-
Notifications
You must be signed in to change notification settings - Fork 308
/
enclosingCircle.js
107 lines (93 loc) · 2.59 KB
/
enclosingCircle.js
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
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
export default function(circles) {
return encloseN(shuffle(circles), []);
}
function shuffle(array) {
var i,
n = (array = array.slice()).length,
head = null,
node = head;
while (n) {
var next = {circle: array[n - 1], next: null};
if (node) node = node.next = next;
else node = head = next;
array[i] = array[--n];
}
return {head: head, tail: node};
}
function encloses(a, b) {
var dx = b.x - a.x,
dy = b.y - a.y,
dr = a.r - b.r;
return dr * dr + 1e-6 > dx * dx + dy * dy;
}
// Returns the smallest circle that contains circles L and intersects circles B.
function encloseN(L, B) {
var circle,
l0 = null,
l1 = L.head,
l2,
p1;
switch (B.length) {
case 1: circle = B[0]; break;
case 2: circle = enclose2(B[0], B[1]); break;
case 3: circle = enclose3(B[0], B[1], B[2]); break;
}
while (l1) {
p1 = l1.circle, l2 = l1.next;
if (!circle || !encloses(circle, p1)) {
// Temporarily truncate L before l1.
if (l0) L.tail = l0, l0.next = null;
else L.head = L.tail = null;
B.push(p1);
circle = encloseN(L, B); // Note: reorders L!
B.pop();
// Move l1 to the front of L and reconnect the truncated list L.
if (L.head) l1.next = L.head, L.head = l1;
else l1.next = null, L.head = L.tail = l1;
l0 = L.tail, l0.next = l2;
} else {
l0 = l1;
}
l1 = l2;
}
L.tail = l0;
return circle;
}
function enclose2(a, b) {
var x1 = a.x, y1 = a.y, r1 = a.r,
x2 = b.x, y2 = b.y, r2 = b.r,
x21 = x2 - x1, y21 = y2 - y1, r21 = r2 - r1,
l = Math.sqrt(x21 * x21 + y21 * y21);
return {
x: (x1 + x2 + x21 / l * r21) / 2,
y: (y1 + y2 + y21 / l * r21) / 2,
r: (l + r1 + r2) / 2
};
}
function enclose3(a, b, c) {
var x1 = a.x, y1 = a.y, r1 = a.r,
x2 = b.x, y2 = b.y, r2 = b.r,
x3 = c.x, y3 = c.y, r3 = c.r,
a2 = 2 * (x1 - x2),
b2 = 2 * (y1 - y2),
c2 = 2 * (r2 - r1),
d2 = x1 * x1 + y1 * y1 - r1 * r1 - x2 * x2 - y2 * y2 + r2 * r2,
a3 = 2 * (x1 - x3),
b3 = 2 * (y1 - y3),
c3 = 2 * (r3 - r1),
d3 = x1 * x1 + y1 * y1 - r1 * r1 - x3 * x3 - y3 * y3 + r3 * r3,
ab = a3 * b2 - a2 * b3,
xa = (b2 * d3 - b3 * d2) / ab - x1,
xb = (b3 * c2 - b2 * c3) / ab,
ya = (a3 * d2 - a2 * d3) / ab - y1,
yb = (a2 * c3 - a3 * c2) / ab,
A = xb * xb + yb * yb - 1,
B = 2 * (xa * xb + ya * yb + r1),
C = xa * xa + ya * ya - r1 * r1,
r = (-B - Math.sqrt(B * B - 4 * A * C)) / (2 * A);
return {
x: xa + xb * r + x1,
y: ya + yb * r + y1,
r: r
};
}