/*global defineSuite*/
defineSuite([
        'Core/Transforms',
        'Core/Cartesian2',
        'Core/Cartesian3',
        'Core/Cartesian4',
        'Core/EarthOrientationParameters',
        'Core/Ellipsoid',
        'Core/GeographicProjection',
        'Core/HeadingPitchRoll',
        'Core/Iau2006XysData',
        'Core/JulianDate',
        'Core/loadJson',
        'Core/Math',
        'Core/Matrix3',
        'Core/Matrix4',
        'Core/Quaternion',
        'Core/TimeInterval'
    ], function(
        Transforms,
        Cartesian2,
        Cartesian3,
        Cartesian4,
        EarthOrientationParameters,
        Ellipsoid,
        GeographicProjection,
        HeadingPitchRoll,
        Iau2006XysData,
        JulianDate,
        loadJson,
        CesiumMath,
        Matrix3,
        Matrix4,
        Quaternion,
        TimeInterval) {
    'use strict';

    var negativeX = new Cartesian4(-1, 0, 0, 0);
    var negativeY = new Cartesian4(0, -1, 0, 0);
    var negativeZ = new Cartesian4(0, 0, -1, 0);

    it('eastNorthUpToFixedFrame works without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);

        var returnedResult = Transforms.eastNorthUpToFixedFrame(origin, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('eastNorthUpToFixedFrame works with a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);
        var result = new Matrix4(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2);

        var returnedResult = Transforms.eastNorthUpToFixedFrame(origin, Ellipsoid.UNIT_SPHERE, result);
        expect(result).toBe(returnedResult);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('eastNorthUpToFixedFrame works at the north pole', function() {
        var northPole = new Cartesian3(0.0, 0.0, 1.0);
        var expectedTranslation = new Cartesian4(northPole.x, northPole.y, northPole.z, 1.0);

        var result = new Matrix4();
        var returnedResult = Transforms.eastNorthUpToFixedFrame(northPole, Ellipsoid.UNIT_SPHERE, result);
        expect(returnedResult).toBe(result);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(negativeX); // north
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('eastNorthUpToFixedFrame works at the south pole', function() {
        var southPole = new Cartesian3(0.0, 0.0, -1.0);
        var expectedTranslation = new Cartesian4(southPole.x, southPole.y, southPole.z, 1.0);

        var returnedResult = Transforms.eastNorthUpToFixedFrame(southPole, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // north
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(negativeZ); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northEastDownToFixedFrame works without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);

        var returnedResult = Transforms.northEastDownToFixedFrame(origin, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(negativeX); // down
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northEastDownToFixedFrame works with a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);
        var result = new Matrix4(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2);

        var returnedResult = Transforms.northEastDownToFixedFrame(origin, Ellipsoid.UNIT_SPHERE, result);
        expect(result).toBe(returnedResult);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(negativeX); // down
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northEastDownToFixedFrame works at the north pole', function() {
        var northPole = new Cartesian3(0.0, 0.0, 1.0);
        var expectedTranslation = new Cartesian4(northPole.x, northPole.y, northPole.z, 1.0);

        var result = new Matrix4();
        var returnedResult = Transforms.northEastDownToFixedFrame(northPole, Ellipsoid.UNIT_SPHERE, result);
        expect(returnedResult).toBe(result);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(negativeX); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(negativeZ); // down
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northEastDownToFixedFrame works at the south pole', function() {
        var southPole = new Cartesian3(0.0, 0.0, -1.0);
        var expectedTranslation = new Cartesian4(southPole.x, southPole.y, southPole.z, 1.0);

        var returnedResult = Transforms.northEastDownToFixedFrame(southPole, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // down
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northUpEastToFixedFrame works without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);

        var returnedResult = Transforms.northUpEastToFixedFrame(origin, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // up
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northUpEastToFixedFrame works with a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);
        var result = new Matrix4(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2);

        var returnedResult = Transforms.northUpEastToFixedFrame(origin, Ellipsoid.UNIT_SPHERE, result);
        expect(result).toBe(returnedResult);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // up
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northUpEastToFixedFrame works at the north pole', function() {
        var northPole = new Cartesian3(0.0, 0.0, 1.0);
        var expectedTranslation = new Cartesian4(northPole.x, northPole.y, northPole.z, 1.0);

        var result = new Matrix4();
        var returnedResult = Transforms.northUpEastToFixedFrame(northPole, Ellipsoid.UNIT_SPHERE, result);
        expect(returnedResult).toBe(result);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(negativeX); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // up
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northUpEastToFixedFrame works at the south pole', function() {
        var southPole = new Cartesian3(0.0, 0.0, -1.0);
        var expectedTranslation = new Cartesian4(southPole.x, southPole.y, southPole.z, 1.0);

        var returnedResult = Transforms.northUpEastToFixedFrame(southPole, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(negativeZ); // up
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Y); // east
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northWestUpToFixedFrame works without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);

        var returnedResult = Transforms.northWestUpToFixedFrame(origin, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(negativeY); // west
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northWestUpToFixedFrame works with a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var expectedTranslation = new Cartesian4(origin.x, origin.y, origin.z, 1.0);
        var result = new Matrix4(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2);

        var returnedResult = Transforms.northWestUpToFixedFrame(origin, Ellipsoid.UNIT_SPHERE, result);
        expect(result).toBe(returnedResult);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(negativeY); // west
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northWestUpToFixedFrame works at the north pole', function() {
        var northPole = new Cartesian3(0.0, 0.0, 1.0);
        var expectedTranslation = new Cartesian4(northPole.x, northPole.y, northPole.z, 1.0);

