import Cartesian3 from "./Cartesian3.js";
import Check from "./Check.js";
import defaultValue from "./defaultValue.js";
import defined from "./defined.js";
import FeatureDetection from "./FeatureDetection.js";
import CesiumMath from "./Math.js";
import Matrix3 from "./Matrix3.js";
/**
* A set of 4-dimensional coordinates used to represent rotation in 3-dimensional space.
* @alias Quaternion
* @constructor
*
* @param {Number} [x=0.0] The X component.
* @param {Number} [y=0.0] The Y component.
* @param {Number} [z=0.0] The Z component.
* @param {Number} [w=0.0] The W component.
*
* @see PackableForInterpolation
*/
function Quaternion(x, y, z, w) {
/**
* The X component.
* @type {Number}
* @default 0.0
*/
this.x = defaultValue(x, 0.0);
/**
* The Y component.
* @type {Number}
* @default 0.0
*/
this.y = defaultValue(y, 0.0);
/**
* The Z component.
* @type {Number}
* @default 0.0
*/
this.z = defaultValue(z, 0.0);
/**
* The W component.
* @type {Number}
* @default 0.0
*/
this.w = defaultValue(w, 0.0);
}
var fromAxisAngleScratch = new Cartesian3();
/**
* Computes a quaternion representing a rotation around an axis.
*
* @param {Cartesian3} axis The axis of rotation.
* @param {Number} angle The angle in radians to rotate around the axis.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.fromAxisAngle = function (axis, angle, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("axis", axis);
Check.typeOf.number("angle", angle);
//>>includeEnd('debug');
var halfAngle = angle / 2.0;
var s = Math.sin(halfAngle);
fromAxisAngleScratch = Cartesian3.normalize(axis, fromAxisAngleScratch);
var x = fromAxisAngleScratch.x * s;
var y = fromAxisAngleScratch.y * s;
var z = fromAxisAngleScratch.z * s;
var w = Math.cos(halfAngle);
if (!defined(result)) {
return new Quaternion(x, y, z, w);
}
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
var fromRotationMatrixNext = [1, 2, 0];
var fromRotationMatrixQuat = new Array(3);
/**
* Computes a Quaternion from the provided Matrix3 instance.
*
* @param {Matrix3} matrix The rotation matrix.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*
* @see Matrix3.fromQuaternion
*/
Quaternion.fromRotationMatrix = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
//>>includeEnd('debug');
var root;
var x;
var y;
var z;
var w;
var m00 = matrix[Matrix3.COLUMN0ROW0];
var m11 = matrix[Matrix3.COLUMN1ROW1];
var m22 = matrix[Matrix3.COLUMN2ROW2];
var trace = m00 + m11 + m22;
if (trace > 0.0) {
// |w| > 1/2, may as well choose w > 1/2
root = Math.sqrt(trace + 1.0); // 2w
w = 0.5 * root;
root = 0.5 / root; // 1/(4w)
x = (matrix[Matrix3.COLUMN1ROW2] - matrix[Matrix3.COLUMN2ROW1]) * root;
y = (matrix[Matrix3.COLUMN2ROW0] - matrix[Matrix3.COLUMN0ROW2]) * root;
z = (matrix[Matrix3.COLUMN0ROW1] - matrix[Matrix3.COLUMN1ROW0]) * root;
} else {
// |w| <= 1/2
var next = fromRotationMatrixNext;
var i = 0;
if (m11 > m00) {
i = 1;
}
if (m22 > m00 && m22 > m11) {
i = 2;
}
var j = next[i];
var k = next[j];
root = Math.sqrt(
matrix[Matrix3.getElementIndex(i, i)] -
matrix[Matrix3.getElementIndex(j, j)] -
matrix[Matrix3.getElementIndex(k, k)] +
1.0
);
var quat = fromRotationMatrixQuat;
quat[i] = 0.5 * root;
root = 0.5 / root;
w =
(matrix[Matrix3.getElementIndex(k, j)] -
matrix[Matrix3.getElementIndex(j, k)]) *
root;
quat[j] =
(matrix[Matrix3.getElementIndex(j, i)] +
matrix[Matrix3.getElementIndex(i, j)]) *
root;
quat[k] =
(matrix[Matrix3.getElementIndex(k, i)] +
matrix[Matrix3.getElementIndex(i, k)]) *
root;
x = -quat[0];
y = -quat[1];
z = -quat[2];
}
if (!defined(result)) {
return new Quaternion(x, y, z, w);
}
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
var scratchHPRQuaternion = new Quaternion();
var scratchHeadingQuaternion = new Quaternion();
var scratchPitchQuaternion = new Quaternion();
var scratchRollQuaternion = new Quaternion();
/**
* Computes a rotation from the given heading, pitch and roll angles. Heading is the rotation about the
* negative z axis. Pitch is the rotation about the negative y axis. Roll is the rotation about
* the positive x axis.
