import Cartesian3 from "./Cartesian3.js";
import Cartesian4 from "./Cartesian4.js";
import defaultValue from "./defaultValue.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import LinearSpline from "./LinearSpline.js";
import Matrix4 from "./Matrix4.js";
import Spline from "./Spline.js";
import TridiagonalSystemSolver from "./TridiagonalSystemSolver.js";
var scratchLower = [];
var scratchDiagonal = [];
var scratchUpper = [];
var scratchRight = [];
function generateClamped(points, firstTangent, lastTangent) {
var l = scratchLower;
var u = scratchUpper;
var d = scratchDiagonal;
var r = scratchRight;
l.length = u.length = points.length - 1;
d.length = r.length = points.length;
var i;
l[0] = d[0] = 1.0;
u[0] = 0.0;
var right = r[0];
if (!defined(right)) {
right = r[0] = new Cartesian3();
}
Cartesian3.clone(firstTangent, right);
for (i = 1; i < l.length - 1; ++i) {
l[i] = u[i] = 1.0;
d[i] = 4.0;
right = r[i];
if (!defined(right)) {
right = r[i] = new Cartesian3();
}
Cartesian3.subtract(points[i + 1], points[i - 1], right);
Cartesian3.multiplyByScalar(right, 3.0, right);
}
l[i] = 0.0;
u[i] = 1.0;
d[i] = 4.0;
right = r[i];
if (!defined(right)) {
right = r[i] = new Cartesian3();
}
Cartesian3.subtract(points[i + 1], points[i - 1], right);
Cartesian3.multiplyByScalar(right, 3.0, right);
d[i + 1] = 1.0;
right = r[i + 1];
if (!defined(right)) {
right = r[i + 1] = new Cartesian3();
}
Cartesian3.clone(lastTangent, right);
return TridiagonalSystemSolver.solve(l, d, u, r);
}
function generateNatural(points) {
var l = scratchLower;
var u = scratchUpper;
var d = scratchDiagonal;
var r = scratchRight;
l.length = u.length = points.length - 1;
d.length = r.length = points.length;
var i;
l[0] = u[0] = 1.0;
d[0] = 2.0;
var right = r[0];
if (!defined(right)) {
right = r[0] = new Cartesian3();
}
Cartesian3.subtract(points[1], points[0], right);
Cartesian3.multiplyByScalar(right, 3.0, right);
for (i = 1; i < l.length; ++i) {
l[i] = u[i] = 1.0;
d[i] = 4.0;
right = r[i];
if (!defined(right)) {
right = r[i] = new Cartesian3();
}
Cartesian3.subtract(points[i + 1], points[i - 1], right);
Cartesian3.multiplyByScalar(right, 3.0, right);
}
d[i] = 2.0;
right = r[i];
if (!defined(right)) {
right = r[i] = new Cartesian3();
}
Cartesian3.subtract(points[i], points[i - 1], right);
Cartesian3.multiplyByScalar(right, 3.0, right);
return TridiagonalSystemSolver.solve(l, d, u, r);
}
/**
* A Hermite spline is a cubic interpolating spline. Points, incoming tangents, outgoing tangents, and times
* must be defined for each control point. The outgoing tangents are defined for points [0, n - 2] and the incoming
* tangents are defined for points [1, n - 1]. For example, when interpolating a segment of the curve between <code>points[i]</code> and
* <code>points[i + 1]</code>, the tangents at the points will be <code>outTangents[i]</code> and <code>inTangents[i]</code>,
* respectively.
*
* @alias HermiteSpline
* @constructor
*
* @param {Object} options Object with the following properties:
* @param {Number[]} options.times An array of strictly increasing, unit-less, floating-point times at each point.
* The values are in no way connected to the clock time. They are the parameterization for the curve.
* @param {Cartesian3[]} options.points The array of {@link Cartesian3} control points.
* @param {Cartesian3[]} options.inTangents The array of {@link Cartesian3} incoming tangents at each control point.
* @param {Cartesian3[]} options.outTangents The array of {@link Cartesian3} outgoing tangents at each control point.
*
* @exception {DeveloperError} points.length must be greater than or equal to 2.
* @exception {DeveloperError} times.length must be equal to points.length.
* @exception {DeveloperError} inTangents and outTangents must have a length equal to points.length - 1.
