Fix edge cases when inner rings are touching (#177)

* fix all except touching-holes4

* other

* fix benchmarks

* viz tweaks, test rotations, and fix other bugs

* rm diffs

* rm extra diff

* perf tweak

* comment

* perf tweaks

bench/basic.js

@@ -1,4 +1,4 @@
-import {earcut, flatten} from '../src/earcut.js';
+import earcut, {flatten} from '../src/earcut.js';
 import {readFileSync} from 'fs';
 
 const data = JSON.parse(readFileSync(new URL('../test/fixtures/building.json', import.meta.url)));

bench/bench.js

@@ -1,4 +1,4 @@
-import {earcut, flatten} from '../src/earcut.js';
+import earcut, {flatten} from '../src/earcut.js';
 import Benchmark from 'benchmark';
 import {readFileSync} from 'fs';
 

src/earcut.js

@@ -140,16 +140,16 @@ function isEar(ear) {
     // now make sure we don't have other points inside the potential ear
     const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y;
 
-    // triangle bbox; min & max are calculated like this for speed
-    const x0 = ax < bx ? (ax < cx ? ax : cx) : (bx < cx ? bx : cx),
-        y0 = ay < by ? (ay < cy ? ay : cy) : (by < cy ? by : cy),
-        x1 = ax > bx ? (ax > cx ? ax : cx) : (bx > cx ? bx : cx),
-        y1 = ay > by ? (ay > cy ? ay : cy) : (by > cy ? by : cy);
+    // triangle bbox
+    const x0 = Math.min(ax, bx, cx),
+        y0 = Math.min(ay, by, cy),
+        x1 = Math.max(ax, bx, cx),
+        y1 = Math.max(ay, by, cy);
 
     let p = c.next;
     while (p !== a) {
         if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 &&
-            pointInTriangle(ax, ay, bx, by, cx, cy, p.x, p.y) &&
+            pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) &&
             area(p.prev, p, p.next) >= 0) return false;
         p = p.next;
     }
@@ -166,11 +166,11 @@ function isEarHashed(ear, minX, minY, invSize) {
 
     const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y;
 
-    // triangle bbox; min & max are calculated like this for speed
-    const x0 = ax < bx ? (ax < cx ? ax : cx) : (bx < cx ? bx : cx),
-        y0 = ay < by ? (ay < cy ? ay : cy) : (by < cy ? by : cy),
-        x1 = ax > bx ? (ax > cx ? ax : cx) : (bx > cx ? bx : cx),
-        y1 = ay > by ? (ay > cy ? ay : cy) : (by > cy ? by : cy);
+    // triangle bbox
+    const x0 = Math.min(ax, bx, cx),
+        y0 = Math.min(ay, by, cy),
+        x1 = Math.max(ax, bx, cx),
+        y1 = Math.max(ay, by, cy);
 
     // z-order range for the current triangle bbox;
     const minZ = zOrder(x0, y0, minX, minY, invSize),
@@ -182,25 +182,25 @@ function isEarHashed(ear, minX, minY, invSize) {
     // look for points inside the triangle in both directions
     while (p && p.z >= minZ && n && n.z <= maxZ) {
         if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c &&
-            pointInTriangle(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false;
+            pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false;
         p = p.prevZ;
 
         if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c &&
-            pointInTriangle(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false;
+            pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false;
         n = n.nextZ;
     }
 
     // look for remaining points in decreasing z-order
     while (p && p.z >= minZ) {
         if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c &&
-            pointInTriangle(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false;
+            pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false;
         p = p.prevZ;
     }
 
     // look for remaining points in increasing z-order
     while (n && n.z <= maxZ) {
         if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c &&
-            pointInTriangle(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false;
+            pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false;
         n = n.nextZ;
     }
 
@@ -268,7 +268,7 @@ function eliminateHoles(data, holeIndices, outerNode, dim) {
         queue.push(getLeftmost(list));
     }
 
-    queue.sort(compareX);
+    queue.sort(compareXYSlope);
 
     // process holes from left to right
     for (let i = 0; i < queue.length; i++) {
@@ -278,8 +278,19 @@ function eliminateHoles(data, holeIndices, outerNode, dim) {
     return outerNode;
 }
 
