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Merge pull request #1873 from twpayne/sphere-interpolate

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Add ol.Sphere#interpolate
This commit is contained in:
Tom Payne
2014-03-19 00:13:46 +01:00
parent f50451698a 0b5f0d0c8e
commit 1fc1cd0b2f
2 changed files with 56 additions and 210 deletions
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36
src/ol/sphere/sphere.js
View File

@@ -139,6 +139,42 @@ ol.Sphere.prototype.haversineDistance = function(c1, c2) {
};
/**
* Returns the point at `fraction` along the segment of the great circle passing
* through c1 and c2.
*
* @param {ol.Coordinate} c1 Coordinate 1.
* @param {ol.Coordinate} c2 Coordinate 2.
* @param {number} fraction Fraction.
* @return {ol.Coordinate} Coordinate between c1 and c2.
*/
ol.Sphere.prototype.interpolate = function(c1, c2, fraction) {
var lat1 = goog.math.toRadians(c1[1]);
var lon1 = goog.math.toRadians(c1[0]);
var lat2 = goog.math.toRadians(c2[1]);
var lon2 = goog.math.toRadians(c2[0]);
var cosLat1 = Math.cos(lat1);
var sinLat1 = Math.sin(lat1);
var cosLat2 = Math.cos(lat2);
var sinLat2 = Math.sin(lat2);
var cosDeltaLon = Math.cos(lon2 - lon1);
var d = sinLat1 * sinLat2 + cosLat1 * cosLat2 * cosDeltaLon;
if (1 <= d) {
return c2.slice();
}
d = fraction * Math.acos(d);
var cosD = Math.cos(d);
var sinD = Math.sin(d);
var y = Math.sin(lon2 - lon1) * cosLat2;
var x = cosLat1 * sinLat2 - sinLat1 * cosLat2 * cosDeltaLon;
var theta = Math.atan2(y, x);
var lat = Math.asin(sinLat1 * cosD + cosLat1 * sinD * Math.cos(theta));
var lon = lon1 + Math.atan2(Math.sin(theta) * sinD * cosLat1,
cosD - sinLat1 * Math.sin(lat));
return [goog.math.toDegrees(lon), goog.math.toDegrees(lat)];
};
/**
* Returns the initial bearing from c1 to c2.
*

