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4x 4x 4x 1x 1x 1x 1x 1x 1x 1x 7x 7x 7x 7x 1x 1x 1x 63x 62x 61x 60x 59x 59x 51x 8x 8x 59x 59x 59x 59x 59x 472x 472x 59x 59x 59x 59x 59x 1x 10x 9x 8x 7x 6x 5x 4x 4x 4x 1x 159x 1x 50x 50x 1x 1x 1x 66x 1x 110x 1x 33x 1x 985x | import Cartesian3 from "./Cartesian3.js";
import Check from "./Check.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 = x ?? 0.0;
/**
* The Y component.
* @type {number}
* @default 0.0
*/
this.y = y ?? 0.0;
/**
* The Z component.
* @type {number}
* @default 0.0
*/
this.z = z ?? 0.0;
/**
* The W component.
* @type {number}
* @default 0.0
*/
this.w = w ?? 0.0;
}
let 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');
const halfAngle = angle / 2.0;
const s = Math.sin(halfAngle);
fromAxisAngleScratch = Cartesian3.normalize(axis, fromAxisAngleScratch);
const x = fromAxisAngleScratch.x * s;
const y = fromAxisAngleScratch.y * s;
const z = fromAxisAngleScratch.z * s;
const 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;
};
const fromRotationMatrixNext = [1, 2, 0];
const 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');
let root;
let x;
let y;
let z;
let w;
const m00 = matrix[Matrix3.COLUMN0ROW0];
const m11 = matrix[Matrix3.COLUMN1ROW1];
const m22 = matrix[Matrix3.COLUMN2ROW2];
const 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
const next = fromRotationMatrixNext;
let i = 0;
if (m11 > m00) {
i = 1;
}
if (m22 > m00 && m22 > m11) {
i = 2;
}
const j = next[i];
const k = next[j];
root = Math.sqrt(
matrix[Matrix3.getElementIndex(i, i)] -
matrix[Matrix3.getElementIndex(j, j)] -
matrix[Matrix3.getElementIndex(k, k)] +
1.0,
);
const 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;
};
const scratchHPRQuaternion = new Quaternion();
let scratchHeadingQuaternion = new Quaternion();
let scratchPitchQuaternion = new Quaternion();
let 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);
};
const sampledQuaternionAxis = new Cartesian3();
const sampledQuaternionRotation = new Cartesian3();
const sampledQuaternionTempQuaternion = new Quaternion();
const sampledQuaternionQuaternion0 = new Quaternion();
const 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 = 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 = 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 (let i = 0, len = lastIndex - startingIndex + 1; i < len; i++) {
const offset = i * 3;
Quaternion.unpack(
packedArray,
(startingIndex + i) * 4,
sampledQuaternionTempQuaternion,
);
Quaternion.multiply(
sampledQuaternionTempQuaternion,
sampledQuaternionQuaternion0Conjugate,
sampledQuaternionTempQuaternion,
);
Iif (sampledQuaternionTempQuaternion.w < 0) {
Quaternion.negate(
sampledQuaternionTempQuaternion,
sampledQuaternionTempQuaternion,
);
}
Quaternion.computeAxis(
sampledQuaternionTempQuaternion,
sampledQuaternionAxis,
);
const angle = Quaternion.computeAngle(sampledQuaternionTempQuaternion);
Iif (!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,
) {
Eif (!defined(result)) {
result = new Quaternion();
}
Cartesian3.fromArray(array, 0, sampledQuaternionRotation);
const magnitude = Cartesian3.magnitude(sampledQuaternionRotation);
Quaternion.unpack(sourceArray, lastIndex * 4, sampledQuaternionQuaternion0);
if (magnitude === 0) {
Quaternion.clone(Quaternion.IDENTITY, sampledQuaternionTempQuaternion);
} else E{
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');
const inverseMagnitude = 1.0 / Quaternion.magnitude(quaternion);
const x = quaternion.x * inverseMagnitude;
const y = quaternion.y * inverseMagnitude;
const z = quaternion.z * inverseMagnitude;
const 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');
const 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');
const leftX = left.x;
const leftY = left.y;
const leftZ = left.z;
const leftW = left.w;
const rightX = right.x;
const rightY = right.y;
const rightZ = right.z;
const rightW = right.w;
const x = leftW * rightX + leftX * rightW + leftY * rightZ - leftZ * rightY;
const y = leftW * rightY - leftX * rightZ + leftY * rightW + leftZ * rightX;
const z = leftW * rightZ + leftX * rightY - leftY * rightX + leftZ * rightW;
const 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');
const w = quaternion.w;
if (
Math.abs(w - 1.0) < CesiumMath.EPSILON6 ||
Math.abs(w + 1.0) < CesiumMath.EPSILON6
) {
result.x = 1;
result.y = result.z = 0;
return result;
}
const 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);
};
let 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);
};
let slerpEndNegated = new Quaternion();
let slerpScaledP = new Quaternion();
let 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');
let 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.
let 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);
}
const 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');
const theta = CesiumMath.acosClamped(quaternion.w);
let thetaOverSinTheta = 0.0;
Eif (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');
const theta = Cartesian3.magnitude(cartesian);
let sinThetaOverTheta = 0.0;
Eif (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;
};
const squadScratchCartesian0 = new Cartesian3();
const squadScratchCartesian1 = new Cartesian3();
const squadScratchQuaternion0 = new Quaternion();
const 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');
const qInv = Quaternion.conjugate(q1, squadScratchQuaternion0);
Quaternion.multiply(qInv, q2, squadScratchQuaternion1);
const cart0 = Quaternion.log(squadScratchQuaternion1, squadScratchCartesian0);
Quaternion.multiply(qInv, q0, squadScratchQuaternion1);
const 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
* const s0 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i - 1], quaternions[i], quaternions[i + 1], new Cesium.Quaternion());
* const s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[i], quaternions[i + 1], quaternions[i + 2], new Cesium.Quaternion());
* const 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.
* const s1 = Cesium.Quaternion.computeInnerQuadrangle(quaternions[0], quaternions[1], quaternions[2], new Cesium.Quaternion());
* const 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');
const slerp0 = Quaternion.slerp(q0, q1, t, squadScratchQuaternion0);
const slerp1 = Quaternion.slerp(s0, s1, t, squadScratchQuaternion1);
return Quaternion.slerp(slerp0, slerp1, 2.0 * t * (1.0 - t), result);
};
const fastSlerpScratchQuaternion = new Quaternion();
// eslint-disable-next-line no-loss-of-precision
const opmu = 1.90110745351730037;
const u = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
const v = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
const bT = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
const bD = FeatureDetection.supportsTypedArrays() ? new Float32Array(8) : [];
for (let i = 0; i < 7; ++i) {
const s = i + 1.0;
const 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');
let x = Quaternion.dot(start, end);
let sign;
if (x >= 0) {
sign = 1.0;
} else {
sign = -1.0;
x = -x;
}
const xm1 = x - 1.0;
const d = 1.0 - t;
const sqrT = t * t;
const sqrD = d * d;
for (let i = 7; i >= 0; --i) {
bT[i] = (u[i] * sqrT - v[i]) * xm1;
bD[i] = (u[i] * sqrD - v[i]) * xm1;
}
const 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]))))))));
const 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]))))))));
const 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');
const slerp0 = Quaternion.fastSlerp(q0, q1, t, squadScratchQuaternion0);
const 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 = 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;
|