# Geometry types

## Vector3 #

Decentraland uses *vector3* data to represent paths, points in space, and directions. Vectors can also be used to define rotation orientations, as a friendlier alternative to *quaternions*. A Vector3 object contains numerical values for each of the *x*, *y*, and *z* axis.

```
const myVector: Vector3 = { x: 8, y: 1, z: 8 }
```

The `Vector3`

namespace contains a series of handy methods that you can call to avoid having to deal with most vector math operations. Write `Vector3.`

, and VS Studio will display a dropdown with all of the available functions.

Below are a few lines showing the syntax for some basic operations with vectors.

```
// Create a vector object
let myVector = Vector3.create(3, 1, 5)
// Alternative syntax to create a vector object
let myOtherVector: Vector3 = { x: 8, y: 1, z: 8 }
// Edit one of its values
myVector.x = 5
// Call functions from the Vector3 namespace,
// All these functions require passing Vector3 objects in their parameters
let normalizedVector = Vector3.normalize(myVector)
let distance = Vector3.distance(myVector, myOtherVector)
let midPoint = Vector3.lerp(myVector, myOtherVector, 0.5)
```

Vector3 objects are often required in the fields of several components. For example, the `Transform`

component contains `Vector3`

values for the *position* and *scale* of the entity.

To create a
custom component
with parameters that require Vector3 values, set the type of these parameters as `Schema.Vector3`

.

ðŸ“” Note:`Vector3`

must be imported via

`import { Vector3 } from "@dcl/sdk/math"`

See Imports for how to handle these easily.

### Shortcuts for writing direction vectors #

The following shortcuts exist for defining generic vectors:

`Vector3.Zero()`

returns*(0, 0, 0)*`Vector3.Up()`

returns*(0, 1, 0)*`Vector3.Down()`

returns*(0, -1, 0)*`Vector3.Left()`

returns*(-1, 0, 0)*`Vector3.Right()`

returns*(1, 0, 0)*`Vector3.Forward()`

returns*(0, 0, 1)*`Vector3.Backward()`

returns*(0, 0, -1)*

## Quaternions #

Quaternions are used to store rotation information for the Transform component. A Quaternion is composed of four numerical values between -1 and 1: *x*, *y*, *z*, *w*.

```
const myQuaternion: Vector3 = { x: 0, y: 0, z: 0, w: 1 }
```

Quaternions are different from
*Euler* angles
, the more common *x*, *y* and *z* notation with numbers that go from 0 to 360 that most people are familiar with. The engine expresses all rotations as Quaternions, so it makes sense to avoid computations to convert to and from euler whenever possible.

The `Quaternion`

namespace contains a series of handy methods that you can call to avoid having to deal with many math operations. Write `Quaternion.`

, and VS Studio will display a dropdown with all of the available functions.

Below are a few lines showing the syntax for some basic operations with Quaternions.

```
// Create a quaternion object
let myQuaternion = Quaternion.crate(0, 0, 0, 1)
// Edit one of its values
myQuaternion.x = 1
// Call functions from the quaternion namespace
let midPoint = Quaternion.slerp(myQuaternion1, myQuaternion2, 0.5)
let rotationDifference = Quaternion.fromToRotation(
myQuaternion1,
myQuaternion2,
Quaternion.Zero()
)
```

Since it’s a lot easier to think in terms of Euler degrees, the SDK includes a couple of functions to convert to and from Quaternions and Euler.

ðŸ’¡ Tip: Avoid running these conversions as part of recurrent logic inside a system, that run on every tick, as that can get expensive. These conversions are mostly useful for one-time operations, like setting the rotation of a new entity.

```
// From euler to Quaternion
let myQuaternion = Quaternion.fromEulerDegrees(90, 0, 0)
// From quaternion to Euler
let myEuler = Quaternion.toEulerAngles(myQuaternion)
```

Quaternion objects are often required in the fields of components. For example, the `Transform`

component contains `Quaternion`

values for rotation of the entity.

To create a
custom component
with parameters that require Quaternion values, set the type of these parameters as `Schema.Quaternion`

.

ðŸ“” Note:`Quaternion`

must be imported via

`import { Quaternion } from "@dcl/sdk/math"`

See Imports for how to handle these easily.

## Scalars #

A scalar is nothing more than a number. For that reason, it doesn’t make much sense to instantiate a `Scalar`

object to store data, as you can do the same with a number. The functions in the `Scalar`

namespace however expose several handy functions (similar to those in the *Vector3* namespace), that can be used on numbers.

```
// Call functions from the Scalar class
let random = Scalar.randomRange(1, 100)
let midPoint = Scalar.lerp(number1, number2, 0.5)
let clampedValue = Scalar.clamp(myInput, 0, 100)
```

ðŸ“” Note:`Scalar`

must be imported via

`import { Scalar } from "@dcl/sdk/math"`

See Imports for how to handle these easily.