        var result = new Matrix4();
        var returnedResult = Transforms.northWestUpToFixedFrame(northPole, Ellipsoid.UNIT_SPHERE, result);
        expect(returnedResult).toBe(result);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(negativeX); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(negativeY); // west
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(Cartesian4.UNIT_Z); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('northWestUpToFixedFrame works at the south pole', function() {
        var southPole = new Cartesian3(0.0, 0.0, -1.0);
        var expectedTranslation = new Cartesian4(southPole.x, southPole.y, southPole.z, 1.0);

        var returnedResult = Transforms.northWestUpToFixedFrame(southPole, Ellipsoid.UNIT_SPHERE);
        expect(Matrix4.getColumn(returnedResult, 0, new Cartesian4())).toEqual(Cartesian4.UNIT_X); // north
        expect(Matrix4.getColumn(returnedResult, 1, new Cartesian4())).toEqual(negativeY); // west
        expect(Matrix4.getColumn(returnedResult, 2, new Cartesian4())).toEqual(negativeZ); // up
        expect(Matrix4.getColumn(returnedResult, 3, new Cartesian4())).toEqual(expectedTranslation); // translation
    });

    it('headingPitchRollToFixedFrame works without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var expectedRotation = Matrix3.fromQuaternion(Quaternion.fromHeadingPitchRoll(heading, pitch, roll));
        var expectedX = Matrix3.getColumn(expectedRotation, 0, new Cartesian3());
        var expectedY = Matrix3.getColumn(expectedRotation, 1, new Cartesian3());
        var expectedZ = Matrix3.getColumn(expectedRotation, 2, new Cartesian3());

        Cartesian3.fromElements(expectedX.z, expectedX.x, expectedX.y, expectedX);
        Cartesian3.fromElements(expectedY.z, expectedY.x, expectedY.y, expectedY);
        Cartesian3.fromElements(expectedZ.z, expectedZ.x, expectedZ.y, expectedZ);

        var returnedResult = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var actualX = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 0, new Cartesian4()));
        var actualY = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 1, new Cartesian4()));
        var actualZ = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 2, new Cartesian4()));
        var actualTranslation = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 3, new Cartesian4()));

        expect(actualX).toEqual(expectedX);
        expect(actualY).toEqual(expectedY);
        expect(actualZ).toEqual(expectedZ);
        expect(actualTranslation).toEqual(origin);
    });

    it('headingPitchRollToFixedFrame works with a HeadingPitchRoll object and without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var expectedRotation = Matrix3.fromQuaternion(Quaternion.fromHeadingPitchRoll(heading, pitch, roll));
        var expectedX = Matrix3.getColumn(expectedRotation, 0, new Cartesian3());
        var expectedY = Matrix3.getColumn(expectedRotation, 1, new Cartesian3());
        var expectedZ = Matrix3.getColumn(expectedRotation, 2, new Cartesian3());

        Cartesian3.fromElements(expectedX.z, expectedX.x, expectedX.y, expectedX);
        Cartesian3.fromElements(expectedY.z, expectedY.x, expectedY.y, expectedY);
        Cartesian3.fromElements(expectedZ.z, expectedZ.x, expectedZ.y, expectedZ);

        var returnedResult = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var actualX = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 0, new Cartesian4()));
        var actualY = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 1, new Cartesian4()));
        var actualZ = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 2, new Cartesian4()));
        var actualTranslation = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 3, new Cartesian4()));

        expect(actualX).toEqual(expectedX);
        expect(actualY).toEqual(expectedY);
        expect(actualZ).toEqual(expectedZ);
        expect(actualTranslation).toEqual(origin);
    });

    it('headingPitchRollToFixedFrame works with a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var expectedRotation = Matrix3.fromQuaternion(Quaternion.fromHeadingPitchRoll(heading, pitch, roll));
        var expectedX = Matrix3.getColumn(expectedRotation, 0, new Cartesian3());
        var expectedY = Matrix3.getColumn(expectedRotation, 1, new Cartesian3());
        var expectedZ = Matrix3.getColumn(expectedRotation, 2, new Cartesian3());

        Cartesian3.fromElements(expectedX.z, expectedX.x, expectedX.y, expectedX);
        Cartesian3.fromElements(expectedY.z, expectedY.x, expectedY.y, expectedY);
        Cartesian3.fromElements(expectedZ.z, expectedZ.x, expectedZ.y, expectedZ);

        var result = new Matrix4();
        var returnedResult = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE, result);
        var actualX = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 0, new Cartesian4()));
        var actualY = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 1, new Cartesian4()));
        var actualZ = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 2, new Cartesian4()));
        var actualTranslation = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 3, new Cartesian4()));

        expect(returnedResult).toBe(result);
        expect(actualX).toEqual(expectedX);
        expect(actualY).toEqual(expectedY);
        expect(actualZ).toEqual(expectedZ);
        expect(actualTranslation).toEqual(origin);
    });

    it('headingPitchRollToFixedFrame works with a HeadingPitchRoll object and a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var expectedRotation = Matrix3.fromQuaternion(Quaternion.fromHeadingPitchRoll(heading, pitch, roll));
        var expectedX = Matrix3.getColumn(expectedRotation, 0, new Cartesian3());
        var expectedY = Matrix3.getColumn(expectedRotation, 1, new Cartesian3());
        var expectedZ = Matrix3.getColumn(expectedRotation, 2, new Cartesian3());