*
* @param {HeadingPitchRoll} headingPitchRoll The rotation expressed as a heading, pitch and roll.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if none was provided.
*/
Quaternion.fromHeadingPitchRoll = function (headingPitchRoll, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("headingPitchRoll", headingPitchRoll);
//>>includeEnd('debug');
scratchRollQuaternion = Quaternion.fromAxisAngle(
Cartesian3.UNIT_X,
headingPitchRoll.roll,
scratchHPRQuaternion
);
scratchPitchQuaternion = Quaternion.fromAxisAngle(
Cartesian3.UNIT_Y,
-headingPitchRoll.pitch,
result
);
result = Quaternion.multiply(
scratchPitchQuaternion,
scratchRollQuaternion,
scratchPitchQuaternion
);
scratchHeadingQuaternion = Quaternion.fromAxisAngle(
Cartesian3.UNIT_Z,
-headingPitchRoll.heading,
scratchHPRQuaternion
);
return Quaternion.multiply(scratchHeadingQuaternion, result, result);
};
var sampledQuaternionAxis = new Cartesian3();
var sampledQuaternionRotation = new Cartesian3();
var sampledQuaternionTempQuaternion = new Quaternion();
var sampledQuaternionQuaternion0 = new Quaternion();
var sampledQuaternionQuaternion0Conjugate = new Quaternion();
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
Quaternion.packedLength = 4;
/**
* Stores the provided instance into the provided array.
*
* @param {Quaternion} value The value to pack.
* @param {Number[]} array The array to pack into.
* @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {Number[]} The array that was packed into
*/
Quaternion.pack = function (value, array, startingIndex) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("value", value);
Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue(startingIndex, 0);
array[startingIndex++] = value.x;
array[startingIndex++] = value.y;
array[startingIndex++] = value.z;
array[startingIndex] = value.w;
return array;
};
/**
* Retrieves an instance from a packed array.
*
* @param {Number[]} array The packed array.
* @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Quaternion} [result] The object into which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.unpack = function (array, startingIndex, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("array", array);
//>>includeEnd('debug');
startingIndex = defaultValue(startingIndex, 0);
if (!defined(result)) {
result = new Quaternion();
}
result.x = array[startingIndex];
result.y = array[startingIndex + 1];
result.z = array[startingIndex + 2];
result.w = array[startingIndex + 3];
return result;
};
/**
* The number of elements used to store the object into an array in its interpolatable form.
* @type {Number}
*/
Quaternion.packedInterpolationLength = 3;
/**
* Converts a packed array into a form suitable for interpolation.
*
* @param {Number[]} packedArray The packed array.
* @param {Number} [startingIndex=0] The index of the first element to be converted.
* @param {Number} [lastIndex=packedArray.length] The index of the last element to be converted.
* @param {Number[]} [result] The object into which to store the result.
