HermiteSpline

new HermiteSpline(options)

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 points[i] and points[i + 1], the tangents at the points will be outTangents[i] and inTangents[i], respectively.
Name Type Description
options Object Object with the following properties:
Name Type Description
times Array.<Number> 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.
points Array.<Cartesian3> The array of Cartesian3 control points.
inTangents Array.<Cartesian3> The array of Cartesian3 incoming tangents at each control point.
outTangents Array.<Cartesian3> The array of Cartesian3 outgoing tangents at each control point.
Throws:
  • DeveloperError : points.length must be greater than or equal to 2.
  • DeveloperError : times.length must be equal to points.length.
  • DeveloperError : inTangents and outTangents must have a length equal to points.length - 1.
Example:
// Create a G<sup>1</sup> continuous Hermite spline
var spline = new Cesium.HermiteSpline({
    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)
    ],
    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[i]);         // equal to positions[i]
var p1 = spline.evaluate(times[i] + delta); // interpolated value when delta < times[i + 1] - times[i]
See:
Source: Core/HermiteSpline.js, line 180

Members

readonlyinTangents :Array.<Cartesian3>

An array of Cartesian3 incoming tangents at each control point.
Source: Core/HermiteSpline.js, line 248

readonlyoutTangents :Array.<Cartesian3>

An array of Cartesian3 outgoing tangents at each control point.
Source: Core/HermiteSpline.js, line 262

readonlypoints :Array.<Cartesian3>

An array of Cartesian3 control points.
Source: Core/HermiteSpline.js, line 234

readonlytimes :Array.<Number>

An array of times for the control points.
Source: Core/HermiteSpline.js, line 220

Methods

staticHermiteSpline.createC1() → HermiteSpline

Creates a spline where the tangents at each control point are the same. The curves are guaranteed to be at least in the class C1.
Name Type Description
options.times Array.<Number> The array of control point times.
options.points Array.<Cartesian3> The array of control points.
options.tangents Array.<Cartesian3> The array of tangents at the control points.
Returns:
A hermite spline.
Throws:
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 = new Cesium.HermiteSpline({
    times : times,
    points : points,
    tangents : tangents
});
Source: Core/HermiteSpline.js, line 306

staticHermiteSpline.createClampedCubic() → HermiteSpline|LinearSpline

Creates a clamped cubic spline. The tangents at the interior control points are generated to create a curve in the class C2.
Name Type Description
options.times Array.<Number> The array of control point times.
options.points Array.<Cartesian3> The array of control points.
options.firstTangent Cartesian3 The outgoing tangent of the first control point.
options.lastTangent Cartesian3 The incoming tangent of the last control point.
Returns:
A hermite spline or a linear spline if less than 3 control points were given.
Throws:
Example:
// Create a clamped cubic spline above the earth from Philadelphia to Los Angeles.
var spline = new Cesium.HermiteSpline({
    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)
});
Source: Core/HermiteSpline.js, line 427

staticHermiteSpline.createNaturalCubic() → HermiteSpline|LinearSpline

Creates a natural cubic spline. The tangents at the control points are generated to create a curve in the class C2.
Name Type Description
options.times Array.<Number> The array of control point times.
options.points Array.<Cartesian3> The array of control points.
Returns:
A hermite spline or a linear spline if less than 3 control points were given.
Throws:
Example:
// Create a natural cubic spline above the earth from Philadelphia to Los Angeles.
var spline = new Cesium.HermiteSpline({
    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)
    ]
});
Source: Core/HermiteSpline.js, line 361

evaluate(time, result) → Cartesian3

Evaluates the curve at a given time.
Name Type Description
time Number The time at which to evaluate the curve.
result Cartesian3 optional The object onto which to store the result.
Returns:
The modified result parameter or a new instance of the point on the curve at the given time.
Throws:
  • DeveloperError : time must be in the range [t0, tn], where t0 is the first element in the array times and tn is the last element in the array times.
Source: Core/HermiteSpline.js, line 500

findTimeInterval(time) → Number

Finds an index i in times such that the parameter time is in the interval [times[i], times[i + 1]].
Name Type Description
time Number The time.
Returns:
The index for the element at the start of the interval.
Throws:
  • DeveloperError : time must be in the range [t0, tn], where t0 is the first element in the array times and tn is the last element in the array times.
Source: Core/HermiteSpline.js, line 484