        Cartesian3.fromElements(expectedX.z, expectedX.x, expectedX.y, expectedX);
        Cartesian3.fromElements(expectedY.z, expectedY.x, expectedY.y, expectedY);
        Cartesian3.fromElements(expectedZ.z, expectedZ.x, expectedZ.y, expectedZ);

        var result = new Matrix4();
        var returnedResult = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE, result);
        var actualX = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 0, new Cartesian4()));
        var actualY = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 1, new Cartesian4()));
        var actualZ = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 2, new Cartesian4()));
        var actualTranslation = Cartesian3.fromCartesian4(Matrix4.getColumn(returnedResult, 3, new Cartesian4()));

        expect(returnedResult).toBe(result);
        expect(actualX).toEqual(expectedX);
        expect(actualY).toEqual(expectedY);
        expect(actualZ).toEqual(expectedZ);
        expect(actualTranslation).toEqual(origin);
    });

    it('headingPitchRollQuaternion works without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var transform = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var expected = Matrix4.getRotation(transform, new Matrix3());

        var quaternion = Transforms.headingPitchRollQuaternion(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var actual = Matrix3.fromQuaternion(quaternion);
        expect(actual).toEqualEpsilon(expected, CesiumMath.EPSILON11);
    });

    it('headingPitchRollQuaternion works with a HeadingPitchRoll object and without a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var transform = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var expected = Matrix4.getRotation(transform, new Matrix3());

        var quaternion = Transforms.headingPitchRollQuaternion(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var actual = Matrix3.fromQuaternion(quaternion);
        expect(actual).toEqualEpsilon(expected, CesiumMath.EPSILON11);
    });

    it('headingPitchRollQuaternion works with a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var transform = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var expected = Matrix4.getRotation(transform, new Matrix3());

        var result = new Quaternion();
        var quaternion = Transforms.headingPitchRollQuaternion(origin, hpr, Ellipsoid.UNIT_SPHERE, result);
        var actual = Matrix3.fromQuaternion(quaternion);
        expect(quaternion).toBe(result);
        expect(actual).toEqualEpsilon(expected, CesiumMath.EPSILON11);
    });

    it('headingPitchRollQuaternion works with a HeadingPitchRoll object and a result parameter', function() {
        var origin = new Cartesian3(1.0, 0.0, 0.0);
        var heading = CesiumMath.toRadians(20.0);
        var pitch = CesiumMath.toRadians(30.0);
        var roll = CesiumMath.toRadians(40.0);
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var transform = Transforms.headingPitchRollToFixedFrame(origin, hpr, Ellipsoid.UNIT_SPHERE);
        var expected = Matrix4.getRotation(transform, new Matrix3());

        var result = new Quaternion();
        var quaternion = Transforms.headingPitchRollQuaternion(origin, hpr, Ellipsoid.UNIT_SPHERE, result);
        var actual = Matrix3.fromQuaternion(quaternion);
        expect(quaternion).toBe(result);
        expect(actual).toEqualEpsilon(expected, CesiumMath.EPSILON11);
    });

    it('computeTemeToPseudoFixedMatrix works before noon', function() {
        var time = JulianDate.fromDate(new Date('June 29, 2015 12:00:00 UTC'));
        var t = Transforms.computeTemeToPseudoFixedMatrix(time);

        // rotation matrix determinants are 1.0
        var det = t[0] * t[4] * t[8] + t[3] * t[7] * t[2] + t[6] * t[1] * t[5] - t[6] * t[4] * t[2] - t[3] * t[1] * t[8] - t[0] * t[7] * t[5];
        expect(det).toEqualEpsilon(1.0, CesiumMath.EPSILON14);

        // rotation matrix inverses are equal to its transpose
        var t4 = Matrix4.fromRotationTranslation(t, Cartesian3.ZERO, new Matrix4());
        expect(Matrix4.inverse(t4, new Matrix4())).toEqualEpsilon(Matrix4.inverseTransformation(t4, new Matrix4()), CesiumMath.EPSILON14);

        time = JulianDate.addHours(time, 23.93447, new JulianDate()); // add one sidereal day
        var u = Transforms.computeTemeToPseudoFixedMatrix(time);
        var tAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(t));
        var uAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(u));
        expect(tAngle).toEqualEpsilon(uAngle, CesiumMath.EPSILON6);
    });

    it('computeTemeToPseudoFixedMatrix works after noon', function() {
        var time = JulianDate.fromDate(new Date('June 29, 2015 12:00:00 UTC'));

        var t = Transforms.computeTemeToPseudoFixedMatrix(time);

        // rotation matrix determinants are 1.0
        var det = t[0] * t[4] * t[8] + t[3] * t[7] * t[2] + t[6] * t[1] * t[5] - t[6] * t[4] * t[2] - t[3] * t[1] * t[8] - t[0] * t[7] * t[5];
        expect(det).toEqualEpsilon(1.0, CesiumMath.EPSILON14);

        // rotation matrix inverses are equal to its transpose
        var t4 = Matrix4.fromRotationTranslation(t);
        expect(Matrix4.inverse(t4, new Matrix4())).toEqualEpsilon(Matrix4.inverseTransformation(t4, new Matrix4()), CesiumMath.EPSILON14);

        time = JulianDate.addHours(time, 23.93447, new JulianDate()); // add one sidereal day
        var u = Transforms.computeTemeToPseudoFixedMatrix(time);
        var tAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(t));
        var uAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(u));
        expect(tAngle).toEqualEpsilon(uAngle, CesiumMath.EPSILON6);
    });

    it('computeTemeToPseudoFixedMatrix works with a result parameter', function() {
        var time = JulianDate.fromDate(new Date('June 29, 2015 12:00:00 UTC'));

        var resultT = new Matrix3();
        var t = Transforms.computeTemeToPseudoFixedMatrix(time, resultT);
        expect(t).toBe(resultT);

