import { Cartesian3 } from "../../Source/Cesium.js";
|
import { HermiteSpline } from "../../Source/Cesium.js";
|
import { Math as CesiumMath } from "../../Source/Cesium.js";
|
|
describe("Core/HermiteSpline", function () {
|
var points;
|
var times;
|
|
beforeEach(function () {
|
points = [
|
new Cartesian3(-1.0, -1.0, 0.0),
|
new Cartesian3(-0.5, -0.125, 0.0),
|
new Cartesian3(0.5, 0.125, 0.0),
|
new Cartesian3(1.0, 1.0, 0.0),
|
];
|
times = [0.0, 1.0, 2.0, 3.0];
|
});
|
|
it("constructor throws without points, times or tangents", function () {
|
expect(function () {
|
return new HermiteSpline();
|
}).toThrowDeveloperError();
|
});
|
|
it("constructor throws when control points length is less than 2", function () {
|
expect(function () {
|
return new HermiteSpline({
|
points: [Cartesian3.ZERO],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("constructor throws when times.length is not equal to points.length", function () {
|
expect(function () {
|
return new HermiteSpline({
|
points: points,
|
times: [0.0, 1.0],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("constructor throws when inTangents or outTangents length is not equal to points.length - 1", function () {
|
expect(function () {
|
return new HermiteSpline({
|
points: points,
|
times: times,
|
inTangents: [Cartesian3.ZERO],
|
outTangents: [Cartesian3.UNIT_X],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
// returns a function for a hermite curve between points p and q
|
// with tangents pT and qT respectively on the interval [0, 1]
|
function createHermiteBasis(p, pT, q, qT) {
|
return function (u) {
|
var a = 2.0 * u * u * u - 3.0 * u * u + 1.0;
|
var b = -2.0 * u * u * u + 3.0 * u * u;
|
var c = u * u * u - 2.0 * u * u + u;
|
var d = u * u * u - u * u;
|
|
var p0 = Cartesian3.multiplyByScalar(p, a, new Cartesian3());
|
var p1 = Cartesian3.multiplyByScalar(q, b, new Cartesian3());
|
var p2 = Cartesian3.multiplyByScalar(pT, c, new Cartesian3());
|
var p3 = Cartesian3.multiplyByScalar(qT, d, new Cartesian3());
|
|
return Cartesian3.add(
|
Cartesian3.add(Cartesian3.add(p0, p1, p0), p2, p0),
|
p3,
|
p0
|
);
|
};
|
}
|
|
it("create spline", function () {
|
var hs = new HermiteSpline({
|
times: [0.0, 1.0, 3.0, 4.5, 6.0],
|
points: [
|
new Cartesian3(1235398.0, -4810983.0, 4146266.0),
|
new Cartesian3(1372574.0, -5345182.0, 4606657.0),
|
new Cartesian3(-757983.0, -5542796.0, 4514323.0),
|
new Cartesian3(-2821260.0, -5248423.0, 4021290.0),
|
new Cartesian3(-2539788.0, -4724797.0, 3620093.0),
|
],
|
outTangents: [
|
new Cartesian3(1125196, -161816, 270551),
|
new Cartesian3(-996690.5, -365906.5, 184028.5),
|
new Cartesian3(-2096917, 48379.5, -292683.5),
|
new Cartesian3(-890902.5, 408999.5, -447115),
|
],
|
inTangents: [
|
new Cartesian3(-1993381, -731813, 368057),
|
new Cartesian3(-4193834, 96759, -585367),
|
new Cartesian3(-1781805, 817999, -894230),
|
new Cartesian3(1165345, 112641, 47281),
|
],
|
});
|
|
var p0 = hs.points[0];
|
var p1 = hs.points[1];
|
var pT0 = hs.outTangents[0];
|
var pT1 = hs.inTangents[0];
|
var interpolate = createHermiteBasis(p0, pT0, p1, pT1);
|
|
var granularity = 0.1;
|
for (var i = 0.0; i < 1.0; i = i + granularity) {
|
expect(hs.evaluate(i)).toEqualEpsilon(
|
interpolate(i),
|
CesiumMath.EPSILON3
|
);
|
}
|
});
|
|
it("createC1 throws without points", function () {
|
expect(function () {
|
return HermiteSpline.createC1();
|
}).toThrowDeveloperError();
|
});
|
|
it("createC1 throws when control points length is less than 2", function () {
|
expect(function () {
|
return HermiteSpline.createC1({
|
points: [Cartesian3.ZERO],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createC1 throws without times", function () {