*/
Quaternion.convertPackedArrayForInterpolation = function (
packedArray,
startingIndex,
lastIndex,
result
) {
Quaternion.unpack(
packedArray,
lastIndex * 4,
sampledQuaternionQuaternion0Conjugate
);
Quaternion.conjugate(
sampledQuaternionQuaternion0Conjugate,
sampledQuaternionQuaternion0Conjugate
);
for (var i = 0, len = lastIndex - startingIndex + 1; i < len; i++) {
var offset = i * 3;
Quaternion.unpack(
packedArray,
(startingIndex + i) * 4,
sampledQuaternionTempQuaternion
);
Quaternion.multiply(
sampledQuaternionTempQuaternion,
sampledQuaternionQuaternion0Conjugate,
sampledQuaternionTempQuaternion
);
if (sampledQuaternionTempQuaternion.w < 0) {
Quaternion.negate(
sampledQuaternionTempQuaternion,
sampledQuaternionTempQuaternion
);
}
Quaternion.computeAxis(
sampledQuaternionTempQuaternion,
sampledQuaternionAxis
);
var angle = Quaternion.computeAngle(sampledQuaternionTempQuaternion);
if (!defined(result)) {
result = [];
}
result[offset] = sampledQuaternionAxis.x * angle;
result[offset + 1] = sampledQuaternionAxis.y * angle;
result[offset + 2] = sampledQuaternionAxis.z * angle;
}
};
/**
* Retrieves an instance from a packed array converted with {@link convertPackedArrayForInterpolation}.
*
* @param {Number[]} array The array previously packed for interpolation.
* @param {Number[]} sourceArray The original packed array.
* @param {Number} [firstIndex=0] The firstIndex used to convert the array.
* @param {Number} [lastIndex=packedArray.length] The lastIndex used to convert the array.
* @param {Quaternion} [result] The object into which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.unpackInterpolationResult = function (
array,
sourceArray,
firstIndex,
lastIndex,
result
) {
if (!defined(result)) {
result = new Quaternion();
}
Cartesian3.fromArray(array, 0, sampledQuaternionRotation);
var magnitude = Cartesian3.magnitude(sampledQuaternionRotation);
Quaternion.unpack(sourceArray, lastIndex * 4, sampledQuaternionQuaternion0);
if (magnitude === 0) {
Quaternion.clone(Quaternion.IDENTITY, sampledQuaternionTempQuaternion);
} else {
Quaternion.fromAxisAngle(
sampledQuaternionRotation,
magnitude,
sampledQuaternionTempQuaternion
);
}
return Quaternion.multiply(
sampledQuaternionTempQuaternion,
sampledQuaternionQuaternion0,
result
);
};
/**
* Duplicates a Quaternion instance.
*
* @param {Quaternion} quaternion The quaternion to duplicate.
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided. (Returns undefined if quaternion is undefined)
*/
Quaternion.clone = function (quaternion, result) {
if (!defined(quaternion)) {
return undefined;
}
if (!defined(result)) {
return new Quaternion(
quaternion.x,
quaternion.y,
quaternion.z,
quaternion.w
);
}
result.x = quaternion.x;
result.y = quaternion.y;
result.z = quaternion.z;
result.w = quaternion.w;
return result;
};
/**
* Computes the conjugate of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to conjugate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.conjugate = function (quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = -quaternion.x;
result.y = -quaternion.y;
result.z = -quaternion.z;
result.w = quaternion.w;
return result;
};
/**
* Computes magnitude squared for the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to conjugate.
* @returns {Number} The magnitude squared.
*/
Quaternion.magnitudeSquared = function (quaternion) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
//>>includeEnd('debug');
return (
quaternion.x * quaternion.x +
quaternion.y * quaternion.y +
quaternion.z * quaternion.z +
quaternion.w * quaternion.w
);
};
/**
* Computes magnitude for the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to conjugate.
* @returns {Number} The magnitude.