        // rotation matrix determinants are 1.0
        var det = t[0] * t[4] * t[8] + t[3] * t[7] * t[2] + t[6] * t[1] * t[5] - t[6] * t[4] * t[2] - t[3] * t[1] * t[8] - t[0] * t[7] * t[5];
        expect(det).toEqualEpsilon(1.0, CesiumMath.EPSILON14);

        // rotation matrix inverses are equal to its transpose
        var t4 = Matrix4.fromRotationTranslation(t);
        expect(Matrix4.inverse(t4, new Matrix4())).toEqualEpsilon(Matrix4.inverseTransformation(t4, new Matrix4()), CesiumMath.EPSILON14);

        time = JulianDate.addHours(time, 23.93447, new JulianDate()); // add one sidereal day
        var resultU = new Matrix3();
        var u = Transforms.computeTemeToPseudoFixedMatrix(time, resultU);
        expect(u).toBe(resultU);
        var tAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(t));
        var uAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(u));
        expect(tAngle).toEqualEpsilon(uAngle, CesiumMath.EPSILON6);
    });

    describe('computeIcrfToFixedMatrix', function() {
        function preloadTransformationData(start, stop, eopDescription) {
            Transforms.earthOrientationParameters = new EarthOrientationParameters(eopDescription);
            var preloadInterval = new TimeInterval({
                start: start,
                stop: stop
            });

            return Transforms.preloadIcrfFixed(preloadInterval);
        }

        it('throws if the date parameter is not specified', function() {
            expect(function() {
                Transforms.computeIcrfToFixedMatrix(undefined);
            }).toThrowDeveloperError();

            expect(function() {
                Transforms.computeFixedToIcrfMatrix(undefined);
            }).toThrowDeveloperError();
        });

        it('works with data from STK Components', function() {
            // This data set represents a set of data encompassing the corresponding EOP data below.
            // The rotation data from Components span before and after the EOP data so as to test
            // what happens when we try evaluating at times when we don't have EOP as well as at
            // times where we do.  The samples are not at exact EOP times, in order to test interpolation.
            return loadJson('Data/EarthOrientationParameters/IcrfToFixedStkComponentsRotationData.json').then(function(componentsData) {
                var start = JulianDate.fromIso8601(componentsData[0].date);
                var stop = JulianDate.fromIso8601(componentsData[componentsData.length - 1].date);

                return preloadTransformationData(start, stop, {
                    url: 'Data/EarthOrientationParameters/EOP-2011-July.json'
                }).then(function() {
                    for (var i = 0; i < componentsData.length; ++i) {
                        var time = JulianDate.fromIso8601(componentsData[i].date);
                        var resultT = new Matrix3();
                        var t = Transforms.computeIcrfToFixedMatrix(time, resultT);
                        expect(t).toBe(resultT);

                        // rotation matrix determinants are 1.0
                        var det = t[0] * t[4] * t[8] + t[3] * t[7] * t[2] + t[6] * t[1] * t[5] - t[6] * t[4] * t[2] - t[3] * t[1] * t[8] - t[0] * t[7] * t[5];
                        expect(det).toEqualEpsilon(1.0, CesiumMath.EPSILON14);

                        // rotation matrix inverses are equal to its transpose
                        var t4 = Matrix4.fromRotationTranslation(t);
                        expect(Matrix4.inverse(t4, new Matrix4())).toEqualEpsilon(Matrix4.inverseTransformation(t4, new Matrix4()), CesiumMath.EPSILON14);

                        var expectedMtx = Matrix3.fromQuaternion(Quaternion.conjugate(componentsData[i].icrfToFixedQuaternion, new Quaternion()));
                        var testInverse = Matrix3.multiply(Matrix3.transpose(t, new Matrix3()), expectedMtx, new Matrix3());
                        var testDiff = new Matrix3();
                        for (var k = 0; k < 9; k++) {
                            testDiff[k] = t[k] - expectedMtx[k];
                        }
                        expect(testInverse).toEqualEpsilon(Matrix3.IDENTITY, CesiumMath.EPSILON14);
                        expect(testDiff).toEqualEpsilon(new Matrix3(), CesiumMath.EPSILON14);
                    }
                });
            });
        });

        it('works with hard-coded data', function() {
            // 2011-07-03 00:00:00 UTC
            var time = new JulianDate(2455745, 43200);

            return preloadTransformationData(time, time, {
                url: 'Data/EarthOrientationParameters/EOP-2011-July.json'
            }).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);
                expect(t).toBe(resultT);

                // rotation matrix determinants are 1.0
                var det = t[0] * t[4] * t[8] + t[3] * t[7] * t[2] + t[6] * t[1] * t[5] - t[6] * t[4] * t[2] - t[3] * t[1] * t[8] - t[0] * t[7] * t[5];
                expect(det).toEqualEpsilon(1.0, CesiumMath.EPSILON14);