-function compareX(a, b) {
-    return a.x - b.x;
+function compareXYSlope(a, b) {
+    let result = a.x - b.x;
+    // when the left-most point of 2 holes meet at a vertex, sort the holes counterclockwise so that when we find
+    // the bridge to the outer shell is always the point that they meet at.
+    if (result === 0) {
+        result = a.y - b.y;
+        if (result === 0) {
+            const aSlope = (a.next.y - a.y) / (a.next.x - a.x);
+            const bSlope = (b.next.y - b.y) / (b.next.x - b.x);
+            result = aSlope - bSlope;
+        }
+    }
+    return result;
 }
 
 // find a bridge between vertices that connects hole with an outer ring and and link it
@@ -306,8 +317,11 @@ function findHoleBridge(hole, outerNode) {
 
     // find a segment intersected by a ray from the hole's leftmost point to the left;
     // segment's endpoint with lesser x will be potential connection point
+    // unless they intersect at a vertex, then choose the vertex
+    if (equals(hole, p)) return p;
     do {
-        if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) {
+        if (equals(hole, p.next)) return p.next;
+        else if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) {
             const x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y);
             if (x <= hx && x > qx) {
                 qx = x;
@@ -463,6 +477,11 @@ function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
            (bx - px) * (cy - py) >= (cx - px) * (by - py);
 }
 
+// check if a point lies within a convex triangle but false if its equal to the first point of the triangle
+function pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, px, py) {
+    return !(ax === px && ay === py) && pointInTriangle(ax, ay, bx, by, cx, cy, px, py);
+}
+
 // check if a diagonal between two polygon nodes is valid (lies in polygon interior)
 function isValidDiagonal(a, b) {
     return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) && // dones't intersect other edges

test/expected.json

@@ -7,7 +7,7 @@
         "water3": 197,
         "water3b": 25,
         "water4": 705,
-        "water-huge": 5177,
+        "water-huge": 5176,
         "water-huge2": 4462,
         "degenerate": 0,
         "bad-hole": 42,
@@ -22,6 +22,11 @@
         "outside-ring": 64,
         "simplified-us-border": 120,
         "touching-holes": 57,
+        "touching-holes2": 10,
+        "touching-holes3": 82,
+        "touching-holes4": 55,
+        "touching-holes5": 133,
+        "touching-holes6": 3098,
         "hole-touching-outer": 77,
         "hilbert": 1024,
         "issue45": 10,
@@ -32,32 +37,38 @@
         "bad-diagonals": 7,
         "issue83": 0,
         "issue107": 0,
-        "issue111": 19,
-        "boxy": 57,
+        "issue111": 18,
+        "boxy": 58,
         "collinear-diagonal": 14,
         "issue119": 18,
         "hourglass": 2,
         "touching2": 8,
         "touching3": 15,
-        "touching4": 20,
+        "touching4": 19,
         "rain": 2681,
         "issue131": 12,
-        "infinite-loop-jhl" : 0,
-        "filtered-bridge-jhl" : 25,
+        "infinite-loop-jhl": 0,
+        "filtered-bridge-jhl": 25,
         "issue149": 2,
         "issue142": 4
     },
     "errors": {
         "dude": 2e-15,
         "water": 0.0008,
         "water-huge": 0.0011,
-        "water-huge2": 0.0028,
+        "water-huge2": 0.004,
         "bad-hole": 0.019,
         "issue16": 4e-16,
         "issue17": 2e-16,
         "issue29": 2e-15,
         "self-touching": 2e-13,
         "eberly-6": 2e-14,
         "issue142": 0.13
+    },
+    "errors-with-rotation": {
+        "water-huge": 0.0035,
+        "water-huge2": 0.061,
+        "bad-hole": 0.04,
+        "issue16": 8e-16
     }
-}
+}

test/fixtures/touching-holes2.json

@@ -0,0 +1 @@
+[[[0,0],[20,0],[20,25],[0,25],[0,0]],[[3,3],[2,12],[9,15],[3,3]],[[9,21],[2,12],[7,22],[9,21]]]