230
test/spec/ol/sphere/sphere.test.js
View File

@@ -60,36 +60,6 @@ describe('ol.Sphere', function() {
initialBearing: 144.73561031724535,
midpoint: [18.434948822922006, -24.0948425521107]
},
{
c1: [0, 0],
c2: [90, 180],
cosineDistance: 10007.543398010286,
equirectangularDistance: 20015.086796020572,
finalBearing: 90,
haversineDistance: 10007.543398010288,
initialBearing: -90,
midpoint: [-45.00000000000005, 4.961398865471767e-15]
},
{
c1: [0, 0],
c2: [-90, 180],
cosineDistance: 10007.543398010286,
equirectangularDistance: 20015.086796020572,
finalBearing: 270,
haversineDistance: 10007.543398010288,
initialBearing: 90,
midpoint: [45.00000000000005, 4.961398865471767e-15]
},
{
c1: [0, 0],
c2: [90, -180],
cosineDistance: 10007.543398010286,
equirectangularDistance: 20015.086796020572,
finalBearing: 90,
haversineDistance: 10007.543398010288,
initialBearing: -90.00000000000001,
midpoint: [-45.00000000000005, -4.961398865471767e-15]
},
{
c1: [45, 45],
c2: [45, 45],
@@ -130,36 +100,6 @@ describe('ol.Sphere', function() {
initialBearing: 180,
midpoint: [45.00000000000005, 0]
},
{
c1: [45, 45],
c2: [90, 180],
cosineDistance: 13343.39119734705,
equirectangularDistance: 15132.953174634127,
finalBearing: 35.264389682754654,
haversineDistance: 13343.391197347048,
initialBearing: -54.735610317245346,
midpoint: [-45.00000000000005, 45.00000000000001]
},
{
c1: [45, 45],
c2: [-90, 180],
cosineDistance: 6671.695598673524,
equirectangularDistance: 16072.9523901477,
finalBearing: 324.73561031724535,
haversineDistance: 6671.695598673525,
initialBearing: 125.26438968275465,
midpoint: [71.56505117707799, 24.094842552110702]
},
{
c1: [45, 45],
c2: [90, -180],
cosineDistance: 13343.39119734705,
equirectangularDistance: 25092.03003421417,
finalBearing: 35.264389682754654,
haversineDistance: 13343.391197347048,
initialBearing: -54.735610317245346,
midpoint: [-45.00000000000005, 45]
},
{
c1: [-45, 45],
c2: [-45, 45],
@@ -190,36 +130,6 @@ describe('ol.Sphere', function() {
initialBearing: 125.26438968275465,
midpoint: [0, 0]
},
{
c1: [-45, 45],
c2: [90, 180],
cosineDistance: 6671.695598673524,
equirectangularDistance: 16072.9523901477,
finalBearing: 35.264389682754654,
haversineDistance: 6671.695598673525,
initialBearing: -125.26438968275465,
midpoint: [-71.56505117707799, 24.094842552110702]
},
{
c1: [-45, 45],
c2: [-90, 180],
cosineDistance: 13343.39119734705,
equirectangularDistance: 15132.953174634127,
finalBearing: 324.73561031724535,
haversineDistance: 13343.391197347048,
initialBearing: 54.735610317245346,
midpoint: [45.00000000000005, 45.00000000000001]
},
{
c1: [-45, 45],
c2: [90, -180],
cosineDistance: 6671.695598673525,
equirectangularDistance: 25669.894779453065,
finalBearing: 35.264389682754654,
haversineDistance: 6671.695598673525,
initialBearing: -125.26438968275465,
midpoint: [-71.56505117707799, 24.0948425521107]
},
{
c1: [-45, -45],
c2: [-45, -45],
@@ -240,36 +150,6 @@ describe('ol.Sphere', function() {
initialBearing: 125.26438968275465,
midpoint: [0, -54.735610317245346]
},
{
c1: [-45, -45],
c2: [90, 180],
cosineDistance: 6671.695598673525,
equirectangularDistance: 25669.894779453065,
finalBearing: 144.73561031724535,
haversineDistance: 6671.695598673525,
initialBearing: -54.735610317245346,
midpoint: [-71.56505117707799, -24.0948425521107]
},
{
c1: [-45, -45],
c2: [-90, 180],
cosineDistance: 13343.39119734705,
equirectangularDistance: 25092.03003421417,
finalBearing: 215.26438968275465,
haversineDistance: 13343.391197347048,
initialBearing: 125.26438968275465,
midpoint: [45.00000000000005, -45]
},
{
c1: [-45, -45],
c2: [90, -180],
cosineDistance: 6671.695598673524,
equirectangularDistance: 16072.9523901477,
finalBearing: 144.73561031724535,
haversineDistance: 6671.695598673525,
initialBearing: -54.73561031724536,
midpoint: [-71.56505117707799, -24.094842552110702]
},
{
c1: [45, -45],
c2: [45, -45],
@@ -279,96 +159,6 @@ describe('ol.Sphere', function() {
haversineDistance: 0,
initialBearing: 0,
midpoint: [45.00000000000005, -45]
},
{
c1: [45, -45],
c2: [90, 180],
cosineDistance: 13343.39119734705,
equirectangularDistance: 25092.03003421417,
finalBearing: 144.73561031724535,
haversineDistance: 13343.391197347048,
initialBearing: -125.26438968275465,
midpoint: [-45.00000000000005, -45]
},
{
c1: [45, -45],
c2: [-90, 180],
cosineDistance: 6671.695598673525,
equirectangularDistance: 25669.894779453065,
finalBearing: 215.26438968275465,
haversineDistance: 6671.695598673525,
initialBearing: 54.735610317245346,
midpoint: [71.56505117707799, -24.0948425521107]
},
{
c1: [45, -45],
c2: [90, -180],
cosineDistance: 13343.39119734705,
equirectangularDistance: 15132.953174634127,
finalBearing: 144.73561031724535,
haversineDistance: 13343.391197347048,
initialBearing: -125.26438968275465,
midpoint: [-45.00000000000005, -45.00000000000001]
},
{
c1: [90, 180],
c2: [90, 180],
cosineDistance: 0,
equirectangularDistance: 0,
finalBearing: 180,
haversineDistance: 0,
initialBearing: 0,
midpoint: [-90, 7.0164775638926606e-15]
},
{
c1: [90, 180],
c2: [-90, 180],
cosineDistance: 20015.086796020572,
equirectangularDistance: 20015.086796020572,
finalBearing: 26.565051177077976,
haversineDistance: 20015.086796020572,
initialBearing: 153.43494882292202,
midpoint: [-180, 63.43494882292201]
},
{
c1: [90, 180],
c2: [90, -180],
cosineDistance: 0,
equirectangularDistance: 40030.173592041145,
finalBearing: 0,
haversineDistance: 1.5603934160404731e-12,
initialBearing: 0,
midpoint: [-90, 0]
},
{
c1: [-90, 180],
c2: [-90, 180],
cosineDistance: 0,
equirectangularDistance: 0,
finalBearing: 180,
haversineDistance: 0,
initialBearing: 0,
midpoint: [90, 7.0164775638926606e-15]
},
{
c1: [-90, 180],
c2: [90, -180],
cosineDistance: 20015.086796020572,
equirectangularDistance: 44755.09465146047,
finalBearing: 270,
haversineDistance: 20015.086796020572,
initialBearing: -90,
midpoint: [-180, 0]
},
{
c1: [90, -180],
c2: [90, -180],
cosineDistance: 0,
equirectangularDistance: 0,
finalBearing: 180,
haversineDistance: 0,
initialBearing: 0,
midpoint: [-90, -7.0164775638926606e-15]
}
];
@@ -437,6 +227,26 @@ describe('ol.Sphere', function() {
});
describe('interpolate', function() {
it('results match at the start, midpoint, and end', function() {
var e, i;
for (i = 0; i < expected.length; ++i) {
e = expected[i];
var c1 = sphere.interpolate(e.c1, e.c2, 0);
expect(c1[0]).to.roughlyEqual(e.c1[0], 1e-9);
expect(c1[1]).to.roughlyEqual(e.c1[1], 1e-9);
var midpoint = sphere.interpolate(e.c1, e.c2, 0.5);
expect(midpoint[0]).to.roughlyEqual(e.midpoint[0], 1e-9);
expect(midpoint[1]).to.roughlyEqual(e.midpoint[1], 1e-9);
var c2 = sphere.interpolate(e.c1, e.c2, 1);
expect(c2[0]).to.roughlyEqual(e.c2[0], 1e-9);
expect(c2[1]).to.roughlyEqual(e.c2[1], 1e-9);
}
});
});
describe('midpoint', function() {
it('results match Chris Veness\'s reference implementation', function() {