# Position and Orientation

A location is often used to describe a place or area where an object is located (e.g. your location is in a certain room). A position is a more precise indicator of where an object is located (e.g. your position is at X=3 and Y=4). Similar to other positioning systems, OpenHPS uses the concepts of relative and absolute positions.

The aforementioned position descriptions such as a place, area or XY position are called absolute positions, they describe a physical point inside a known space such as the Earth or a building.

When describing a position that uses a certain landmark to describe the position, the position is relative to this landmark. Relative positions can be expressed in distance, angle or velocity and could potentially be used to determine a more precise absolute position. In general, a relative position can not be used if the position is contained by the landmark - in that particular case you are talking about an absolute position relative to the landmark (e.g. you are in the center of a building).

## Cartesian position

A cartesian position can be created using an Absolute2DPosition or Absolute3DPosition.

tsimport { Absolute2DPosition } from '@openhps/core'; const pos = new Absolute2DPosition(1, 2);

## Geographical position

By default, geographical positions use the WGS-84 coordinate system with a latitude, longitude and elevation in meters.

tsimport { GeographicalPosition } from '@openhps/core'; const pos = new GeographicalPosition(50.820466, 4.392189, 9);

### Geographical Coordinate System

Geographical positions can be constructed from other coordinate systems than WGS-84, but will always be stored using this coordinate system. You can find more information on available coordinate systems here.

Name Function Note
EPSG4326 GCS.EPSG4326
WGS-84 GCS.WGS84 (alias for EPSG4326)
ECEF GCS.ECEF
EPSG3857 GCS.EPSG3857
tsimport { GeographicalPosition, Vector3, GCS } from '@openhps/core'; const pos = new GeographicalPosition();pos.fromVector(new Vector3(50.820466, 4.392189, 9), GCS.WGS84);

Likewise, the toVector3() function on an AbsolutePosition accepts an optional argument for the coordinate system.

tsimport { GeographicalPosition, GCS } from '@openhps/core'; const pos = new GeographicalPosition(50.820466, 4.392189, 9);pos.toVector3(GCS.ECEF);

## Relative position

• RelativeDistance: Distance to another data object.
• RelativeRSSI: Received signal strength to another (transmitting) data object.
• RelativeAngle: Angle to another data object.
• RelativeVelocity: Relative velocity towards another object.
tsimport { RelativeDistance } from '@openhps/core'; object.addRelativePosition(new RelativeDistance("WAP_1", 10));object.addRelativePosition(new RelativeDistance("WAP_2", 5));object.addRelativePosition(new RelativeDistance("WAP_3", 8));

## Orientation

Every absolute position can contain an orientation. The orientation is stored as a quaternion but can be initialized through euler angles or axis angles.

tsimport { Orientation, AngleUnit } from '@openhps/core'; const orientation = Orientation.fromEuler({    pitch: 0,    roll: 0,    yaw: 90,    unit: AngleUnit.DEGREE});position.orientation = orientation;

An orientation offers the same quaternion methods as Three.js. You can find more information about available methods here.

### Examples

You can find an ObservableHQ notebook with examples for creating an orientation here.

## Creating a Pose

A Pose is a position and orientation combined. It is represented as a 4x4 matrix.

The pose is composed of a translation (position) denoted as $M$ and a rotation matrix.

$M=\begin{pmatrix} 1 & 0 & 0 & t_x\\ 0 & 1 & 0 & t_y\\ 0 & 0 & 1 & t_z\\ 0 & 0 & 0 & 1 \end{pmatrix}$$R_X(\theta)=\begin{pmatrix} 1 & 0 & 0 & 0\\ 0 & cos(\theta) & sin(\theta) & 0\\ 0 & -sin(\theta) & cos(\theta) & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}$$R_Y(\theta)=\begin{pmatrix} cos(\theta) & 0 & -sin(\theta) & 0\\ 0 & 1 & 0 & 0\\ sin(\theta) & 0 & cos(\theta) & 0\\ 0 & 0 & 0 & 1 \end{pmatrix}$$R_Z(\theta)=\begin{pmatrix} cos(\theta) & -sin(\theta) & 0 & 0\\ sin(\theta) & cos(\theta) & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{pmatrix}$

## Position accuracy and probability

Accuracy defines how accurate the position is from the given or calculated coordinates. An accuracy can be defined in 1D, 2D or a 3D spheroid but should always support being expressed as a one dimensional value.

Accuracy is always present in an absolute position and can be directly updated with setAccuracy.

tsposition.setAccuracy(20, LengthUnit.CENTIMETER);

Alternatively you can specify a 2D, 3D or custom accuracy.

tsimport { Accuracy1D, Accuracy2D, Accuracy3D, LengthUnit } from '@openhps/core';position.accuracy = new Accuracy1D(5, LengthUnit.METER);// orposition.accuracy = new Accuracy2D(5, 3, LengthUnit.METER);// orposition.accuracy = new Accuracy3D(5, 3, 1, LengthUnit.METER);`