                // rotation matrix inverses are equal to its transpose
                var t4 = Matrix4.fromRotationTranslation(t);
                expect(Matrix4.inverse(t4, new Matrix4())).toEqualEpsilon(Matrix4.inverseTransformation(t4, new Matrix4()), CesiumMath.EPSILON14);

                time = JulianDate.addHours(time, 23.93447, new JulianDate()); // add one sidereal day
                var resultU = new Matrix3();
                var u = Transforms.computeIcrfToFixedMatrix(time, resultU);
                expect(u).toBe(resultU);
                var tAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(t));
                var uAngle = Quaternion.computeAngle(Quaternion.fromRotationMatrix(u));
                expect(tAngle).toEqualEpsilon(uAngle, CesiumMath.EPSILON6);

                // The rotation matrix from STK Components corresponding to the time and data inputs above
                var expectedMtx = new Matrix3(0.18264414843630006, -0.98317906144315947, -0.00021950336420248503, 0.98317840915224974, 0.18264428011734501, -0.0011325710874539787, 0.0011536112127187594, -0.0000089534866085598909, 0.99999933455028112);

                var testInverse = Matrix3.multiply(Matrix3.transpose(t, new Matrix3()), expectedMtx, new Matrix3());
                var testDiff = new Matrix3();
                for (var i = 0; i < 9; i++) {
                    testDiff[i] = t[i] - expectedMtx[i];
                }
                expect(testInverse).toEqualEpsilon(Matrix3.IDENTITY, CesiumMath.EPSILON14);
                expect(testDiff).toEqualEpsilon(new Matrix3(), CesiumMath.EPSILON14);
            });
        });

        it('works over day boundary', function() {

            var time = new JulianDate(2455745, 86395);

            return preloadTransformationData(time, time, {
                url: 'Data/EarthOrientationParameters/EOP-2011-July.json'
            }).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);

                // The rotation matrix from STK Components corresponding to the time and data inputs above
                var expectedMtx = new Matrix3(-0.19073578935932833, 0.98164138366748721, 0.00022919174269963536, -0.98164073712836186, -0.19073592679333939, 0.0011266944449015753, 0.0011497249933208494, -0.000010082996932331842, 0.99999933901516791);

                var testInverse = Matrix3.multiply(Matrix3.transpose(t, new Matrix3()), expectedMtx, new Matrix3());
                var testDiff = new Matrix3();
                for (var i = 0; i < 9; i++) {
                    testDiff[i] = t[i] - expectedMtx[i];
                }
                expect(testInverse).toEqualEpsilon(Matrix3.IDENTITY, CesiumMath.EPSILON14);
                expect(testDiff).toEqualEpsilon(new Matrix3(), CesiumMath.EPSILON14);
            });
        });

        it('works over day boundary backwards', function() {
            var time = new JulianDate(2455745, 10);

            return preloadTransformationData(time, time, {
                url: 'Data/EarthOrientationParameters/EOP-2011-July.json'
            }).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);

                //The rotation matrix from STK Components corresponding to the time and data inputs above
                var expectedMtx = new Matrix3(-0.17489910479510423, 0.984586338811966, 0.00021110831245616662, -0.98458569065286827, -0.17489923190143036, 0.0011297972845023996, 0.0011493056536445096, -0.00001025368996280683, 0.99999933949547);

                var testInverse = Matrix3.multiply(Matrix3.transpose(t, new Matrix3()), expectedMtx, new Matrix3());
                var testDiff = new Matrix3();
                for (var i = 0; i < 9; i++) {
                    testDiff[i] = t[i] - expectedMtx[i];
                }
                expect(testInverse).toEqualEpsilon(Matrix3.IDENTITY, CesiumMath.EPSILON14);
                expect(testDiff).toEqualEpsilon(new Matrix3(), CesiumMath.EPSILON14);
            });
        });

        it('works with position rotation', function() {
            // GEO Satellite position
            var inertialPos = new Cartesian3(-7322101.15395708, -41525699.1558387, 0);
            // The following is the value computed by STK Components for the date specified below
            var expectedFixedPos = new Cartesian3(39489858.9917795, -14783363.192887, -8075.05820056297);

            // 2011-07-03 00:00:00 UTC
            var time = new JulianDate(2455745, 43200);

            return preloadTransformationData(time, time, {
                url: 'Data/EarthOrientationParameters/EOP-2011-July.json'
            }).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);

                var result = Matrix3.multiplyByVector(t, inertialPos, new Cartesian3());
                var error = Cartesian3.subtract(result, expectedFixedPos, new Cartesian3());

                // Given the magnitude of the positions involved (1e8)
                // this tolerance represents machine precision
                expect(error).toEqualEpsilon(Cartesian3.ZERO, CesiumMath.EPSILON7);
            });
        });

        it('undefined prior to 1974', function() {
            // 1970 jan 1 0h UTC
            var time = new JulianDate(2440587, 43200);
            // Purposefully do not load EOP!  EOP doesn't make a lot of sense before 1972.
            // Even though we are trying to load the data for 1970,
            // we don't have the data in Cesium to load.
            return preloadTransformationData(time, JulianDate.addDays(time, 1, new JulianDate())).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);
                // Check that we get undefined, since we don't have ICRF data
                expect(t).toEqual(undefined);
            });
        });

        it('works after 2028', function() {
            // 2030 jan 1 0h UTC
            var time = new JulianDate(2462502, 43200);
            // Purposefully do not load EOP!  EOP doesn't exist yet that far into the future
            // Even though we are trying to load the data for 2030,
            // we don't have the data in Cesium to load.
            return preloadTransformationData(time, JulianDate.addDays(time, 1, new JulianDate())).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);
                expect(t).toBeDefined();
            });
        });

        it('works without EOP data loaded', function() {
            // GEO Satellite position
            var inertialPos = new Cartesian3(-7322101.15395708, -41525699.1558387, 0);
            // The following is the value computed by STK Components for the date specified below
            var expectedFixedPos = new Cartesian3(39489545.7583001, -14784199.9085371, -8034.77037239318);