*
*
* @example
* // Create a G<sup>1</sup> continuous Hermite spline
* var times = [ 0.0, 1.5, 3.0, 4.5, 6.0 ];
* var spline = new Cesium.HermiteSpline({
* times : times,
* points : [
* new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
* new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
* new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
* new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
* new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
* ],
* outTangents : [
* new Cesium.Cartesian3(1125196, -161816, 270551),
* new Cesium.Cartesian3(-996690.5, -365906.5, 184028.5),
* new Cesium.Cartesian3(-2096917, 48379.5, -292683.5),
* new Cesium.Cartesian3(-890902.5, 408999.5, -447115)
* ],
* inTangents : [
* new Cesium.Cartesian3(-1993381, -731813, 368057),
* new Cesium.Cartesian3(-4193834, 96759, -585367),
* new Cesium.Cartesian3(-1781805, 817999, -894230),
* new Cesium.Cartesian3(1165345, 112641, 47281)
* ]
* });
*
* var p0 = spline.evaluate(times[0]);
*
* @see CatmullRomSpline
* @see LinearSpline
* @see QuaternionSpline
* @see WeightSpline
*/
function HermiteSpline(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var points = options.points;
var times = options.times;
var inTangents = options.inTangents;
var outTangents = options.outTangents;
//>>includeStart('debug', pragmas.debug);
if (
!defined(points) ||
!defined(times) ||
!defined(inTangents) ||
!defined(outTangents)
) {
throw new DeveloperError(
"times, points, inTangents, and outTangents are required."
);
}
if (points.length < 2) {
throw new DeveloperError(
"points.length must be greater than or equal to 2."
);
}
if (times.length !== points.length) {
throw new DeveloperError("times.length must be equal to points.length.");
}
if (
inTangents.length !== outTangents.length ||
inTangents.length !== points.length - 1
) {
throw new DeveloperError(
"inTangents and outTangents must have a length equal to points.length - 1."
);
}
//>>includeEnd('debug');
this._times = times;
this._points = points;
this._inTangents = inTangents;
this._outTangents = outTangents;
this._lastTimeIndex = 0;
}
Object.defineProperties(HermiteSpline.prototype, {
/**
* An array of times for the control points.
*
* @memberof HermiteSpline.prototype
*
* @type {Number[]}
* @readonly
*/
times: {
get: function () {
return this._times;
},
},
/**
* An array of {@link Cartesian3} control points.
*
* @memberof HermiteSpline.prototype
*
* @type {Cartesian3[]}
* @readonly
*/
points: {
get: function () {
return this._points;
},
},
/**
* An array of {@link Cartesian3} incoming tangents at each control point.
*
* @memberof HermiteSpline.prototype
*
* @type {Cartesian3[]}
* @readonly
*/
inTangents: {
get: function () {
return this._inTangents;
},
},
/**
* An array of {@link Cartesian3} outgoing tangents at each control point.
*
* @memberof HermiteSpline.prototype
*
* @type {Cartesian3[]}
* @readonly
*/
outTangents: {
get: function () {
return this._outTangents;
},
},
});
/**
* Creates a spline where the tangents at each control point are the same.
* The curves are guaranteed to be at least in the class C<sup>1</sup>.
*
* @param {Object} options Object with the following properties:
* @param {Number[]} options.times The array of control point times.
* @param {Cartesian3[]} options.points The array of control points.
* @param {Cartesian3[]} options.tangents The array of tangents at the control points.
* @returns {HermiteSpline} A hermite spline.
*
* @exception {DeveloperError} points, times and tangents are required.
* @exception {DeveloperError} points.length must be greater than or equal to 2.
* @exception {DeveloperError} times, points and tangents must have the same length.
*
* @example
* var points = [
* new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
* new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
* new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
* new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
* new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
* ];
*
* // Add tangents
* var tangents = new Array(points.length);
* tangents[0] = new Cesium.Cartesian3(1125196, -161816, 270551);
* var temp = new Cesium.Cartesian3();
* for (var i = 1; i < tangents.length - 1; ++i) {
* tangents[i] = Cesium.Cartesian3.multiplyByScalar(Cesium.Cartesian3.subtract(points[i + 1], points[i - 1], temp), 0.5, new Cesium.Cartesian3());
* }
* tangents[tangents.length - 1] = new Cesium.Cartesian3(1165345, 112641, 47281);
*
* var spline = Cesium.HermiteSpline.createC1({
* times : times,
* points : points,
* tangents : tangents
* });
*/
HermiteSpline.createC1 = function (options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var times = options.times;
var points = options.points;
var tangents = options.tangents;
//>>includeStart('debug', pragmas.debug);
if (!defined(points) || !defined(times) || !defined(tangents)) {
throw new DeveloperError("points, times and tangents are required.");
}
if (points.length < 2) {
throw new DeveloperError(
"points.length must be greater than or equal to 2."
