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More reliable ear test and point in triangle arithmetic #40

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merged 4 commits into from
Oct 21, 2015
Merged

More reliable ear test and point in triangle arithmetic #40

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708e6d1
more reliable point in triangle calculation
mourner Oct 20, 2015
8afd211
more reliable ear test
mourner Oct 21, 2015
4aad5c4
simplify orientation calc
mourner Oct 21, 2015
375d6de
add a few test cases from #39
mourner Oct 21, 2015
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144 changes: 47 additions & 97 deletions src/earcut.js
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Original file line number Diff line number Diff line change
Expand Up @@ -71,7 +71,7 @@ function filterPoints(data, start, end) {
do {
again = false;

if (!node.steiner && (equals(data, node.i, node.next.i) || orient(data, node.prev.i, node.i, node.next.i) === 0)) {
if (!node.steiner && (equals(data, node.i, node.next.i) || area(data, node.prev.i, node.i, node.next.i) === 0)) {
removeNode(node);
node = end = node.prev;
if (node === node.next) return null;
Expand Down Expand Up @@ -143,27 +143,18 @@ function isEar(data, ear, minX, minY, size) {

var a = ear.prev.i,
b = ear.i,
c = ear.next.i,
c = ear.next.i;

ax = data[a], ay = data[a + 1],
bx = data[b], by = data[b + 1],
cx = data[c], cy = data[c + 1],

abd = ax * by - ay * bx,
acd = ax * cy - ay * cx,
cbd = cx * by - cy * bx,
A = abd - acd - cbd;
if (area(data, a, b, c) >= 0) return false; // reflex, can't be an ear

if (A <= 0) return false; // reflex, can't be an ear
var ax = data[a], ay = data[a + 1],
bx = data[b], by = data[b + 1],
cx = data[c], cy = data[c + 1];

// now make sure we don't have other points inside the potential ear;
// the code below is a bit verbose and repetitive but this is done for performance

var cay = cy - ay,
acx = ax - cx,
aby = ay - by,
bax = bx - ax,
i, px, py, s, t, k, node;
var i, node;

// if we use z-order curve hashing, iterate through the curve
if (minX !== undefined) {
Expand All @@ -183,41 +174,21 @@ function isEar(data, ear, minX, minY, size) {

while (node && node.z <= maxZ) {
i = node.i;
if (node !== ear.prev && node !== ear.next &&
pointInTriangle(ax, ay, bx, by, cx, cy, data[i], data[i + 1]) &&
area(data, node.prev.i, i, node.next.i) >= 0) return false;
node = node.nextZ;
if (i === a || i === c) continue;

px = data[i];
py = data[i + 1];

s = cay * px + acx * py - acd;
if (s >= 0) {
t = aby * px + bax * py + abd;
if (t >= 0) {
k = A - s - t;
if ((k >= 0) && ((s && t) || (s && k) || (t && k))) return false;
}
}
}

// then look for points in decreasing z-order
node = ear.prevZ;

while (node && node.z >= minZ) {
i = node.i;
if (node !== ear.prev && node !== ear.next &&
pointInTriangle(ax, ay, bx, by, cx, cy, data[i], data[i + 1]) &&
area(data, node.prev.i, i, node.next.i) >= 0) return false;
node = node.prevZ;
if (i === a || i === c) continue;

px = data[i];
py = data[i + 1];

s = cay * px + acx * py - acd;
if (s >= 0) {
t = aby * px + bax * py + abd;
if (t >= 0) {
k = A - s - t;
if ((k >= 0) && ((s && t) || (s && k) || (t && k))) return false;
}
}
}

// if we don't use z-order curve hash, simply iterate through all other points
Expand All @@ -226,19 +197,9 @@ function isEar(data, ear, minX, minY, size) {

while (node !== ear.prev) {
i = node.i;
if (pointInTriangle(ax, ay, bx, by, cx, cy, data[i], data[i + 1]) &&
area(data, node.prev.i, i, node.next.i) >= 0) return false;
node = node.next;

px = data[i];
py = data[i + 1];

s = cay * px + acx * py - acd;
if (s >= 0) {
t = aby * px + bax * py + abd;
if (t >= 0) {
k = A - s - t;
if ((k >= 0) && ((s && t) || (s && k) || (t && k))) return false;
}
}
}
}

Expand All @@ -253,9 +214,8 @@ function cureLocalIntersections(data, start, triangles, dim) {
b = node.next.next;

