HermiteSpline - Cesium Documentation

HermiteSpline

new HermiteSpline

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.

Parameters:

Name	Type	Description
`options.times`	Array	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.
`options.points`	Array	The array of Cartesian3 control points.
`options.inTangents`	Array	The array of Cartesian3 incoming tangents at each control point.
`options.outTangents`	Array	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 G¹ 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:

/Source/Core/HermiteSpline.js

Members

findTimeInterval :DeveloperError

Finds an index i in times such that the parameter time is in the interval [times[i], times[i + 1]].

<readonly> inTangents :Array

An array of Cartesian3 incoming tangents at each control point.

<readonly> outTangents :Array

An array of Cartesian3 outgoing tangents at each control point.

<readonly> points :Array

An array of Cartesian3 control points.

<readonly> times :Array

An array of times for the control points.

Methods

evaluate

Evaluates the curve at a given time.

Parameters:

Name	Type	Argument	Description
`time`	Number		The time at which to evaluate the curve.
`result`	Cartesian3	<optional>	The object onto which to store the result.

Throws:

DeveloperError : time must be in the range [t₀, t_n], where t₀ is the first element in the array times and t_n is the last element in the array times.

Returns:

Cartesian3 The modified result parameter or a new instance of the point on the curve at the given time.

<static> createC1

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.

Parameters:

Name	Type	Description
`options.times`	Array	The array of control point times.
`options.points`	Array	The array of control points.
`options.tangents`	Array	The array of tangents at the control points.

Throws:

DeveloperError : points, times and tangents are required.
DeveloperError : points.length must be greater than or equal to 2.
DeveloperError : times, points and tangents must have the same length.

Returns:

HermiteSpline A hermite spline.

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);
for (var i = 1; i < tangents.length - 1; ++i) {
    tangents[i] = Cesium.Cartesian3.multiplyByScalar(Cesium.Cartesian3.subtract(points[i + 1], points[i - 1]), 0.5);
}
tangents[tangents.length - 1] = new Cesium.Cartesian3(1165345, 112641, 47281);

var spline = new Cesium.HermiteSpline({
    times : times,
    points : points,
    tangents : tangents
});

<static> createClampedCubic

Creates a clamped cubic spline. The tangents at the interior control points are generated to create a curve in the class C².

Parameters:

Name	Type	Description
`options.times`	Array	The array of control point times.
`options.points`	Array	The array of control points.
`options.firstTangent`	Cartesian3	The outgoing tangent of the first control point.

Throws:

DeveloperError : points, times, firstTangent and lastTangent are required.
DeveloperError : points.length must be greater than or equal to 2.
DeveloperError : times.length must be equal to points.length.

Returns:

HermiteSpline | LinearSpline A hermite spline or a linear spline if less than 3 control points were given.

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)
});

<static> createNaturalCubic

Creates a natural cubic spline. The tangents at the control points are generated to create a curve in the class C².

Parameters:

Name	Type	Description
`options.times`	Array	The array of control point times.
`options.points`	Array	The array of control points.

Throws:

DeveloperError : points and times are required.
DeveloperError : points.length must be greater than or equal to 2.
DeveloperError : times.length must be equal to points.length.

Returns:

HermiteSpline | LinearSpline A hermite spline or a linear spline if less than 3 control points were given.

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)
    ]
});