From 696b299020044f712a30056416a0a4c90a301fec Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Philippe=20Rivi=C3=A8re?= <fil@rezo.net>
Date: Fri, 30 Aug 2019 08:59:08 +0200
Subject: [PATCH] More robust orientation tests (#51)

Closes #43.

* test for issue #43 (broken hull)
* Decide the triangle orientation with a symmetric formula (in this case a majority vote)
Solves #43.
* use error-bound orientation tests
---
 index.js                   | 15 +++++++++++++--
 test/fixtures/issue43.json |  7 +++++++
 test/test.js               | 21 +++++++++++++++++++--
 3 files changed, 39 insertions(+), 4 deletions(-)
 create mode 100644 test/fixtures/issue43.json

diff --git a/index.js b/index.js
index baa9cde..2a84659 100644
--- a/index.js
+++ b/index.js
@@ -378,8 +378,19 @@ function dist(ax, ay, bx, by) {
     return dx * dx + dy * dy;
 }
 
-function orient(px, py, qx, qy, rx, ry) {
-    return (qy - py) * (rx - qx) - (qx - px) * (ry - qy) < 0;
+// return 2d orientation sign if we're confident in it through J. Shewchuk's error bound check
+function orientIfSure(px, py, rx, ry, qx, qy) {
+    const l = (ry - py) * (qx - px);
+    const r = (rx - px) * (qy - py);
+    return Math.abs(l - r) >= 3.3306690738754716e-16 * Math.abs(l + r) ? l - r : 0;
+}
+
+// a more robust orientation test that's stable in a given triangle (to fix robustness issues)
+function orient(rx, ry, qx, qy, px, py) {
+    const sign = orientIfSure(px, py, rx, ry, qx, qy) ||
+    orientIfSure(rx, ry, qx, qy, px, py) ||
+    orientIfSure(qx, qy, px, py, rx, ry);
+    return sign < 0;
 }
 
 function inCircle(ax, ay, bx, by, cx, cy, px, py) {
diff --git a/test/fixtures/issue43.json b/test/fixtures/issue43.json
new file mode 100644
index 0000000..f4854b2
--- /dev/null
+++ b/test/fixtures/issue43.json
@@ -0,0 +1,7 @@
+[
+  [-537.7739674441619, -122.26130468750004],
+  [-495.533967444162, -183.39195703125006],
+  [-453.29396744416204, -244.5226093750001],
+  [-411.0539674441621, -305.6532617187501],
+  [-164, -122]
+]
\ No newline at end of file
diff --git a/test/test.js b/test/test.js
index 25e978a..3354cc1 100644
--- a/test/test.js
+++ b/test/test.js
@@ -4,6 +4,7 @@ import Delaunator from '../index.js';
 
 import points from './fixtures/ukraine.json';
 import issue13 from './fixtures/issue13.json';
+import issue43 from './fixtures/issue43.json';
 import issue44 from './fixtures/issue44.json';
 import robustness1 from './fixtures/robustness1.json';
 import robustness2 from './fixtures/robustness2.json';
@@ -59,13 +60,18 @@ test('issue #11', (t) => {
     t.end();
 });
 
+test('issue #13', (t) => {
+    validate(t, issue13);
+    t.end();
+});
+
 test('issue #24', (t) => {
     validate(t, [[382, 302], [382, 328], [382, 205], [623, 175], [382, 188], [382, 284], [623, 87], [623, 341], [141, 227]]);
     t.end();
 });
 
-test('issue #13', (t) => {
-    validate(t, issue13);
+test('issue #43', (t) => {
+    validate(t, issue43);
     t.end();
 });
 
@@ -114,6 +120,15 @@ test('supports custom point format', (t) => {
     t.end();
 });
 
+function orient([px, py], [rx, ry], [qx, qy]) {
+    const l = (ry - py) * (qx - px);
+    const r = (rx - px) * (qy - py);
+    return Math.abs(l - r) >= 3.3306690738754716e-16 * Math.abs(l + r) ? l - r : 0;
+}
+function convex(r, q, p) {
+    return (orient(p, r, q) || orient(r, q, p) || orient(q, p, r)) >= 0;
+}
+
 function validate(t, points, d = Delaunator.from(points)) {
     // validate halfedges
     for (let i = 0; i < d.halfedges.length; i++) {
@@ -130,6 +145,8 @@ function validate(t, points, d = Delaunator.from(points)) {
         const [x0, y0] = points[d.hull[j]];
         const [x, y] = points[d.hull[i]];
         hullAreas.push((x - x0) * (y + y0));
+        const c = convex(points[d.hull[j]], points[d.hull[(j + 1) % d.hull.length]],  points[d.hull[(j + 3) % d.hull.length]]);
+        if (!c) t.fail(`hull is not convex at ${j}`);
     }
     const hullArea = sum(hullAreas);