|
expect(function () {
|
return HermiteSpline.createC1({
|
points: points,
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createC1 throws when times.length is not equal to points.length", function () {
|
expect(function () {
|
return HermiteSpline.createC1({
|
points: points,
|
times: [0.0, 1.0],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createC1 throws without tangents", function () {
|
expect(function () {
|
return HermiteSpline.createC1({
|
points: points,
|
times: times,
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createC1 throws when tangents.length is not equal to times.length", function () {
|
expect(function () {
|
return HermiteSpline.createC1({
|
points: points,
|
times: times,
|
tangents: [Cartesian3.ZERO],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("C1 spline", function () {
|
var times = [0.0, 1.0, 3.0, 4.5, 6.0];
|
var points = [
|
new Cartesian3(1235398.0, -4810983.0, 4146266.0),
|
new Cartesian3(1372574.0, -5345182.0, 4606657.0),
|
new Cartesian3(-757983.0, -5542796.0, 4514323.0),
|
new Cartesian3(-2821260.0, -5248423.0, 4021290.0),
|
new Cartesian3(-2539788.0, -4724797.0, 3620093.0),
|
];
|
|
var tangents = new Array(points.length);
|
tangents[0] = new Cartesian3(1125196, -161816, 270551);
|
for (var i = 1; i < tangents.length - 1; ++i) {
|
tangents[i] = Cartesian3.multiplyByScalar(
|
Cartesian3.subtract(points[i + 1], points[i - 1], new Cartesian3()),
|
0.5,
|
new Cartesian3()
|
);
|
}
|
tangents[tangents.length - 1] = new Cartesian3(1165345, 112641, 47281);
|
|
var interpolate = createHermiteBasis(
|
points[0],
|
tangents[0],
|
points[1],
|
tangents[1]
|
);
|
var hs = HermiteSpline.createC1({
|
times: times,
|
points: points,
|
tangents: tangents,
|
});
|
|
var granularity = 0.1;
|
for (var j = times[0]; j < times[1]; j = j + granularity) {
|
expect(hs.evaluate(j)).toEqualEpsilon(
|
interpolate(j),
|
CesiumMath.EPSILON3
|
);
|
}
|
});
|
|
it("createNaturalCubic throws without points", function () {
|
expect(function () {
|
return HermiteSpline.createNaturalCubic();
|
}).toThrowDeveloperError();
|
});
|
|
it("createNaturalCubic throws when control points length is less than 2", function () {
|
expect(function () {
|
return HermiteSpline.createNaturalCubic({
|
points: [Cartesian3.ZERO],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createNaturalCubic throws without times", function () {
|
expect(function () {
|
return HermiteSpline.createNaturalCubic({
|
points: points,
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createNaturalCubic throws when times.length is not equal to points.length", function () {
|
expect(function () {
|
return HermiteSpline.createNaturalCubic({
|
points: points,
|
times: [0.0, 1.0],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("natural cubic spline", function () {
|
points = [
|
new Cartesian3(1.0, 0.0, 0.0),
|
new Cartesian3(0.0, 1.0, CesiumMath.PI_OVER_TWO),
|
new Cartesian3(-1.0, 0.0, Math.PI),
|
new Cartesian3(0.0, -1.0, CesiumMath.THREE_PI_OVER_TWO),
|
];
|
|
var p0Tangent = new Cartesian3(-0.87, 1.53, 1.57);
|
var p1Tangent = new Cartesian3(-1.27, -0.07, 1.57);
|
|
var interpolate = createHermiteBasis(
|
points[0],
|
p0Tangent,
|
points[1],
|
p1Tangent
|
);
|
var hs = HermiteSpline.createNaturalCubic({
|
points: points,
|
times: times,
|
});
|
|
var granularity = 0.1;
|
for (var i = times[0]; i < times[1]; i = i + granularity) {
|
expect(hs.evaluate(i)).toEqualEpsilon(
|
interpolate(i),
|
CesiumMath.EPSILON3
|
);
|
}
|
});
|
|
it("createClampedCubic throws without points", function () {
|
