# Core / vec4

Back to Beyond the Codea in-app reference

## vec4() function

### Introduction

The 'Vector' chapter of Codea's in-app reference documents most of the `vec4()` function. The function is similar to the `vec3()` function, except that it returns a userdata value that is a vector in four dimensions rather than three.

### Returning a four dimensional vector

The `vec4()` function is used to return a new four-dimensional vector value as in the following examples:

```v1 = vec4(x1, y1, z1, w1)         -- x1, y1, z1, w1 contain numbers for the respective co-ordinates
print(vec4() == vec4(0, 0, 0, 1)) -- Output: true
```

If `vec4()` is called without arguments it returns the origin in three-dimensional space, but in homogeneous co-ordinates (with the w co-ordinate equal to 1).

### Setting and getting individual coordinates

Indexing can be used to set and get individual coordinates, either by ordinal number or by letter - (x, y, z, w) or (r, g, b, a), as summarised in the table below:

Co-ordinateIndex schemeIndex schemeIndex scheme
First`v1``v1.x` or `v1["x"]``v1.r` or `v1["r"]`
Second`v1``v1.y` or `v1["y"]``v1.g` or `v1["g"]`
Third`v1``v1.z` or `v1["z"]``v1.b` or `v1["b"]`
Fourth`v1``v1.w` or `v1["w"]``v1.a` or `v1["a"]`

### Operators

As in the case of `vec3()`, the result of the `vec4()` function supports the `-` (uniary), `*`, `/`, `+`, `-`, and `==` operators, where the second operand is a number value in the case of `*` (multiplication by a scalar) and `/` (division by a scalar).

### Functions

The result also supports `tostring()` to produce nicely-formatted output. Consequently, `print()` also generates nicely-formatted output.

Also as in the case of `vec3()`, the result of the `vec4()` function supports the indexed functions `dot()`, `cross()`, `len()`, `lenSqr()`, `dist()` and `distSqr()`. For example:

```v1 = vec4(1, -1, 3, 4)
v2 = vec4(-2, 5, -3, 0)

-- Calculate the dot (scalar) product of two vectors
d = v1.dot(v1, v2)       -- This syntax is equivalent ...
d = v1:dot(v2)           -- ... to this syntax, using Lua's colon notation.

-- Calculate the length (magnitude) of first vector
l = v1.len(v1)           -- This syntax is equivalent ...
l = v1:len()             -- ... to this syntax, using Lua's colon notation.
```

#### v1:cross(v2)

The `cross()` function returns a four dimensional vector where the first three co-ordinates are the cross product of the three dimensional vectors corresponding to the first three co-ordinates of the two vectors and the fourth co-ordinate is `0`.

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