);
}
if (times.length !== points.length || times.length !== tangents.length) {
throw new DeveloperError(
"times, points and tangents must have the same length."
);
}
//>>includeEnd('debug');
var outTangents = tangents.slice(0, tangents.length - 1);
var inTangents = tangents.slice(1, tangents.length);
return new HermiteSpline({
times: times,
points: points,
inTangents: inTangents,
outTangents: outTangents,
});
};
/**
* Creates a natural cubic spline. The tangents at the control points are generated
* to create a curve in the class C<sup>2</sup>.
*
* @param {Object} options Object with the following properties:
* @param {Number[]} options.times The array of control point times.
* @param {Cartesian3[]} options.points The array of control points.
* @returns {HermiteSpline|LinearSpline} A hermite spline or a linear spline if less than 3 control points were given.
*
* @exception {DeveloperError} points and times are required.
* @exception {DeveloperError} points.length must be greater than or equal to 2.
* @exception {DeveloperError} times.length must be equal to points.length.
*
* @example
* // Create a natural cubic spline above the earth from Philadelphia to Los Angeles.
* var spline = Cesium.HermiteSpline.createNaturalCubic({
* times : [ 0.0, 1.5, 3.0, 4.5, 6.0 ],
* points : [
* new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
* new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
* new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
* new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
* new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
* ]
* });
*/
HermiteSpline.createNaturalCubic = function (options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var times = options.times;
var points = options.points;
//>>includeStart('debug', pragmas.debug);
if (!defined(points) || !defined(times)) {
throw new DeveloperError("points and times are required.");
}
if (points.length < 2) {
throw new DeveloperError(
"points.length must be greater than or equal to 2."
);
}
if (times.length !== points.length) {
throw new DeveloperError("times.length must be equal to points.length.");
}
//>>includeEnd('debug');
if (points.length < 3) {
return new LinearSpline({
points: points,
times: times,
});
}
var tangents = generateNatural(points);
var outTangents = tangents.slice(0, tangents.length - 1);
var inTangents = tangents.slice(1, tangents.length);
return new HermiteSpline({
times: times,
points: points,
inTangents: inTangents,
outTangents: outTangents,
});
};
/**
* Creates a clamped cubic spline. The tangents at the interior control points are generated
* to create a curve in the class C<sup>2</sup>.
*
* @param {Object} options Object with the following properties:
* @param {Number[]} options.times The array of control point times.
* @param {Cartesian3[]} options.points The array of control points.
* @param {Cartesian3} options.firstTangent The outgoing tangent of the first control point.
* @param {Cartesian3} options.lastTangent The incoming tangent of the last control point.
* @returns {HermiteSpline|LinearSpline} A hermite spline or a linear spline if less than 3 control points were given.
*
* @exception {DeveloperError} points, times, firstTangent and lastTangent are required.
* @exception {DeveloperError} points.length must be greater than or equal to 2.
* @exception {DeveloperError} times.length must be equal to points.length.
*
* @example
* // Create a clamped cubic spline above the earth from Philadelphia to Los Angeles.
* var spline = Cesium.HermiteSpline.createClampedCubic({
* times : [ 0.0, 1.5, 3.0, 4.5, 6.0 ],
* points : [
* new Cesium.Cartesian3(1235398.0, -4810983.0, 4146266.0),
* new Cesium.Cartesian3(1372574.0, -5345182.0, 4606657.0),
* new Cesium.Cartesian3(-757983.0, -5542796.0, 4514323.0),
* new Cesium.Cartesian3(-2821260.0, -5248423.0, 4021290.0),
* new Cesium.Cartesian3(-2539788.0, -4724797.0, 3620093.0)
* ],
* firstTangent : new Cesium.Cartesian3(1125196, -161816, 270551),
* lastTangent : new Cesium.Cartesian3(1165345, 112641, 47281)
* });
*/
HermiteSpline.createClampedCubic = function (options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var times = options.times;
var points = options.points;
var firstTangent = options.firstTangent;
var lastTangent = options.lastTangent;
//>>includeStart('debug', pragmas.debug);
if (
!defined(points) ||
!defined(times) ||
!defined(firstTangent) ||
!defined(lastTangent)
) {
throw new DeveloperError(
"points, times, firstTangent and lastTangent are required."