expect(function () {
|
return HermiteSpline.createClampedCubic();
|
}).toThrowDeveloperError();
|
});
|
|
it("createClampedCubic throws when control points length is less than 2", function () {
|
expect(function () {
|
return HermiteSpline.createClampedCubic({
|
points: [Cartesian3.ZERO],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createClampedCubic throws without times", function () {
|
expect(function () {
|
return HermiteSpline.createClampedCubic({
|
points: points,
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createClampedCubic throws when times.length is not equal to points.length", function () {
|
expect(function () {
|
return HermiteSpline.createClampedCubic({
|
points: points,
|
times: [0.0, 1.0],
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createClampedCubic throws without firstTangent", function () {
|
expect(function () {
|
return HermiteSpline.createClampedCubic({
|
points: points,
|
times: times,
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("createClampedCubic throws without lastTangent", function () {
|
expect(function () {
|
return HermiteSpline.createClampedCubic({
|
points: points,
|
times: times,
|
firstTangent: Cartesian3.ZERO,
|
});
|
}).toThrowDeveloperError();
|
});
|
|
it("clamped cubic spline", function () {
|
points = [
|
new Cartesian3(1.0, 0.0, 0.0),
|
new Cartesian3(0.0, 1.0, CesiumMath.PI_OVER_TWO),
|
new Cartesian3(-1.0, 0.0, Math.PI),
|
new Cartesian3(0.0, -1.0, CesiumMath.THREE_PI_OVER_TWO),
|
];
|
|
var firstTangent = new Cartesian3(0.0, 1.0, 0.0);
|
var lastTangent = new Cartesian3(1.0, 0.0, 0.0);
|
|
var p0Tangent = firstTangent;
|
var p1Tangent = new Cartesian3(-1.53, 0.13, 1.88);
|
|
var interpolate = createHermiteBasis(
|
points[0],
|
p0Tangent,
|
points[1],
|
p1Tangent
|
);
|
var hs = HermiteSpline.createClampedCubic({
|
points: points,
|
times: times,
|
firstTangent: firstTangent,
|
lastTangent: lastTangent,
|
});
|
|
var granularity = 0.1;
|
for (var i = points[0].time; i < points[1].time; i = i + granularity) {
|
expect(hs.evaluate(i)).toEqualEpsilon(
|
interpolate(i),
|
CesiumMath.EPSILON3
|
);
|
}
|
});
|
|
it("evaluate fails with undefined time", function () {
|
var hs = HermiteSpline.createNaturalCubic({
|
points: points,
|
times: times,
|
});
|
expect(function () {
|
hs.evaluate();
|
}).toThrowDeveloperError();
|
});
|
|
it("evaluate fails with time out of range", function () {
|
var hs = HermiteSpline.createNaturalCubic({
|
points: points,
|
times: times,
|
});
|
expect(function () {
|
hs.evaluate(times[0] - 1.0);
|
}).toThrowDeveloperError();
|
});
|
|
it("evaluate with result parameter", function () {
|
var hs = HermiteSpline.createNaturalCubic({
|
points: points,
|
times: times,
|
});
|
var result = new Cartesian3();
|
var point = hs.evaluate(times[0], result);
|
expect(point).toBe(result);
|
expect(result).toEqual(points[0]);
|
});
|
|
it("createNaturalCubic with 2 control points defaults to lerp", function () {
|
points = points.slice(0, 2);
|
times = times.slice(0, 2);
|
|
var hs = HermiteSpline.createNaturalCubic({
|
points: points,
|
times: times,
|
});
|
|
var t = (times[0] + times[1]) * 0.5;
|
expect(hs.evaluate(t)).toEqual(
|
Cartesian3.lerp(points[0], points[1], t, new Cartesian3())
|
);
|
});
|
|
it("createClampedCubic with 2 control points defaults to lerp", function () {
|
points = points.slice(0, 2);
|
times = times.slice(0, 2);
|
|
var hs = HermiteSpline.createNaturalCubic({
|
points: points,
|
times: times,
|
});
|
|
var t = (times[0] + times[1]) * 0.5;
|
expect(hs.evaluate(t)).toEqual(
|
Cartesian3.lerp(points[0], points[1], t, new Cartesian3())
|
);
|
});
|
});
|