            // 2011-07-03 00:00:00 UTC
            var time = new JulianDate(2455745, 43200);

            return preloadTransformationData(time, time, undefined).then(function() {
                var resultT = new Matrix3();
                var t = Transforms.computeIcrfToFixedMatrix(time, resultT);

                var result = Matrix3.multiplyByVector(t, inertialPos, new Cartesian3());
                var error = Cartesian3.subtract(result, expectedFixedPos, new Cartesian3());

                // Given the magnitude of the positions involved (1e8)
                // this tolerance represents machine precision
                expect(error).toEqualEpsilon(Cartesian3.ZERO, CesiumMath.EPSILON7);
            });
        });

        it('throws a RuntimeError when asked to compute with invalid EOP data', function() {
            // 2011-07-03 00:00:00 UTC
            var time = new JulianDate(2455745, 43200);

            return preloadTransformationData(time, time, {
                url: 'Data/EarthOrientationParameters/EOP-Invalid.json'
            }).then(function() {
                expect(function() {
                    return Transforms.computeIcrfToFixedMatrix(time);
                }).toThrowRuntimeError();
            });
        });

        it('throws a RuntimeError when asked to compute with a missing EOP data file', function() {
            // 2011-07-03 00:00:00 UTC
            var time = new JulianDate(2455745, 43200);

            return preloadTransformationData(time, time, {
                url: 'Data/EarthOrientationParameters/EOP-DoesNotExist.json'
            }).then(function() {
                expect(function() {
                    return Transforms.computeIcrfToFixedMatrix(time);
                }).toThrowRuntimeError();
            });
        });

        it('returns undefined before XYS data is loaded.', function() {
            Transforms.earthOrientationParameters = new EarthOrientationParameters();
            Transforms.iau2006XysData = new Iau2006XysData();

            var time = new JulianDate(2455745, 43200);
            expect(Transforms.computeIcrfToFixedMatrix(time)).toBeUndefined();
        });

        it('returns undefined before EOP data is loaded.', function() {
            var time = new JulianDate(2455745, 43200);
            return preloadTransformationData(time, time).then(function() {
                expect(Transforms.computeIcrfToFixedMatrix(time)).toBeDefined();
                Transforms.earthOrientationParameters = new EarthOrientationParameters({
                    url: 'Data/EarthOrientationParameters/EOP-2011-July.json'
                });
                expect(Transforms.computeIcrfToFixedMatrix(time)).toBeUndefined();
            });
        });
    });

    var width = 1024.0;
    var height = 768.0;
    var perspective = Matrix4.computePerspectiveFieldOfView(CesiumMath.toRadians(60.0), width / height, 1.0, 10.0, new Matrix4());
    var vpTransform = Matrix4.computeViewportTransformation({
        width: width,
        height: height
    }, 0, 1, new Matrix4());

    it('pointToGLWindowCoordinates works at the center', function() {
        var view = Matrix4.fromCamera({
            position: Cartesian3.multiplyByScalar(Cartesian3.UNIT_X, 2.0, new Cartesian3()),
            direction: Cartesian3.negate(Cartesian3.UNIT_X, new Cartesian3()),
            up: Cartesian3.UNIT_Z
        });
        var mvpMatrix = Matrix4.multiply(perspective, view, new Matrix4());

        var expected = new Cartesian2(width * 0.5, height * 0.5);
        var returnedResult = Transforms.pointToGLWindowCoordinates(mvpMatrix, vpTransform, Cartesian3.ZERO);
        expect(returnedResult).toEqual(expected);
    });

    it('pointToGLWindowCoordinates works with a result parameter', function() {
        var view = Matrix4.fromCamera({
            position: Cartesian3.multiplyByScalar(Cartesian3.UNIT_X, 2.0, new Cartesian3()),
            direction: Cartesian3.negate(Cartesian3.UNIT_X, new Cartesian3()),
            up: Cartesian3.UNIT_Z
        });
        var mvpMatrix = Matrix4.multiply(perspective, view, new Matrix4());

        var expected = new Cartesian2(width * 0.5, height * 0.5);
        var result = new Cartesian2();
        var returnedResult = Transforms.pointToGLWindowCoordinates(mvpMatrix, vpTransform, Cartesian3.ZERO, result);
        expect(result).toBe(returnedResult);
        expect(returnedResult).toEqual(expected);
    });

    it('pointToGLWindowCoordinates works at the lower left', function() {
        var z = -perspective[Matrix4.COLUMN3ROW2] / perspective[Matrix4.COLUMN2ROW2];
        var x = z / perspective[Matrix4.COLUMN0ROW0];
        var y = z / perspective[Matrix4.COLUMN1ROW1];
        var point = new Cartesian3(x, y, z);

        var expected = new Cartesian2(0.0, 0.0);
        var returnedResult = Transforms.pointToGLWindowCoordinates(perspective, vpTransform, point);
        expect(returnedResult).toEqualEpsilon(expected, CesiumMath.EPSILON12);
    });

    it('pointToGLWindowCoordinates works at the upper right', function() {
        var z = -perspective[Matrix4.COLUMN3ROW2] / perspective[Matrix4.COLUMN2ROW2];
        var x = -z / perspective[Matrix4.COLUMN0ROW0];
        var y = -z / perspective[Matrix4.COLUMN1ROW1];
        var point = new Cartesian3(x, y, z);
        var expected = new Cartesian2(width, height);