test/fixtures/touching-holes3.json

@@ -0,0 +1 @@
+[[[0,0],[20,0],[20,25],[0,25],[0,0]],[[2,12],[4,23],[5,23],[2,12]],[[2,12],[6,23],[7,23],[2,12]],[[2,12],[8,23],[9,23],[2,12]],[[2,12],[10,23],[11,23],[2,12]],[[2,12],[12,23],[13,23],[2,12]],[[2,12],[14,23],[15,23],[2,12]],[[2,12],[16,23],[17,23],[2,12]],[[2,12],[18,23],[18,22],[2,12]],[[2,12],[18,21],[18,20],[2,12]],[[2,12],[18,19],[18,18],[2,12]],[[2,12],[18,17],[18,16],[2,12]],[[2,12],[18,15],[18,14],[2,12]],[[2,12],[18,13],[18,12],[2,12]],[[2,12],[18,11],[18,10],[2,12]],[[2,12],[18,9],[18,8],[2,12]],[[2,12],[18,7],[18,6],[2,12]],[[2,12],[18,5],[18,4],[2,12]],[[2,12],[18,3],[18,2],[2,12]],[[2,12],[18,1],[17,1],[2,12]],[[2,12],[16,1],[15,1],[2,12]],[[2,12],[14,1],[13,1],[2,12]],[[2,12],[12,1],[11,1],[2,12]],[[2,12],[10,1],[9,1],[2,12]],[[2,12],[8,1],[7,1],[2,12]],[[2,12],[6,1],[5,1],[2,12]],[[2,12],[4,1],[3,1],[2,12]]]

test/fixtures/touching-holes4.json

@@ -0,0 +1 @@
+[[[-20,0],[20,0],[20,25],[-20,25],[-20,0]],[[2,12],[-1,23],[0,23],[2,12]],[[2,12],[-3,23],[-2,23],[2,12]],[[2,12],[-5,23],[-4,23],[2,12]],[[2,12],[-7,23],[-6,23],[2,12]],[[2,12],[-9,23],[-8,23],[2,12]],[[2,12],[-11,23],[-10,23],[2,12]],[[2,12],[-13,23],[-12,23],[2,12]],[[2,12],[-14,22],[-14,23],[2,12]],[[2,12],[-14,20],[-14,21],[2,12]],[[2,12],[-14,18],[-14,19],[2,12]],[[2,12],[-14,16],[-14,17],[2,12]],[[2,12],[-14,14],[-14,15],[2,12]],[[2,12],[-14,12],[-14,13],[2,12]],[[2,12],[-14,10],[-14,11],[2,12]],[[2,12],[-14,8],[-14,9],[2,12]],[[2,12],[-14,6],[-14,7],[2,12]],[[2,12],[-14,4],[-14,5],[2,12]],[[2,12],[-14,2],[-14,3],[2,12]],[[2,12],[-13,1],[-14,1],[2,12]],[[2,12],[-11,1],[-12,1],[2,12]],[[2,12],[-9,1],[-10,1],[2,12]],[[2,12],[-7,1],[-8,1],[2,12]],[[2,12],[-5,1],[-6,1],[2,12]],[[2,12],[-3,1],[-4,1],[2,12]],[[2,12],[-1,1],[-2,1],[2,12]],[[2,12],[1,1],[0,1],[2,12]]]

