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CatmullRomSpline.js
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CatmullRomSpline.js
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/*global define*/
define([
'./Cartesian3',
'./Cartesian4',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./HermiteSpline',
'./Matrix4',
'./Spline'
], function(
Cartesian3,
Cartesian4,
defaultValue,
defined,
defineProperties,
DeveloperError,
HermiteSpline,
Matrix4,
Spline) {
"use strict";
var scratchTimeVec = new Cartesian4();
var scratchTemp0 = new Cartesian3();
var scratchTemp1 = new Cartesian3();
function createEvaluateFunction(spline) {
var points = spline.points;
var times = spline.times;
if (points.length < 3) {
var t0 = times[0];
var invSpan = 1.0 / (times[1] - t0);
var p0 = points[0];
var p1 = points[1];
return function(time, result) {
if (!defined(result)){
result = new Cartesian3();
}
var u = (time - t0) * invSpan;
return Cartesian3.lerp(p0, p1, u, result);
};
}
return function(time, result) {
if (!defined(result)) {
result = new Cartesian3();
}
var i = spline._lastTimeIndex = spline.findTimeInterval(time, spline._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 p0;
var p1;
var p2;
var p3;
var coefs;
if (i === 0) {
p0 = points[0];
p1 = points[1];
p2 = spline.firstTangent;
p3 = Cartesian3.subtract(points[2], p0, scratchTemp0);
Cartesian3.multiplyByScalar(p3, 0.5, p3);
coefs = Matrix4.multiplyByVector(HermiteSpline.hermiteCoefficientMatrix, timeVec, timeVec);
} else if (i === points.length - 2) {
p0 = points[i];
p1 = points[i + 1];
p3 = spline.lastTangent;
p2 = Cartesian3.subtract(p1, points[i - 1], scratchTemp0);
Cartesian3.multiplyByScalar(p2, 0.5, p2);
coefs = Matrix4.multiplyByVector(HermiteSpline.hermiteCoefficientMatrix, timeVec, timeVec);
} else {
p0 = points[i - 1];
p1 = points[i];
p2 = points[i + 1];
p3 = points[i + 2];
coefs = Matrix4.multiplyByVector(CatmullRomSpline.catmullRomCoefficientMatrix, timeVec, timeVec);
}
result = Cartesian3.multiplyByScalar(p0, coefs.x, result);
Cartesian3.multiplyByScalar(p1, coefs.y, scratchTemp1);
Cartesian3.add(result, scratchTemp1, result);
Cartesian3.multiplyByScalar(p2, coefs.z, scratchTemp1);
Cartesian3.add(result, scratchTemp1, result);
Cartesian3.multiplyByScalar(p3, coefs.w, scratchTemp1);
return Cartesian3.add(result, scratchTemp1, result);
};
}
var firstTangentScratch = new Cartesian3();
var lastTangentScratch = new Cartesian3();
/**
* A Catmull-Rom spline is a cubic spline where the tangent at control points,
* except the first and last, are computed using the previous and next control points.
* Catmull-Rom splines are in the class C<sup>1</sup>.
*
* @alias CatmullRomSpline
* @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.firstTangent] The tangent of the curve at the first control point.
* If the tangent is not given, it will be estimated.
* @param {Cartesian3} [options.lastTangent] The tangent of the curve at the last control point.
* If the tangent is not given, it will be estimated.
*
* @exception {DeveloperError} points.length must be greater than or equal to 2.
* @exception {DeveloperError} times.length must be equal to points.length.
*
*
* @example
* // spline above the earth from Philadelphia to Los Angeles
* var spline = new Cesium.CatmullRomSpline({
* 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)
* ]
* });
*
* 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 HermiteSpline
* @see LinearSpline
* @see QuaternionSpline
*/
function CatmullRomSpline(options) {
options = defaultValue(options, defaultValue.EMPTY_OBJECT);
var points = options.points;
var times = options.times;
var firstTangent = options.firstTangent;
var lastTangent = options.lastTangent;
//>>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 > 2) {
if (!defined(firstTangent)) {
firstTangent = firstTangentScratch;
Cartesian3.multiplyByScalar(points[1], 2.0, firstTangent);
Cartesian3.subtract(firstTangent, points[2], firstTangent);
Cartesian3.subtract(firstTangent, points[0], firstTangent);
Cartesian3.multiplyByScalar(firstTangent, 0.5, firstTangent);
}
if (!defined(lastTangent)) {
var n = points.length - 1;
lastTangent = lastTangentScratch;
Cartesian3.multiplyByScalar(points[n - 1], 2.0, lastTangent);
Cartesian3.subtract(points[n], lastTangent, lastTangent);
Cartesian3.add(lastTangent, points[n - 2], lastTangent);
Cartesian3.multiplyByScalar(lastTangent, 0.5, lastTangent);
}
}
this._times = times;
this._points = points;
this._firstTangent = Cartesian3.clone(firstTangent);
this._lastTangent = Cartesian3.clone(lastTangent);
this._evaluateFunction = createEvaluateFunction(this);
this._lastTimeIndex = 0;
}
defineProperties(CatmullRomSpline.prototype, {
/**
* An array of times for the control points.
*
* @memberof CatmullRomSpline.prototype
*
* @type {Number[]}
* @readonly
*/
times : {
get : function() {
return this._times;
}
},
/**
* An array of {@link Cartesian3} control points.
*
* @memberof CatmullRomSpline.prototype
*
* @type {Cartesian3[]}
* @readonly
*/
points : {
get : function() {
return this._points;
}
},
/**
* The tangent at the first control point.
*
* @memberof CatmullRomSpline.prototype
*
* @type {Cartesian3}
* @readonly
*/
firstTangent : {
get : function() {
return this._firstTangent;
}
},
/**
* The tangent at the last control point.
*
* @memberof CatmullRomSpline.prototype
*
* @type {Cartesian3}
* @readonly
*/
lastTangent : {
get : function() {
return this._lastTangent;
}
}
});
/**
* @private
*/
CatmullRomSpline.catmullRomCoefficientMatrix = new Matrix4(
-0.5, 1.0, -0.5, 0.0,
1.5, -2.5, 0.0, 1.0,
-1.5, 2.0, 0.5, 0.0,
0.5, -0.5, 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>.
*/
CatmullRomSpline.prototype.findTimeInterval = Spline.prototype.findTimeInterval;
/**
* 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>.
*/
CatmullRomSpline.prototype.evaluate = function(time, result) {
return this._evaluateFunction(time, result);
};
return CatmullRomSpline;
});