# Transforms

#### Transforms()

Contains functions for transforming positions to various reference frames.

### Members

#### staticCesium.Transforms.eastNorthUpToFixedFrame

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

#### staticCesium.Transforms.northEastDownToFixedFrame

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

#### staticCesium.Transforms.northUpEastToFixedFrame

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

#### staticCesium.Transforms.northWestUpToFixedFrame

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

### Methods

#### staticCesium.Transforms.computeFixedToIcrfMatrix(date, result) → Matrix3

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.
var now = Cesium.JulianDate.now();
var pointInFixed = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
var fixedToIcrf = Cesium.Transforms.computeIcrfToFixedMatrix(now);
var pointInInertial = new Cesium.Cartesian3();
if (Cesium.defined(fixedToIcrf)) {
pointInInertial = Cesium.Matrix3.multiplyByVector(fixedToIcrf, pointInFixed, pointInInertial);
}``````

#### staticCesium.Transforms.computeIcrfToFixedMatrix(date, result) → Matrix3

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.preRender.addEventListener(function(scene, time) {
var icrfToFixed = Cesium.Transforms.computeIcrfToFixedMatrix(time);
if (Cesium.defined(icrfToFixed)) {
var offset = Cesium.Matrix4.multiplyByPoint(camera.transform, camera.position, new Cesium.Cartesian3());
var transform = Cesium.Matrix4.fromRotationTranslation(icrfToFixed)
var inverseTransform = Cesium.Matrix4.inverseTransformation(transform, new Cesium.Matrix4());
Cesium.Matrix4.multiplyByPoint(inverseTransform, offset, offset);
camera.lookAtTransform(transform, offset);
}
});``````

#### staticCesium.Transforms.computeTemeToPseudoFixedMatrix(date, result) → Matrix3

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 in the inertial frame.
var now = Cesium.JulianDate.now();
var offset = Cesium.Matrix4.multiplyByPoint(camera.transform, camera.position, new Cesium.Cartesian3());
var transform = Cesium.Matrix4.fromRotationTranslation(Cesium.Transforms.computeTemeToPseudoFixedMatrix(now));
var inverseTransform = Cesium.Matrix4.inverseTransformation(transform, new Cesium.Matrix4());
Cesium.Matrix4.multiplyByPoint(inverseTransform, offset, offset);
camera.lookAtTransform(transform, offset);
});``````

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.
`fixedFrameTransformOrResult` 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.
var center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
var pitch = Cesium.Math.PI_OVER_FOUR;
var roll = 0.0;

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.
`fixedFrameTransformOrResult` 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.
var center = Cesium.Cartesian3.fromDegrees(0.0, 0.0);
var pitch = Cesium.Math.PI_OVER_FOUR;
var roll = 0.0;

#### staticCesium.Transforms.localFrameToFixedFrameGenerator(firstAxis, secondAxis) → localFrameToFixedFrameGenerator~resultat

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,

#### staticCesium.Transforms.pointToWindowCoordinates(modelViewProjectionMatrix, viewportTransformation, point, result) → Cartesian2

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.

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:
``````var interval = new Cesium.TimeInterval(...);
// the data is now loaded
});``````

### Type Definitions

#### LocalFrameToFixedFrame(origin, ellipsoid, result) → Matrix4

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.