test/fixtures/touching-holes5.json

@@ -0,0 +1 @@
+[[[-20,0],[20,0],[20,25],[-20,25],[-20,0]],[[2,12],[4,23],[5,23],[2,12]],[[2,12],[6,23],[7,23],[2,12]],[[2,12],[8,23],[9,23],[2,12]],[[2,12],[10,23],[11,23],[2,12]],[[2,12],[12,23],[13,23],[2,12]],[[2,12],[14,23],[15,23],[2,12]],[[2,12],[16,23],[17,23],[2,12]],[[2,12],[18,23],[18,22],[2,12]],[[2,12],[18,21],[18,20],[2,12]],[[2,12],[18,19],[18,18],[2,12]],[[2,12],[18,17],[18,16],[2,12]],[[2,12],[18,15],[18,14],[2,12]],[[2,12],[18,13],[18,12],[2,12]],[[2,12],[18,11],[18,10],[2,12]],[[2,12],[18,9],[18,8],[2,12]],[[2,12],[18,7],[18,6],[2,12]],[[2,12],[18,5],[18,4],[2,12]],[[2,12],[18,3],[18,2],[2,12]],[[2,12],[18,1],[17,1],[2,12]],[[2,12],[16,1],[15,1],[2,12]],[[2,12],[14,1],[13,1],[2,12]],[[2,12],[12,1],[11,1],[2,12]],[[2,12],[10,1],[9,1],[2,12]],[[2,12],[8,1],[7,1],[2,12]],[[2,12],[6,1],[5,1],[2,12]],[[2,12],[4,1],[3,1],[2,12]],[[2,12],[-1,23],[0,23],[2,12]],[[2,12],[-3,23],[-2,23],[2,12]],[[2,12],[-5,23],[-4,23],[2,12]],[[2,12],[-7,23],[-6,23],[2,12]],[[2,12],[-9,23],[-8,23],[2,12]],[[2,12],[-11,23],[-10,23],[2,12]],[[2,12],[-13,23],[-12,23],[2,12]],[[2,12],[-14,22],[-14,23],[2,12]],[[2,12],[-14,20],[-14,21],[2,12]],[[2,12],[-14,18],[-14,19],[2,12]],[[2,12],[-14,16],[-14,17],[2,12]],[[2,12],[-14,14],[-14,15],[2,12]],[[2,12],[-14,12],[-14,13],[2,12]],[[2,12],[-14,10],[-14,11],[2,12]],[[2,12],[-14,8],[-14,9],[2,12]],[[2,12],[-14,6],[-14,7],[2,12]],[[2,12],[-14,4],[-14,5],[2,12]],[[2,12],[-14,2],[-14,3],[2,12]],[[2,12],[-13,1],[-14,1],[2,12]],[[2,12],[-11,1],[-12,1],[2,12]],[[2,12],[-9,1],[-10,1],[2,12]],[[2,12],[-7,1],[-8,1],[2,12]],[[2,12],[-5,1],[-6,1],[2,12]],[[2,12],[-3,1],[-4,1],[2,12]],[[2,12],[-1,1],[-2,1],[2,12]],[[2,12],[1,1],[0,1],[2,12]]]

test/test.js

@@ -22,20 +22,39 @@ test('empty', () => {
 
 for (const id of Object.keys(expected.triangles)) {
 
-    test(id, () => {
-        const data = flatten(JSON.parse(fs.readFileSync(new URL(`fixtures/${id}.json`, import.meta.url)))),
-            indices = earcut(data.vertices, data.holes, data.dimensions),
-            err = deviation(data.vertices, data.holes, data.dimensions, indices),
-            expectedTriangles = expected.triangles[id],
-            expectedDeviation = expected.errors[id] || 0;
-
-        const numTriangles = indices.length / 3;
-        assert.ok(numTriangles === expectedTriangles, `${numTriangles} triangles when expected ${expectedTriangles}`);
-
-        if (expectedTriangles > 0) {
-            assert.ok(err <= expectedDeviation, `deviation ${err} <= ${expectedDeviation}`);
-        }
-    });
+    for (const rotation of [0, 90, 180, 270]) {
+        test(`${id} rotation ${rotation}`, () => {
+            const coords = JSON.parse(fs.readFileSync(new URL(`fixtures/${id}.json`, import.meta.url)));
+            const theta = rotation * Math.PI / 180;
+            const xx = Math.round(Math.cos(theta));
+            const xy = Math.round(-Math.sin(theta));
+            const yx = Math.round(Math.sin(theta));
+            const yy = Math.round(Math.cos(theta));
+            if (rotation) {
+                for (const ring of coords) {
+                    for (const coord of ring) {
+                        const [x, y] = coord;
+                        coord[0] = xx * x + xy * y;
+                        coord[1] = yx * x + yy * y;
+                    }
+                }
+            }
+            const data = flatten(coords),
+                indices = earcut(data.vertices, data.holes, data.dimensions),
+                err = deviation(data.vertices, data.holes, data.dimensions, indices),
+                expectedTriangles = expected.triangles[id],
+                expectedDeviation = (rotation !== 0 && expected['errors-with-rotation'][id]) || expected.errors[id] || 0;
+
+            const numTriangles = indices.length / 3;
+            if (rotation === 0) {
+                assert.ok(numTriangles === expectedTriangles, `${numTriangles} triangles when expected ${expectedTriangles}`);
+            }
+
+            if (expectedTriangles > 0) {
+                assert.ok(err <= expectedDeviation, `deviation ${err} <= ${expectedDeviation}`);
+            }
+        });
+    }
 }
 
 test('infinite-loop', () => {