 49, 121]

// extract every second character of a string str = "SomeText"; list2 = [ for (i = [0 : 2 : len(str) - 1]) str[i] ]; echo(list2); // ECHO: ["S", "m", "T", "x"]

a = 0,0],[1,1],[2,2],[3,3],[4,4; p = [4,0,3]; list2 = select(a,p); echo(list2);      // ECHO: 4, 4], [0, 0], [3, 3

function select(source_vector,select_vector)= [ for (i = [0 : len(select_vector) - 1]) source_vector[select_vector[i]] ];

e = [ [1], [], [3,4,5], "string", "x", 10,11],[12,13,14],[[15,16],[17] ]; // length 6 s= [2,0,5]; a = 2; echo( e[s[a]] );