# Transforms

engine/Source/Core/Transforms.js 22
Contains functions for transforming positions to various reference frames.

### Methods

#### static Cesium.Transforms.computeFixedToIcrfMatrix(date, result) → Matrix3
engine/Source/Core/Transforms.js 763

Computes a rotation matrix to transform a point or vector from the Earth-Fixed frame axes (ITRF) to the International Celestial Reference Frame (GCRF/ICRF) inertial frame axes at a given time. This function may return undefined if the data necessary to do the transformation is not yet loaded.

Name | Type | Description
--- | --- | ---
`date` | JulianDate | The time at which to compute the rotation matrix.
`result` | Matrix3 | optional The object onto which to store the result. If this parameter is not specified, a new instance is created and returned.

##### Returns:

The rotation matrix, or undefined if the data necessary to do the transformation is not yet loaded.

##### Example:

    // Transform a point from the ICRF axes to the Fixed axes.
    const now = Cesium.JulianDate.now();
    const pointInFixed = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const fixedToIcrf = Cesium.Transforms.computeIcrfToFixedMatrix(now);
    let pointInInertial = new Cesium.Cartesian3();
    if (Cesium.defined(fixedToIcrf)) {
        pointInInertial = Cesium.Matrix3.multiplyByVector(fixedToIcrf, pointInFixed, pointInInertial);
    }

##### See:

- Transforms.preloadIcrfFixed

#### static Cesium.Transforms.computeIcrfToFixedMatrix(date, result) → Matrix3
engine/Source/Core/Transforms.js 708

Computes a rotation matrix to transform a point or vector from the International Celestial Reference Frame (GCRF/ICRF) inertial frame axes to the Earth-Fixed frame axes (ITRF) at a given time. This function may return undefined if the data necessary to do the transformation is not yet loaded.

Name | Type | Description
--- | --- | ---
`date` | JulianDate | The time at which to compute the rotation matrix.
`result` | Matrix3 | optional The object onto which to store the result. If this parameter is not specified, a new instance is created and returned.

##### Returns:

The rotation matrix, or undefined if the data necessary to do the transformation is not yet loaded.

##### Example:

    scene.postUpdate.addEventListener(function(scene, time) {
      // View in ICRF.
      const icrfToFixed = Cesium.Transforms.computeIcrfToFixedMatrix(time);
      if (Cesium.defined(icrfToFixed)) {
        const offset = Cesium.Cartesian3.clone(camera.position);
        const transform = Cesium.Matrix4.fromRotationTranslation(icrfToFixed);
        camera.lookAtTransform(transform, offset);
      }
    });

##### See:

- Transforms.preloadIcrfFixed

#### static Cesium.Transforms.computeTemeToPseudoFixedMatrix(date, result) → Matrix3
engine/Source/Core/Transforms.js 557

Computes a rotation matrix to transform a point or vector from True Equator Mean Equinox (TEME) axes to the pseudo-fixed axes at a given time. This method treats the UT1 time standard as equivalent to UTC.

Name | Type | Description
--- | --- | ---
`date` | JulianDate | The time at which to compute the rotation matrix.
`result` | Matrix3 | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix3 instance if none was provided.

##### Example:

    //Set the view to the inertial frame.
    scene.postUpdate.addEventListener(function(scene, time) {
       const now = Cesium.JulianDate.now();
       const offset = Cesium.Matrix4.multiplyByPoint(camera.transform, camera.position, new Cesium.Cartesian3());
       const transform = Cesium.Matrix4.fromRotationTranslation(Cesium.Transforms.computeTemeToPseudoFixedMatrix(now));
       const inverseTransform = Cesium.Matrix4.inverseTransformation(transform, new Cesium.Matrix4());
       Cesium.Matrix4.multiplyByPoint(inverseTransform, offset, offset);
       camera.lookAtTransform(transform, offset);
    });

#### static Cesium.Transforms.eastNorthUpToFixedFrame(origin, ellipsoid, result) → Matrix4
engine/Source/Core/Transforms.js 274

Computes a 4x4 transformation matrix from a reference frame with an east-north-up axes centered at the provided origin to the provided ellipsoid's fixed reference frame. The local axes are defined as:

- The `x` axis points in the local east direction.
- The `y` axis points in the local north direction.
- The `z` axis points in the direction of the ellipsoid surface normal which passes through the position.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`result` | Matrix4 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix4 instance if none was provided.