        var returnedResult = Transforms.pointToGLWindowCoordinates(perspective, vpTransform, point);
        expect(returnedResult).toEqualEpsilon(expected, CesiumMath.EPSILON12);
    });

    it('pointToWindowCoordinates works at the center', function() {
        var view = Matrix4.fromCamera({
            position: Cartesian3.multiplyByScalar(Cartesian3.UNIT_X, 2.0, new Cartesian3()),
            direction: Cartesian3.negate(Cartesian3.UNIT_X, new Cartesian3()),
            up: Cartesian3.UNIT_Z
        });
        var mvpMatrix = Matrix4.multiply(perspective, view, new Matrix4());

        var expected = new Cartesian2(width * 0.5, height * 0.5);
        var returnedResult = Transforms.pointToWindowCoordinates(mvpMatrix, vpTransform, Cartesian3.ZERO);
        expect(returnedResult).toEqual(expected);
    });

    it('pointToWindowCoordinates works with a result parameter', function() {
        var view = Matrix4.fromCamera({
            position: Cartesian3.multiplyByScalar(Cartesian3.UNIT_X, 2.0, new Cartesian3()),
            direction: Cartesian3.negate(Cartesian3.UNIT_X, new Cartesian3()),
            up: Cartesian3.UNIT_Z
        });
        var mvpMatrix = Matrix4.multiply(perspective, view, new Matrix4());

        var expected = new Cartesian2(width * 0.5, height * 0.5);
        var result = new Cartesian2();
        var returnedResult = Transforms.pointToWindowCoordinates(mvpMatrix, vpTransform, Cartesian3.ZERO, result);
        expect(result).toBe(returnedResult);
        expect(returnedResult).toEqual(expected);
    });

    it('pointToWindowCoordinates works at the lower left', function() {
        var z = -perspective[Matrix4.COLUMN3ROW2] / perspective[Matrix4.COLUMN2ROW2];
        var x = z / perspective[Matrix4.COLUMN0ROW0];
        var y = z / perspective[Matrix4.COLUMN1ROW1];
        var point = new Cartesian3(x, y, z);

        var expected = new Cartesian2(0.0, height);
        var returnedResult = Transforms.pointToWindowCoordinates(perspective, vpTransform, point);
        expect(returnedResult).toEqualEpsilon(expected, CesiumMath.EPSILON12);
    });

    it('pointToWindowCoordinates works at the upper right', function() {
        var z = -perspective[Matrix4.COLUMN3ROW2] / perspective[Matrix4.COLUMN2ROW2];
        var x = -z / perspective[Matrix4.COLUMN0ROW0];
        var y = -z / perspective[Matrix4.COLUMN1ROW1];
        var point = new Cartesian3(x, y, z);
        var expected = new Cartesian2(width, 0.0);

        var returnedResult = Transforms.pointToWindowCoordinates(perspective, vpTransform, point);
        expect(returnedResult).toEqualEpsilon(expected, CesiumMath.EPSILON12);
    });

    it('basisTo2D projects translation', function() {
        var ellipsoid = Ellipsoid.WGS84;
        var projection = new GeographicProjection(ellipsoid);
        var origin = Cartesian3.fromDegrees(-72.0, 40.0, 100.0, ellipsoid);
        var heading = CesiumMath.toRadians(90.0);
        var pitch = CesiumMath.toRadians(45.0);
        var roll = 0.0;
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var modelMatrix = Transforms.headingPitchRollToFixedFrame(origin, hpr, ellipsoid);
        var modelMatrix2D = Transforms.basisTo2D(projection, modelMatrix, new Matrix4());

        var translation2D = Cartesian3.fromCartesian4(Matrix4.getColumn(modelMatrix2D, 3, new Cartesian4()));

        var carto = ellipsoid.cartesianToCartographic(origin);
        var expected = projection.project(carto);
        Cartesian3.fromElements(expected.z, expected.x, expected.y, expected);

        expect(translation2D).toEqual(expected);
    });

    it('basisTo2D transforms rotation', function() {
        var ellipsoid = Ellipsoid.WGS84;
        var projection = new GeographicProjection(ellipsoid);
        var origin = Cartesian3.fromDegrees(-72.0, 40.0, 100.0, ellipsoid);
        var heading = CesiumMath.toRadians(90.0);
        var pitch = CesiumMath.toRadians(45.0);
        var roll = 0.0;
        var hpr = new HeadingPitchRoll(heading, pitch, roll);

        var modelMatrix = Transforms.headingPitchRollToFixedFrame(origin, hpr, ellipsoid);
        var modelMatrix2D = Transforms.basisTo2D(projection, modelMatrix, new Matrix4());

        var rotation2D = Matrix4.getRotation(modelMatrix2D, new Matrix3());

        var enu = Transforms.eastNorthUpToFixedFrame(origin, ellipsoid);
        var enuInverse = Matrix4.inverseTransformation(enu, enu);

        var hprPlusTranslate = Matrix4.multiply(enuInverse, modelMatrix, new Matrix4());
        var hpr2 = Matrix4.getRotation(hprPlusTranslate, new Matrix3());

        var row0 = Matrix3.getRow(hpr2, 0, new Cartesian3());
        var row1 = Matrix3.getRow(hpr2, 1, new Cartesian3());
        var row2 = Matrix3.getRow(hpr2, 2, new Cartesian3());

