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:
|
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.
-
DeveloperError : inTangents and outTangents must be of the same type as points.
Example:
// Create a G<sup>1</sup> continuous Hermite spline
const times = [ 0.0, 1.5, 3.0, 4.5, 6.0 ];
const 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)
]
});
const p0 = spline.evaluate(times[0]);
See:
Members
readonly inTangents : Array.<Cartesian3>
An array of incoming tangents at each control point.
readonly outTangents : Array.<Cartesian3>
An array of outgoing tangents at each control point.
readonly points : Array.<Cartesian3>
An array of control points.
An array of times for the control points.
Methods
static Cesium.HermiteSpline.createC1(options) → 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 |
object |
Object with the following properties:
|
Returns:
A hermite spline.
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.
Example:
const 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
const tangents = new Array(points.length);
tangents[0] = new Cesium.Cartesian3(1125196, -161816, 270551);
const temp = new Cesium.Cartesian3();
for (let 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);
const spline = Cesium.HermiteSpline.createC1({
times : times,
points : points,
tangents : tangents
});
static Cesium.HermiteSpline.createClampedCubic(options) → 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 |
object |
Object with the following properties:
|
Returns:
A hermite spline, or a linear spline if less than 3 control points were given.
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.
-
DeveloperError : firstTangent and lastTangent must be of the same type as points.
Example:
// Create a clamped cubic spline above the earth from Philadelphia to Los Angeles.
const 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)
});
static Cesium.HermiteSpline.createNaturalCubic(options) → 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 |
object |
Object with the following properties:
|
Returns:
A hermite spline, or a linear spline if less than 3 control points were given.
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.
Example:
// Create a natural cubic spline above the earth from Philadelphia to Los Angeles.
const 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)
]
});
Clamps the given time to the period covered by the spline.
Name | Type | Description |
---|---|---|
time |
number | The time. |
Returns:
The time, clamped to the animation period.
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]
, wheret0
is the first element in the arraytimes
andtn
is the last element in the arraytimes
.
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]
, wheret0
is the first element in the arraytimes
andtn
is the last element in the arraytimes
.
Wraps the given time to the period covered by the spline.
Name | Type | Description |
---|---|---|
time |
number | The time. |
Returns:
The time, wrapped around to the updated animation.