// a self-intersection where edge (v[i-1],v[i]) intersects (v[i+1],v[i+2])
if (a.i !== b.i && intersects(data, a.i, node.i, node.next.i, b.i) &&
locallyInside(data, a, b) && locallyInside(data, b, a) &&
orient(data, a.i, node.i, b.i) && orient(data, a.i, node.next.i, b.i)) {
if (intersects(data, a.i, node.i, node.next.i, b.i) &&
locallyInside(data, a, b) && locallyInside(data, b, a)) {

triangles.push(a.i / dim);
triangles.push(node.i / dim);
Expand Down Expand Up @@ -341,7 +301,7 @@ function findHoleBridge(data, holeNode, outerNode) {
i = holeNode.i,
px = data[i],
py = data[i + 1],
qMax = -Infinity,
qx = -Infinity,
mNode, a, b;

// find a segment intersected by a ray from the hole's leftmost point to the left;
Expand All @@ -351,9 +311,9 @@ function findHoleBridge(data, holeNode, outerNode) {
b = node.next.i;

if (py <= data[a + 1] && py >= data[b + 1]) {
var qx = data[a] + (py - data[a + 1]) * (data[b] - data[a]) / (data[b + 1] - data[a + 1]);
if (qx <= px && qx > qMax) {
qMax = qx;
var x = data[a] + (py - data[a + 1]) * (data[b] - data[a]) / (data[b + 1] - data[a + 1]);
if (x <= px && x > qx) {
qx = x;
mNode = data[a] < data[b] ? node : node.next;
}
}
Expand All @@ -362,45 +322,29 @@ function findHoleBridge(data, holeNode, outerNode) {

if (!mNode) return null;

// look for points strictly inside the triangle of hole point, segment intersection and endpoint;
// look for points inside the triangle of hole point, segment intersection and endpoint;
// if there are no points found, we have a valid connection;
// otherwise choose the point of the minimum angle with the ray as connection point

var bx = data[mNode.i],
by = data[mNode.i + 1],
pbd = px * by - py * bx,
pcd = px * py - py * qMax,
cpy = py - py,
pcx = px - qMax,
pby = py - by,
bpx = bx - px,
A = pbd - pcd - (qMax * by - py * bx),
sign = A <= 0 ? -1 : 1,
stop = mNode,
tanMin = Infinity,
mx, my, amx, s, t, tan;
mx, my, tan;

node = mNode.next;

while (node !== stop) {

mx = data[node.i];
my = data[node.i + 1];
amx = px - mx;

if (amx >= 0 && mx >= bx) {
s = (cpy * mx + pcx * my - pcd) * sign;
if (s >= 0) {
t = (pby * mx + bpx * my + pbd) * sign;

if (t >= 0 && A * sign - s - t >= 0) {
tan = Math.abs(py - my) / amx; // tangential
if ((tan < tanMin || (tan === tanMin && mx > bx)) &&
locallyInside(data, node, holeNode)) {
mNode = node;
tanMin = tan;
}
}

if (px >= mx && mx >= bx && pointInTriangle(py < by ? px : qx, py, bx, by, py < by ? qx : px, py, mx, my)) {
tan = Math.abs(py - my) / (px - mx); // tangential

if ((tan < tanMin || (tan === tanMin && mx > bx)) && locallyInside(data, node, holeNode)) {
mNode = node;
tanMin = tan;
}
}

Expand Down Expand Up @@ -520,19 +464,25 @@ function getLeftmost(data, start) {
return leftmost;
}

// check if a point lies within a convex triangle
function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
(ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
(bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;
}

// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
function isValidDiagonal(data, a, b) {
return a.next.i !== b.i && a.prev.i !== b.i &&
return equals(data, a.i, b.i) ||
a.next.i !== b.i && a.prev.i !== b.i &&
!intersectsPolygon(data, a, a.i, b.i) &&
locallyInside(data, a, b) && locallyInside(data, b, a) &&
middleInside(data, a, a.i, b.i);
}

// winding order of triangle formed by 3 given points
function orient(data, p, q, r) {
var o = (data[q + 1] - data[p + 1]) * (data[r] - data[q]) - (data[q] - data[p]) * (data[r + 1] - data[q + 1]);
return o > 0 ? 1 :
o < 0 ? -1 : 0;
// signed area of a triangle
function area(data, p, q, r) {
return (data[q + 1] - data[p + 1]) * (data[r] - data[q]) - (data[q] - data[p]) * (data[r + 1] - data[q + 1]);
}

// check if two points are equal
Expand All @@ -542,8 +492,8 @@ function equals(data, p1, p2) {

// check if two segments intersect
function intersects(data, p1, q1, p2, q2) {
return orient(data, p1, q1, p2) !== orient(data, p1, q1, q2) &&
orient(data, p2, q2, p1) !== orient(data, p2, q2, q1);
return area(data, p1, q1, p2) > 0 !== area(data, p1, q1, q2) > 0 &&
area(data, p2, q2, p1) > 0 !== area(data, p2, q2, q1) > 0;
}

// check if a polygon diagonal intersects any polygon segments
Expand All @@ -563,9 +513,9 @@ function intersectsPolygon(data, start, a, b) {