*/
Quaternion.magnitude = function (quaternion) {
return Math.sqrt(Quaternion.magnitudeSquared(quaternion));
};
/**
* Computes the normalized form of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to normalize.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.normalize = function (quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var inverseMagnitude = 1.0 / Quaternion.magnitude(quaternion);
var x = quaternion.x * inverseMagnitude;
var y = quaternion.y * inverseMagnitude;
var z = quaternion.z * inverseMagnitude;
var w = quaternion.w * inverseMagnitude;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Computes the inverse of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to normalize.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.inverse = function (quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var magnitudeSquared = Quaternion.magnitudeSquared(quaternion);
result = Quaternion.conjugate(quaternion, result);
return Quaternion.multiplyByScalar(result, 1.0 / magnitudeSquared, result);
};
/**
* Computes the componentwise sum of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.add = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x + right.x;
result.y = left.y + right.y;
result.z = left.z + right.z;
result.w = left.w + right.w;
return result;
};
/**
* Computes the componentwise difference of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.subtract = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = left.x - right.x;
result.y = left.y - right.y;
result.z = left.z - right.z;
result.w = left.w - right.w;
return result;
};
/**
* Negates the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to be negated.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.negate = function (quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = -quaternion.x;
result.y = -quaternion.y;
result.z = -quaternion.z;
result.w = -quaternion.w;
return result;
};
/**
* Computes the dot (scalar) product of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @returns {Number} The dot product.
*/
Quaternion.dot = function (left, right) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
//>>includeEnd('debug');
return (
left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w
);
};
/**
* Computes the product of two quaternions.
*
* @param {Quaternion} left The first quaternion.
* @param {Quaternion} right The second quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.multiply = function (left, right, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("left", left);
Check.typeOf.object("right", right);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var leftX = left.x;
var leftY = left.y;
var leftZ = left.z;
var leftW = left.w;
var rightX = right.x;
var rightY = right.y;
var rightZ = right.z;
var rightW = right.w;
var x = leftW * rightX + leftX * rightW + leftY * rightZ - leftZ * rightY;
var y = leftW * rightY - leftX * rightZ + leftY * rightW + leftZ * rightX;
var z = leftW * rightZ + leftX * rightY - leftY * rightX + leftZ * rightW;
var w = leftW * rightW - leftX * rightX - leftY * rightY - leftZ * rightZ;
result.x = x;
result.y = y;
result.z = z;
result.w = w;
return result;
};
/**
* Multiplies the provided quaternion componentwise by the provided scalar.
*
* @param {Quaternion} quaternion The quaternion to be scaled.
* @param {Number} scalar The scalar to multiply with.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.multiplyByScalar = function (quaternion, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
Check.typeOf.number("scalar", scalar);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = quaternion.x * scalar;
result.y = quaternion.y * scalar;
result.z = quaternion.z * scalar;
result.w = quaternion.w * scalar;
return result;
};
/**
* Divides the provided quaternion componentwise by the provided scalar.
*
* @param {Quaternion} quaternion The quaternion to be divided.
* @param {Number} scalar The scalar to divide by.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.divideByScalar = function (quaternion, scalar, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
Check.typeOf.number("scalar", scalar);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
result.x = quaternion.x / scalar;
result.y = quaternion.y / scalar;
result.z = quaternion.z / scalar;
result.w = quaternion.w / scalar;
return result;
};
/**
* Computes the axis of rotation of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to use.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Quaternion.computeAxis = function (quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var w = quaternion.w;
if (Math.abs(w - 1.0) < CesiumMath.EPSILON6) {
result.x = result.y = result.z = 0;
return result;
}
var scalar = 1.0 / Math.sqrt(1.0 - w * w);
result.x = quaternion.x * scalar;
result.y = quaternion.y * scalar;
result.z = quaternion.z * scalar;
return result;
};
/**
* Computes the angle of rotation of the provided quaternion.
*
* @param {Quaternion} quaternion The quaternion to use.
* @returns {Number} The angle of rotation.
*/
Quaternion.computeAngle = function (quaternion) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
//>>includeEnd('debug');
if (Math.abs(quaternion.w - 1.0) < CesiumMath.EPSILON6) {
return 0.0;
}
return 2.0 * Math.acos(quaternion.w);
};
var lerpScratch = new Quaternion();
/**
* Computes the linear interpolation or extrapolation at t using the provided quaternions.