##### Example:

    // Get the transform from local east-north-up at cartographic (0.0, 0.0) to Earth's fixed frame.
    const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const transform = Cesium.Transforms.eastNorthUpToFixedFrame(center);

#### static Cesium.Transforms.fixedFrameToHeadingPitchRoll(transform, ellipsoid, fixedFrameTransform, result) → HeadingPitchRoll
engine/Source/Core/Transforms.js 479

Computes heading-pitch-roll angles from a transform in a particular reference frame. Heading is the rotation from the local north direction where a positive angle is increasing eastward. Pitch is the rotation from the local east-north plane. Positive pitch angles are above the plane. Negative pitch angles are below the plane. Roll is the first rotation applied about the local east axis.

Name | Type | Default | Description
--- | --- | --- | ---
`transform` | Matrix4 |  | The transform
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`fixedFrameTransform` | Transforms.LocalFrameToFixedFrame | `Transforms.eastNorthUpToFixedFrame` | optional A 4x4 transformation matrix from a reference frame to the provided ellipsoid's fixed reference frame
`result` | HeadingPitchRoll |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new HeadingPitchRoll instance if none was provided.

#### static Cesium.Transforms.headingPitchRollQuaternion(origin, headingPitchRoll, ellipsoid, fixedFrameTransform, result) → Quaternion
engine/Source/Core/Transforms.js 439

Computes a quaternion from a reference frame with axes computed from the heading-pitch-roll angles centered at the provided origin. Heading is the rotation from the local north direction where a positive angle is increasing eastward. Pitch is the rotation from the local east-north plane. Positive pitch angles are above the plane. Negative pitch angles are below the plane. Roll is the first rotation applied about the local east axis.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`headingPitchRoll` | HeadingPitchRoll |  | The heading, pitch, and roll.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`fixedFrameTransform` | Transforms.LocalFrameToFixedFrame | `Transforms.eastNorthUpToFixedFrame` | optional A 4x4 transformation matrix from a reference frame to the provided ellipsoid's fixed reference frame
`result` | Quaternion |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Quaternion instance if none was provided.

##### Example:

    // Get the quaternion from local heading-pitch-roll at cartographic (0.0, 0.0) to Earth's fixed frame.
    const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const heading = -Cesium.Math.PI_OVER_TWO;
    const pitch = Cesium.Math.PI_OVER_FOUR;
    const roll = 0.0;
    const hpr = new HeadingPitchRoll(heading, pitch, roll);
    const quaternion = Cesium.Transforms.headingPitchRollQuaternion(center, hpr);

#### static Cesium.Transforms.headingPitchRollToFixedFrame(origin, headingPitchRoll, ellipsoid, fixedFrameTransform, result) → Matrix4
engine/Source/Core/Transforms.js 384

Computes a 4x4 transformation matrix from a reference frame with axes computed from the heading-pitch-roll angles centered at the provided origin to the provided ellipsoid's fixed reference frame. Heading is the rotation from the local north direction where a positive angle is increasing eastward. Pitch is the rotation from the local east-north plane. Positive pitch angles are above the plane. Negative pitch angles are below the plane. Roll is the first rotation applied about the local east axis.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`headingPitchRoll` | HeadingPitchRoll |  | The heading, pitch, and roll.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`fixedFrameTransform` | Transforms.LocalFrameToFixedFrame | `Transforms.eastNorthUpToFixedFrame` | optional A 4x4 transformation matrix from a reference frame to the provided ellipsoid's fixed reference frame
`result` | Matrix4 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix4 instance if none was provided.

##### Example:

    // Get the transform from local heading-pitch-roll at cartographic (0.0, 0.0) to Earth's fixed frame.
    const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const heading = -Cesium.Math.PI_OVER_TWO;
    const pitch = Cesium.Math.PI_OVER_FOUR;
    const roll = 0.0;
    const hpr = new Cesium.HeadingPitchRoll(heading, pitch, roll);
    const transform = Cesium.Transforms.headingPitchRollToFixedFrame(center, hpr);

#### static Cesium.Transforms.localFrameToFixedFrameGenerator(firstAxis, secondAxis) → Transforms.LocalFrameToFixedFrame
engine/Source/Core/Transforms.js 100

Generates a function that computes a 4x4 transformation matrix from a reference frame centered at the provided origin to the provided ellipsoid's fixed reference frame.

Name | Type | Description
--- | --- | ---
`firstAxis` | string | name of the first axis of the local reference frame. Must be 'east', 'north', 'up', 'west', 'south' or 'down'.
`secondAxis` | string | name of the second axis of the local reference frame. Must be 'east', 'north', 'up', 'west', 'south' or 'down'.