        var expected = new Matrix3();
        Matrix3.setRow(expected, 0, row2, expected);
        Matrix3.setRow(expected, 1, row0, expected);
        Matrix3.setRow(expected, 2, row1, expected);

        expect(rotation2D).toEqualEpsilon(expected, CesiumMath.EPSILON3);
    });

    it('wgs84To2DModelMatrix creates a model matrix to transform vertices centered origin to 2D', function() {
        var ellipsoid = Ellipsoid.WGS84;
        var projection = new GeographicProjection(ellipsoid);
        var origin = Cartesian3.fromDegrees(-72.0, 40.0, 100.0, ellipsoid);

        var actual = Transforms.wgs84To2DModelMatrix(projection, origin, new Matrix4());
        var expected = Matrix4.fromTranslation(origin);
        Transforms.basisTo2D(projection, expected, expected);

        var actualRotation = Matrix4.getRotation(actual, new Matrix3());
        var expectedRotation = Matrix4.getRotation(expected, new Matrix3());
        expect(actualRotation).toEqualEpsilon(expectedRotation, CesiumMath.EPSILON14);

        var fromENU = Transforms.eastNorthUpToFixedFrame(origin, ellipsoid, new Matrix4());
        var toENU = Matrix4.inverseTransformation(fromENU, new Matrix4());
        var toENUTranslation = Matrix4.getTranslation(toENU, new Cartesian4());
        var projectedTranslation = Matrix4.getTranslation(expected, new Cartesian4());

        var expectedTranslation = new Cartesian4();
        expectedTranslation.x = projectedTranslation.x + toENUTranslation.z;
        expectedTranslation.y = projectedTranslation.y + toENUTranslation.x;
        expectedTranslation.z = projectedTranslation.z + toENUTranslation.y;

        var actualTranslation = Matrix4.getTranslation(actual, new Cartesian4());

        expect(actualTranslation).toEqualEpsilon(expectedTranslation, CesiumMath.EPSILON14);
    });

    it('eastNorthUpToFixedFrame throws without an origin', function() {
        expect(function() {
            Transforms.eastNorthUpToFixedFrame(undefined, Ellipsoid.WGS84);
        }).toThrowDeveloperError();
    });

    it('northEastDownToFixedFrame throws without an origin', function() {
        expect(function() {
            Transforms.northEastDownToFixedFrame(undefined, Ellipsoid.WGS84);
        }).toThrowDeveloperError();
    });

    it('northWestUpToFixedFrame throws without an origin', function() {
        expect(function() {
            Transforms.northWestUpToFixedFrame(undefined, Ellipsoid.WGS84);
        }).toThrowDeveloperError();
    });

    it('headingPitchRollToFixedFrame throws without an origin', function() {
        expect(function() {
            Transforms.headingPitchRollToFixedFrame(undefined, 0.0, 0.0, 0.0);
        }).toThrowDeveloperError();
    });

    it('headingPitchRollToFixedFrame throws without a headingPitchRoll', function() {
        expect(function() {
            Transforms.headingPitchRollToFixedFrame(Cartesian3.ZERO, undefined);
        }).toThrowDeveloperError();
    });

    it('computeTemeToPseudoFixedMatrix throws without a date', function() {
        expect(function() {
            Transforms.computeTemeToPseudoFixedMatrix(undefined);
        }).toThrowDeveloperError();
    });

    it('pointToWindowCoordinates throws without modelViewProjectionMatrix', function() {
        expect(function() {
            Transforms.pointToWindowCoordinates(undefined, Matrix4.IDENTITY, Cartesian3.ZERO);
        }).toThrowDeveloperError();
    });

    it('pointToWindowCoordinates throws without viewportTransformation', function() {
        expect(function() {
            Transforms.pointToWindowCoordinates(Matrix4.IDENTITY, undefined, Cartesian3.ZERO);
        }).toThrowDeveloperError();
    });

    it('pointToWindowCoordinates throws without a point', function() {
        expect(function() {
            Transforms.pointToWindowCoordinates(Matrix4.IDENTITY, Matrix4.IDENTITY, undefined);
        }).toThrowDeveloperError();
    });

    it('basisTo2D throws without projection', function() {
        expect(function() {
            Transforms.basisTo2D(undefined, Matrix4.IDENTITY, new Matrix4());
        }).toThrowDeveloperError();
    });

    it('basisTo2D throws without matrix', function() {
        expect(function() {
            Transforms.basisTo2D(new GeographicProjection(), undefined, new Matrix4());
        }).toThrowDeveloperError();
    });

    it('basisTo2D throws without result', function() {
        expect(function() {
            Transforms.basisTo2D(new GeographicProjection(), Matrix4.IDENTITY, undefined);
        }).toThrowDeveloperError();
    });

    it ('wgs84To2DModelMatrix throws without projection', function() {
        expect(function() {
            Transforms.wgs84To2DModelMatrix(undefined, Cartesian3.UNIT_X, new Matrix4());
        }).toThrowDeveloperError();
    });

    it ('wgs84To2DModelMatrix throws without center', function() {
        expect(function() {
            Transforms.wgs84To2DModelMatrix(new GeographicProjection(), undefined, new Matrix4());
        }).toThrowDeveloperError();
    });

    it ('wgs84To2DModelMatrix throws without result', function() {
        expect(function() {
            Transforms.wgs84To2DModelMatrix(new GeographicProjection(), Cartesian3.UNIT_X, undefined);
        }).toThrowDeveloperError();
    });
});