*
* @param {Quaternion} start The value corresponding to t at 0.0.
* @param {Quaternion} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.lerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("start", start);
Check.typeOf.object("end", end);
Check.typeOf.number("t", t);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
lerpScratch = Quaternion.multiplyByScalar(end, t, lerpScratch);
result = Quaternion.multiplyByScalar(start, 1.0 - t, result);
return Quaternion.add(lerpScratch, result, result);
};
var slerpEndNegated = new Quaternion();
var slerpScaledP = new Quaternion();
var slerpScaledR = new Quaternion();
/**
* Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
*
* @param {Quaternion} start The value corresponding to t at 0.0.
* @param {Quaternion} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
* @see Quaternion#fastSlerp
*/
Quaternion.slerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("start", start);
Check.typeOf.object("end", end);
Check.typeOf.number("t", t);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var dot = Quaternion.dot(start, end);
// The angle between start must be acute. Since q and -q represent
// the same rotation, negate q to get the acute angle.
var r = end;
if (dot < 0.0) {
dot = -dot;
r = slerpEndNegated = Quaternion.negate(end, slerpEndNegated);
}
// dot > 0, as the dot product approaches 1, the angle between the
// quaternions vanishes. use linear interpolation.
if (1.0 - dot < CesiumMath.EPSILON6) {
return Quaternion.lerp(start, r, t, result);
}
var theta = Math.acos(dot);
slerpScaledP = Quaternion.multiplyByScalar(
start,
Math.sin((1 - t) * theta),
slerpScaledP
);
slerpScaledR = Quaternion.multiplyByScalar(
r,
Math.sin(t * theta),
slerpScaledR
);
result = Quaternion.add(slerpScaledP, slerpScaledR, result);
return Quaternion.multiplyByScalar(result, 1.0 / Math.sin(theta), result);
};
/**
* The logarithmic quaternion function.
*
* @param {Quaternion} quaternion The unit quaternion.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
Quaternion.log = function (quaternion, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("quaternion", quaternion);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var theta = CesiumMath.acosClamped(quaternion.w);
var thetaOverSinTheta = 0.0;
if (theta !== 0.0) {
thetaOverSinTheta = theta / Math.sin(theta);
}
return Cartesian3.multiplyByScalar(quaternion, thetaOverSinTheta, result);
};
/**
* The exponential quaternion function.
*
* @param {Cartesian3} cartesian The cartesian.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*/
Quaternion.exp = function (cartesian, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("cartesian", cartesian);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var theta = Cartesian3.magnitude(cartesian);
var sinThetaOverTheta = 0.0;
if (theta !== 0.0) {
sinThetaOverTheta = Math.sin(theta) / theta;
}
result.x = cartesian.x * sinThetaOverTheta;
result.y = cartesian.y * sinThetaOverTheta;
result.z = cartesian.z * sinThetaOverTheta;
result.w = Math.cos(theta);
return result;
};
var squadScratchCartesian0 = new Cartesian3();
var squadScratchCartesian1 = new Cartesian3();
var squadScratchQuaternion0 = new Quaternion();
var squadScratchQuaternion1 = new Quaternion();
/**
* Computes an inner quadrangle point.
* <p>This will compute quaternions that ensure a squad curve is C<sup>1</sup>.</p>
*
* @param {Quaternion} q0 The first quaternion.
* @param {Quaternion} q1 The second quaternion.
* @param {Quaternion} q2 The third quaternion.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
* @see Quaternion#squad
*/
Quaternion.computeInnerQuadrangle = function (q0, q1, q2, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("q0", q0);
Check.typeOf.object("q1", q1);
Check.typeOf.object("q2", q2);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var qInv = Quaternion.conjugate(q1, squadScratchQuaternion0);
Quaternion.multiply(qInv, q2, squadScratchQuaternion1);
var cart0 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian0);
Quaternion.multiply(qInv, q0, squadScratchQuaternion1);
var cart1 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian1);
Cartesian3.add(cart0, cart1, cart0);
Cartesian3.multiplyByScalar(cart0, 0.25, cart0);
Cartesian3.negate(cart0, cart0);
Quaternion.exp(cart0, squadScratchQuaternion0);
return Quaternion.multiply(q1, squadScratchQuaternion0, result);
};
/**
* Computes the spherical quadrangle interpolation between quaternions.
