1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
|
import adder from "./adder.js";
import {atan2, cos, quarterPi, radians, sin, tau} from "./math.js";
import noop from "./noop.js";
import stream from "./stream.js";
export var areaRingSum = adder();
var areaSum = adder(),
lambda00,
phi00,
lambda0,
cosPhi0,
sinPhi0;
export var areaStream = {
point: noop,
lineStart: noop,
lineEnd: noop,
polygonStart: function() {
areaRingSum.reset();
areaStream.lineStart = areaRingStart;
areaStream.lineEnd = areaRingEnd;
},
polygonEnd: function() {
var areaRing = +areaRingSum;
areaSum.add(areaRing < 0 ? tau + areaRing : areaRing);
this.lineStart = this.lineEnd = this.point = noop;
},
sphere: function() {
areaSum.add(tau);
}
};
function areaRingStart() {
areaStream.point = areaPointFirst;
}
function areaRingEnd() {
areaPoint(lambda00, phi00);
}
function areaPointFirst(lambda, phi) {
areaStream.point = areaPoint;
lambda00 = lambda, phi00 = phi;
lambda *= radians, phi *= radians;
lambda0 = lambda, cosPhi0 = cos(phi = phi / 2 + quarterPi), sinPhi0 = sin(phi);
}
function areaPoint(lambda, phi) {
lambda *= radians, phi *= radians;
phi = phi / 2 + quarterPi; // half the angular distance from south pole
// Spherical excess E for a spherical triangle with vertices: south pole,
// previous point, current point. Uses a formula derived from Cagnoli’s
// theorem. See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2).
var dLambda = lambda - lambda0,
sdLambda = dLambda >= 0 ? 1 : -1,
adLambda = sdLambda * dLambda,
cosPhi = cos(phi),
sinPhi = sin(phi),
k = sinPhi0 * sinPhi,
u = cosPhi0 * cosPhi + k * cos(adLambda),
v = k * sdLambda * sin(adLambda);
areaRingSum.add(atan2(v, u));
// Advance the previous points.
lambda0 = lambda, cosPhi0 = cosPhi, sinPhi0 = sinPhi;
}
export default function(object) {
areaSum.reset();
stream(object, areaStream);
return areaSum * 2;
}
|
