# distance

## Description

## Examples

### Calculate Distance Between Two States in SE3

Create an SE(3) state space.

space = stateSpaceSE3

space = stateSpaceSE3 with properties: Name: 'SE3' StateBounds: [7x2 double] NumStateVariables: 7 WeightXYZ: 1 WeightQuaternion: 0.1000

Calculate distance between two states.

dist = distance(space,[2 10 3 0.2 0 0 0.8],[0 -2.5 4 0.7 0.3 0 0])

dist = 12.7269

Calculate Euclidean distance between two states.

space.WeightQuaternion = 0; distEuc = distance(space,[2 10 3 0.2 0 0 0.8; 4 5 2 1 2 4 2],[62 5 33 0.2 0 0 0.8; 9 9 3 3 1 3.1 7])

`distEuc = `*2×1*
67.2681
6.4807

## Input Arguments

`space`

— State space object

`stateSpaceSE2`

object | `stateSpaceSE3`

object | `stateSpaceDubins`

object | `stateSpaceReedsShepp`

object

State space object, specified as a `stateSpaceSE2`

,
`stateSpaceSE3`

,
`stateSpaceDubins`

, or `stateSpaceReedsShepp`

object.

`states1`

— Initial states for distance calculation

*n*-by-3 matrix of real values | *n*-by-7 matrix of real values

Initial states for distance calculation, specified as an *n*-by-3
or *n*-by-7 matrix of real values. *n* is the number
of specified states.

For the 2-D state space objects `stateSpaceSE2`

,
`stateSpaceDubins`

, and `stateSpaceReedsShepp`

, each row is of form `[x y theta]`

,
which defines the *xy*-position and orientation angle
`theta`

of a state in the state space.

For the 3-D state space object `stateSpaceSE3`

,
each row is of form `[x y z qw qx qy qz]`

, which defines the
*xyz*-position and quaternion orientation ```
[qw qx qy
qz]
```

of a state in the state space.

The function supports following combinations for distance calculation:

*n*-to-*n*—*n*number of states in`states1`

and*n*number of states in`states2`

.For example,

`distance(space,rand(10,7),rand(10,7))`

1-to-

*n*— 1 state in`states1`

and*n*number of states in`states2`

.For example,

`distance(space,rand(1,7),rand(10,7))`

*n*-to-1 —*n*number of states in`states1`

and 1 state in`states2`

.For example,

`distance(space,rand(10,7),rand(1,7))`

**Data Types: **`single`

| `double`

`states2`

— Final states for distance calculation

*n*-by-3 matrix of real values | *n*-by-7 matrix of real values

Final states for distance calculation, specified as an *n*-by-3 or
*n*-by-7 matrix of real values. *n* is the number of
specified states.

For the 2-D state space objects `stateSpaceSE2`

,
`stateSpaceDubins`

, and `stateSpaceReedsShepp`

, each row is of form `[x y theta]`

,
which defines the *xy*-position and orientation angle
`theta`

of a state in the state space.

For the 3-D state space object `stateSpaceSE3`

,
each row is of form `[x y z qw qx qy qz]`

, which defines the
*xyz*-position and quaternion orientation ```
[qw qx qy
qz]
```

of a state in the state space.

The function supports following combinations for distance calculation:

*n*-to-*n*—*n*number of states in`states1`

and*n*number of states in`states2`

.For example,

`distance(space,rand(10,7),rand(10,7))`

1-to-

*n*— 1 state in`states1`

and*n*number of states in`states2`

.For example,

`distance(space,rand(1,7),rand(10,7))`

*n*-to-1 —*n*number of states in`states1`

and 1 state in`states2`

.For example,

`distance(space,rand(10,7),rand(1,7))`

**Data Types: **`single`

| `double`

## Output Arguments

`dist`

— Distance between states

*n*-element column vector

Distance between states, returned as an *n*-element column vector.
*n* is the number of specified states.

The function supports following combinations for distance calculation:

**Data Types: **`single`

| `double`

## Version History

**Introduced in R2019b**

## See Also

`stateSpaceSE2`

| `stateSpaceSE3`

| `stateSpaceDubins`

| `stateSpaceReedsShepp`

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