*
* @param {Quaternion} q0 The first quaternion.
* @param {Quaternion} q1 The second quaternion.
* @param {Quaternion} s0 The first inner quadrangle.
* @param {Quaternion} s1 The second inner quadrangle.
* @param {Number} t The time in [0,1] used to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
*
* @example
* // 1. compute the squad interpolation between two quaternions on a curve
* var s0 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1], new Cesium.Quaternion());
* var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2], new Cesium.Quaternion());
* var q = Cesium.Quaternion.squad(quaternions[i], quaternions[i + 1], s0, s1, t, new Cesium.Quaternion());
*
* // 2. compute the squad interpolation as above but where the first quaternion is a end point.
* var s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[0], quaternions[1], quaternions[2], new Cesium.Quaternion());
* var q = Cesium.Quaternion.squad(quaternions[0], quaternions[1], quaternions[0], s1, t, new Cesium.Quaternion());
*
* @see Quaternion#computeInnerQuadrangle
*/
Quaternion.squad = function (q0, q1, s0, s1, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("q0", q0);
Check.typeOf.object("q1", q1);
Check.typeOf.object("s0", s0);
Check.typeOf.object("s1", s1);
Check.typeOf.number("t", t);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var slerp0 = Quaternion.slerp(q0, q1, t, squadScratchQuaternion0);
var slerp1 = Quaternion.slerp(s0, s1, t, squadScratchQuaternion1);
return Quaternion.slerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
};
var fastSlerpScratchQuaternion = new Quaternion();
var opmu = 1.90110745351730037;
var u = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
var v = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
var bT = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
var bD = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
for (var i = 0; i < 7; ++i) {
var s = i + 1.0;
var t = 2.0 * s + 1.0;
u[i] = 1.0 / (s * t);
v[i] = s / t;
}
u[7] = opmu / (8.0 * 17.0);
v[7] = (opmu * 8.0) / 17.0;
/**
* Computes the spherical linear interpolation or extrapolation at t using the provided quaternions.
* This implementation is faster than {@link Quaternion#slerp}, but is only accurate up to 10<sup>-6</sup>.
*
* @param {Quaternion} start The value corresponding to t at 0.0.
* @param {Quaternion} end The value corresponding to t at 1.0.
* @param {Number} t The point along t at which to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter.
*
* @see Quaternion#slerp
*/
Quaternion.fastSlerp = function (start, end, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("start", start);
Check.typeOf.object("end", end);
Check.typeOf.number("t", t);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var x = Quaternion.dot(start, end);
var sign;
if (x >= 0) {
sign = 1.0;
} else {
sign = -1.0;
x = -x;
}
var xm1 = x - 1.0;
var d = 1.0 - t;
var sqrT = t * t;
var sqrD = d * d;
for (var i = 7; i >= 0; --i) {
bT[i] = (u[i] * sqrT - v[i]) * xm1;
bD[i] = (u[i] * sqrD - v[i]) * xm1;
}
var cT =
sign *
t *
(1.0 +
bT[0] *
(1.0 +
bT[1] *
(1.0 +
bT[2] *
(1.0 +
bT[3] *
(1.0 +
bT[4] *
(1.0 + bT[5] * (1.0 + bT[6] * (1.0 + bT[7]))))))));
var cD =
d *
(1.0 +
bD[0] *
(1.0 +
bD[1] *
(1.0 +
bD[2] *
(1.0 +
bD[3] *
(1.0 +
bD[4] *
(1.0 + bD[5] * (1.0 + bD[6] * (1.0 + bD[7]))))))));
var temp = Quaternion.multiplyByScalar(start, cD, fastSlerpScratchQuaternion);
Quaternion.multiplyByScalar(end, cT, result);
return Quaternion.add(temp, result, result);
};
/**
* Computes the spherical quadrangle interpolation between quaternions.
