Merge patch-2.17.1

Patch 2.17.1

README.md

@@ -42,6 +42,7 @@ Shapes with position in space:
 - [scalar2](https://axelpale.github.io/affineplane/docs/API.html#affineplanescalar2), a second-order measure (area), `ss`
 - [scalar3](https://axelpale.github.io/affineplane/docs/API.html#affineplanescalar3), a third-order measure (volume), `sss`
 - [segment2](https://axelpale.github.io/affineplane/docs/API.html#affineplanesegment2), a line segment in 2D space, `[{x,y},{x,y}]`
+- [segment2](https://axelpale.github.io/affineplane/docs/API.html#affineplanesegment3), a line segment in 3D space, `[{x,y,z},{x,y,z}]`
 - [size2](https://axelpale.github.io/affineplane/docs/API.html#affineplanesize2), a rectangle size in 2D, `{w,h}`
 - [size3](https://axelpale.github.io/affineplane/docs/API.html#affineplanesize3), a cuboid size in 3D, `{w,h,d}`
 - [sphere2](https://axelpale.github.io/affineplane/docs/API.html#affineplanesphere2), a circle in 2D, `{x,y,r}`

docs/API.md

@@ -1,5 +1,5 @@
 <a name="top"></a>
-# Affineplane API Documentation v2.17.0
+# Affineplane API Documentation v2.17.1
 
 Welcome to affineplane API reference documentation. These docs are generated with [yamdog](https://axelpale.github.io/yamdog/).
 

lib/sphere2/collisionArea.js

@@ -29,22 +29,23 @@ module.exports = (c, cc) => {
     return 0
   }
 
-  if (d === 0) {
-    // Concentric circles. Area of the smaller is the overlap.
+  if (d + Math.min(r, rr) <= Math.max(r, rr)) {
+    // Nested circles. Area of the smaller is the overlap.
     if (r <= rr) {
       return Math.PI * r2
     }
     return Math.PI * rr2
   }
 
-  if (d > r + rr) {
+  if (d >= r + rr) {
     // Circles too distant. Just for optimization.
     return 0
   }
 
-  const area = r2 * Math.acos((d2 + r2 - rr2) / (2 * d * r)) +
-    rr2 * Math.acos((d2 + rr2 - r2) / (2 * d * rr)) -
-    0.5 * Math.sqrt((-d + r + rr) * (d + r - rr) * (d - r + rr) * (d + r + rr))
+  const acosr = Math.acos((d2 + r2 - rr2) / (2 * d * r))
+  const acosrr = Math.acos((d2 + rr2 - r2) / (2 * d * rr))
+  const dddd = (-d + r + rr) * (d + r - rr) * (d - r + rr) * (d + r + rr)
+  const area = r2 * acosr + rr2 * acosrr - 0.5 * Math.sqrt(dddd)
 
   return area
 }

package.json

@@ -1,6 +1,6 @@
 {
   "name": "affineplane",
-  "version": "2.17.0",
+  "version": "2.17.1",
   "description": "Affine geometry library for 2D and 3D spaces",
   "keywords": [
     "affine",

test/sphere2/collisionArea.test.js

@@ -1,4 +1,6 @@
 const sphere2 = require('../../lib/sphere2')
+const sqrt = Math.sqrt
+const acos = Math.acos
 
 module.exports = (ts) => {
   ts.test('case: basic collisionArea', (t) => {
@@ -25,7 +27,21 @@ module.exports = (ts) => {
       // overlap = 2 * segment
       // segment = π/3 - sqrt(3)/4
       (2 * Math.PI / 3) - Math.sqrt(3) / 2,
-      'spheres overlap'
+      'spheres overlap, sector angle < 180'
+    )
+
+    t.almostEqual(
+      sphere2.collisionArea({ x: 0, y: 0, r: 3 }, { x: 2, y: 0, r: 2 }),
+      // overlap = small circle - small circle segment + large circle segment
+      4 * Math.PI + 9 * acos(3 / 4) - 4 * acos(1 / 8) - 3 * sqrt(7) / 2,
+      'spheres overlap, sector angle > 180'
+    )
+
+    t.almostEqual(
+      sphere2.collisionArea({ x: 967, y: 485, r: 212 }, { x: 667, y: 485, r: 825 }),
+      // overlap = small circle
+      Math.PI * 212 * 212,
+      'real world numbers'
     )
 
     t.end()