// check if a polygon diagonal is locally inside the polygon
function locallyInside(data, a, b) {
return orient(data, a.prev.i, a.i, a.next.i) === -1 ?
orient(data, a.i, b.i, a.next.i) !== -1 && orient(data, a.i, a.prev.i, b.i) !== -1 :
orient(data, a.i, b.i, a.prev.i) === -1 || orient(data, a.i, a.next.i, b.i) === -1;
return area(data, a.prev.i, a.i, a.next.i) < 0 ?
area(data, a.i, b.i, a.next.i) >= 0 && area(data, a.i, a.prev.i, b.i) >= 0 :
area(data, a.i, b.i, a.prev.i) < 0 || area(data, a.i, a.next.i, b.i) < 0;
}

// check if the middle point of a polygon diagonal is inside the polygon
Expand Down
1 change: 1 addition & 0 deletions test/fixtures/hole-touching-outer.json
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Original file line number Diff line number Diff line change
@@ -0,0 +1 @@
[[[-64,-64],[253,-64],[491,358],[697,298],[928,197],[929,505],[1346,507],[1347,303],[1771,306],[1770,512],[2191,509],[2198,933],[2621,932],[2623,1115],[2577,1120],[2494,1183],[2390,1329],[2326,1590],[2287,1678],[2286,1407],[2229,1407],[2182,1493],[2106,1494],[2068,1460],[2019,1460],[2016,1775],[1889,1923],[1953,1989],[2097,1866],[2198,1925],[2203,1973],[2311,1976],[2320,1831],[2352,1824],[2358,1797],[2378,1780],[3350,1782],[3307,2086],[3139,2088],[3143,2203],[3493,2205],[3543,2187],[3540,2260],[3661,2264],[3665,1906],[3630,1902],[3626,1784],[4160,1786],[4160,2631],[4076,2631],[4021,2683],[3930,2701],[3915,2693],[3898,2639],[2630,2630],[2635,3476],[2287,3478],[2118,3203],[2180,3145],[2327,3087],[2610,2643],[2613,2536],[2658,2495],[2650,2203],[1829,2189],[1732,2241],[1551,2245],[933,1183],[890,1152],[455,401],[398,412],[89,547],[-64,606],[-64,-64]],[[1762,928],[1770,512],[1343,513],[1345,715],[931,719],[932,930],[1762,928]]]
1 change: 1 addition & 0 deletions test/fixtures/touching-holes.json
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@@ -0,0 +1 @@
[[[3694,2061],[3794,2035],[3812,2123],[3784,2123],[3708,2139],[3694,2061]],[[3752,2109],[3740,2102],[3712,2109],[3715,2125],[3723,2128],[3740,2124],[3742,2112],[3752,2109]],[[3797,2101],[3787,2096],[3780,2106],[3788,2114],[3797,2101]],[[3734,2099],[3732,2091],[3719,2094],[3721,2102],[3734,2099]],[[3777,2082],[3774,2071],[3772,2086],[3765,2091],[3748,2088],[3749,2062],[3738,2081],[3745,2095],[3761,2099],[3777,2082]],[[3719,2079],[3712,2079],[3706,2091],[3712,2097],[3721,2080],[3719,2079]],[[3773,2067],[3761,2053],[3753,2061],[3753,2071],[3756,2075],[3773,2067]],[[3708,2079],[3712,2079],[3714,2076],[3719,2079],[3722,2079],[3718,2088],[3723,2089],[3734,2075],[3730,2068],[3717,2065],[3708,2079]]]
8 changes: 5 additions & 3 deletions test/test.js
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Original file line number Diff line number Diff line change
Expand Up @@ -7,13 +7,13 @@ var test = require('tape'),

areaTest('building', 12);
areaTest('dude', 106);
areaTest('water', 2482, 0.0019);
areaTest('water', 2482, 0.0008);
areaTest('water2', 1211);
areaTest('water3', 197);
areaTest('water3b', 25);
areaTest('water4', 705);
areaTest('water-huge', 5164, 0.0015);
areaTest('water-huge2', 4462, 0.0019);
areaTest('water-huge', 5159, 0.008);
areaTest('water-huge2', 4458, 0.0019);
areaTest('degenerate', 0);
areaTest('bad-hole', 34, 0.0420);
areaTest('empty-square', 0);
Expand All @@ -26,6 +26,8 @@ areaTest('issue35', 844);
areaTest('self-touching', 124, 3.4e-14);
areaTest('outside-ring', 64);
areaTest('simplified-us-border', 120);
areaTest('touching-holes', 57);
areaTest('hole-touching-outer', 77);

test('indices-2d', function (t) {
var indices = earcut([10, 0, 0, 50, 60, 60, 70, 10]);
Expand Down