##### Returns:

The function that will computes a 4x4 transformation matrix from a reference frame, with first axis and second axis compliant with the parameters,

#### static Cesium.Transforms.northEastDownToFixedFrame(origin, ellipsoid, result) → Matrix4
engine/Source/Core/Transforms.js 300

Computes a 4x4 transformation matrix from a reference frame with an north-east-down axes centered at the provided origin to the provided ellipsoid's fixed reference frame. The local axes are defined as:

- The `x` axis points in the local north direction.
- The `y` axis points in the local east direction.
- The `z` axis points in the opposite direction of the ellipsoid surface normal which passes through the position.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`result` | Matrix4 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix4 instance if none was provided.

##### Example:

    // Get the transform from local north-east-down at cartographic (0.0, 0.0) to Earth's fixed frame.
    const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const transform = Cesium.Transforms.northEastDownToFixedFrame(center);

#### static Cesium.Transforms.northUpEastToFixedFrame(origin, ellipsoid, result) → Matrix4
engine/Source/Core/Transforms.js 326

Computes a 4x4 transformation matrix from a reference frame with an north-up-east axes centered at the provided origin to the provided ellipsoid's fixed reference frame. The local axes are defined as:

- The `x` axis points in the local north direction.
- The `y` axis points in the direction of the ellipsoid surface normal which passes through the position.
- The `z` axis points in the local east direction.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`result` | Matrix4 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix4 instance if none was provided.

##### Example:

    // Get the transform from local north-up-east at cartographic (0.0, 0.0) to Earth's fixed frame.
    const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const transform = Cesium.Transforms.northUpEastToFixedFrame(center);

#### static Cesium.Transforms.northWestUpToFixedFrame(origin, ellipsoid, result) → Matrix4
engine/Source/Core/Transforms.js 352

Computes a 4x4 transformation matrix from a reference frame with an north-west-up axes centered at the provided origin to the provided ellipsoid's fixed reference frame. The local axes are defined as:

- The `x` axis points in the local north direction.
- The `y` axis points in the local west direction.
- The `z` axis points in the direction of the ellipsoid surface normal which passes through the position.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`result` | Matrix4 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix4 instance if none was provided.

##### Example:

    // Get the transform from local north-West-Up at cartographic (0.0, 0.0) to Earth's fixed frame.
    const center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
    const transform = Cesium.Transforms.northWestUpToFixedFrame(center);

#### static Cesium.Transforms.pointToWindowCoordinates(modelViewProjectionMatrix, viewportTransformation, point, result) → Cartesian2
engine/Source/Core/Transforms.js 886

Transform a point from model coordinates to window coordinates.

Name | Type | Description
--- | --- | ---
`modelViewProjectionMatrix` | Matrix4 | The 4x4 model-view-projection matrix.
`viewportTransformation` | Matrix4 | The 4x4 viewport transformation.
`point` | Cartesian3 | The point to transform.
`result` | Cartesian2 | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Cartesian2 instance if none was provided.

#### static Cesium.Transforms.preloadIcrfFixed(timeInterval) → Promise.<void>
engine/Source/Core/Transforms.js 668

Preloads the data necessary to transform between the ICRF and Fixed axes, in either direction, over a given interval. This function returns a promise that, when resolved, indicates that the preload has completed.

Name | Type | Description
--- | --- | ---
`timeInterval` | TimeInterval | The interval to preload.

##### Returns:

A promise that, when resolved, indicates that the preload has completed and evaluation of the transformation between the fixed and ICRF axes will no longer return undefined for a time inside the interval.

##### Example:

    const interval = new Cesium.TimeInterval(...);
    await Cesium.Transforms.preloadIcrfFixed(interval));
    // the data is now loaded

##### See:

- Transforms.computeIcrfToFixedMatrix
- Transforms.computeFixedToIcrfMatrix

#### static Cesium.Transforms.rotationMatrixFromPositionVelocity(position, velocity, ellipsoid, result) → Matrix3
engine/Source/Core/Transforms.js 954

Transform a position and velocity to a rotation matrix.

Name | Type | Default | Description
--- | --- | --- | ---
`position` | Cartesian3 |  | The position to transform.
`velocity` | Cartesian3 |  | The velocity vector to transform.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`result` | Matrix3 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix3 instance if none was provided.

### Type Definitions

#### Cesium.Transforms.LocalFrameToFixedFrame(origin, ellipsoid, result) → Matrix4
engine/Source/Core/Transforms.js 111

Computes a 4x4 transformation matrix from a reference frame centered at the provided origin to the provided ellipsoid's fixed reference frame.

Name | Type | Default | Description
--- | --- | --- | ---
`origin` | Cartesian3 |  | The center point of the local reference frame.
`ellipsoid` | Ellipsoid | `Ellipsoid.WGS84` | optional The ellipsoid whose fixed frame is used in the transformation.
`result` | Matrix4 |  | optional The object onto which to store the result.

##### Returns:

The modified result parameter or a new Matrix4 instance if none was provided.

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