);
}
if (points.length < 2) {
throw new DeveloperError(
"points.length must be greater than or equal to 2."
);
}
if (times.length !== points.length) {
throw new DeveloperError("times.length must be equal to points.length.");
}
//>>includeEnd('debug');
if (points.length < 3) {
return new LinearSpline({
points: points,
times: times,
});
}
var tangents = generateClamped(points, firstTangent, lastTangent);
var outTangents = tangents.slice(0, tangents.length - 1);
var inTangents = tangents.slice(1, tangents.length);
return new HermiteSpline({
times: times,
points: points,
inTangents: inTangents,
outTangents: outTangents,
});
};
HermiteSpline.hermiteCoefficientMatrix = new Matrix4(
2.0,
-3.0,
0.0,
1.0,
-2.0,
3.0,
0.0,
0.0,
1.0,
-2.0,
1.0,
0.0,
1.0,
-1.0,
0.0,
0.0
);
/**
* Finds an index <code>i</code> in <code>times</code> such that the parameter
* <code>time</code> is in the interval <code>[times[i], times[i + 1]]</code>.
* @function
*
* @param {Number} time The time.
* @returns {Number} The index for the element at the start of the interval.
*
* @exception {DeveloperError} time must be in the range <code>[t<sub>0</sub>, t<sub>n</sub>]</code>, where <code>t<sub>0</sub></code>
* is the first element in the array <code>times</code> and <code>t<sub>n</sub></code> is the last element
* in the array <code>times</code>.
*/
HermiteSpline.prototype.findTimeInterval = Spline.prototype.findTimeInterval;
var scratchTimeVec = new Cartesian4();
var scratchTemp = new Cartesian3();
/**
* Wraps the given time to the period covered by the spline.
* @function
*
* @param {Number} time The time.
* @return {Number} The time, wrapped around to the updated animation.
*/
HermiteSpline.prototype.wrapTime = Spline.prototype.wrapTime;
/**
* Clamps the given time to the period covered by the spline.
* @function
*
* @param {Number} time The time.
* @return {Number} The time, clamped to the animation period.
*/
HermiteSpline.prototype.clampTime = Spline.prototype.clampTime;
/**
* Evaluates the curve at a given time.
*
* @param {Number} time The time at which to evaluate the curve.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new instance of the point on the curve at the given time.
*
* @exception {DeveloperError} time must be in the range <code>[t<sub>0</sub>, t<sub>n</sub>]</code>, where <code>t<sub>0</sub></code>
* is the first element in the array <code>times</code> and <code>t<sub>n</sub></code> is the last element
* in the array <code>times</code>.
*/
HermiteSpline.prototype.evaluate = function (time, result) {
if (!defined(result)) {
result = new Cartesian3();
}
var points = this.points;
var times = this.times;
var inTangents = this.inTangents;
var outTangents = this.outTangents;
var i = (this._lastTimeIndex = this.findTimeInterval(
time,
this._lastTimeIndex
));
var u = (time - times[i]) / (times[i + 1] - times[i]);
var timeVec = scratchTimeVec;
timeVec.z = u;
timeVec.y = u * u;
timeVec.x = timeVec.y * u;
timeVec.w = 1.0;
var coefs = Matrix4.multiplyByVector(
HermiteSpline.hermiteCoefficientMatrix,
timeVec,
timeVec
);
result = Cartesian3.multiplyByScalar(points[i], coefs.x, result);
Cartesian3.multiplyByScalar(points[i + 1], coefs.y, scratchTemp);
Cartesian3.add(result, scratchTemp, result);
Cartesian3.multiplyByScalar(outTangents[i], coefs.z, scratchTemp);
Cartesian3.add(result, scratchTemp, result);
Cartesian3.multiplyByScalar(inTangents[i], coefs.w, scratchTemp);
return Cartesian3.add(result, scratchTemp, result);
};
export default HermiteSpline;