* An implementation that is faster than {@link Quaternion#squad}, but less accurate.
*
* @param {Quaternion} q0 The first quaternion.
* @param {Quaternion} q1 The second quaternion.
* @param {Quaternion} s0 The first inner quadrangle.
* @param {Quaternion} s1 The second inner quadrangle.
* @param {Number} t The time in [0,1] used to interpolate.
* @param {Quaternion} result The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new instance if none was provided.
*
* @see Quaternion#squad
*/
Quaternion.fastSquad = function (q0, q1, s0, s1, t, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("q0", q0);
Check.typeOf.object("q1", q1);
Check.typeOf.object("s0", s0);
Check.typeOf.object("s1", s1);
Check.typeOf.number("t", t);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
var slerp0 = Quaternion.fastSlerp(q0, q1, t, squadScratchQuaternion0);
var slerp1 = Quaternion.fastSlerp(s0, s1, t, squadScratchQuaternion1);
return Quaternion.fastSlerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
};
/**
* Compares the provided quaternions componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Quaternion} [left] The first quaternion.
* @param {Quaternion} [right] The second quaternion.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
Quaternion.equals = function (left, right) {
return (
left === right ||
(defined(left) &&
defined(right) &&
left.x === right.x &&
left.y === right.y &&
left.z === right.z &&
left.w === right.w)
);
};
/**
* Compares the provided quaternions componentwise and returns
* <code>true</code> if they are within the provided epsilon,
* <code>false</code> otherwise.
*
* @param {Quaternion} [left] The first quaternion.
* @param {Quaternion} [right] The second quaternion.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Quaternion.equalsEpsilon = function (left, right, epsilon) {
epsilon = defaultValue(epsilon, 0);
return (
left === right ||
(defined(left) &&
defined(right) &&
Math.abs(left.x - right.x) <= epsilon &&
Math.abs(left.y - right.y) <= epsilon &&
Math.abs(left.z - right.z) <= epsilon &&
Math.abs(left.w - right.w) <= epsilon)
);
};
/**
* An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 0.0).
*
* @type {Quaternion}
* @constant
*/
Quaternion.ZERO = Object.freeze(new Quaternion(0.0, 0.0, 0.0, 0.0));
/**
* An immutable Quaternion instance initialized to (0.0, 0.0, 0.0, 1.0).
*
* @type {Quaternion}
* @constant
*/
Quaternion.IDENTITY = Object.freeze(new Quaternion(0.0, 0.0, 0.0, 1.0));
/**
* Duplicates this Quaternion instance.
*
* @param {Quaternion} [result] The object onto which to store the result.
* @returns {Quaternion} The modified result parameter or a new Quaternion instance if one was not provided.
*/
Quaternion.prototype.clone = function (result) {
return Quaternion.clone(this, result);
};
/**
* Compares this and the provided quaternion componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {Quaternion} [right] The right hand side quaternion.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
Quaternion.prototype.equals = function (right) {
return Quaternion.equals(this, right);
};
/**
* Compares this and the provided quaternion componentwise and returns
* <code>true</code> if they are within the provided epsilon,
* <code>false</code> otherwise.
*
* @param {Quaternion} [right] The right hand side quaternion.
* @param {Number} [epsilon=0] The epsilon to use for equality testing.
* @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
*/
Quaternion.prototype.equalsEpsilon = function (right, epsilon) {
return Quaternion.equalsEpsilon(this, right, epsilon);
};
/**
* Returns a string representing this quaternion in the format (x, y, z, w).
*
* @returns {String} A string representing this Quaternion.
*/
Quaternion.prototype.toString = function () {
return "(" + this.x + ", " + this.y + ", " + this.z + ", " + this.w + ")";
};
export default Quaternion;
