From 9cf7431a0623a85f274021262a1c52307bc00c79 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Fri, 28 Apr 2023 15:56:28 +0300
Subject: [PATCH 01/21] init ray3

---
 lib/index.js            |  3 +--
 lib/ray3/copy.js        | 21 +++++++++++++++++++++
 lib/ray3/index.js       |  8 ++++++++
 test/index.test.js      |  1 +
 test/ray3/copy.test.js  | 13 +++++++++++++
 test/ray3/index.test.js | 10 ++++++++++
 6 files changed, 54 insertions(+), 2 deletions(-)
 create mode 100644 lib/ray3/copy.js
 create mode 100644 lib/ray3/index.js
 create mode 100644 test/ray3/copy.test.js
 create mode 100644 test/ray3/index.test.js

diff --git a/lib/index.js b/lib/index.js
index 7d6ef79..f8f4ac9 100644
--- a/lib/index.js
+++ b/lib/index.js
@@ -56,8 +56,7 @@ exports.point3 = require('./point3')
 
 // TODO exports.range1 = require('./range1')
 
-// TODO Ray. A line but into one direction only.
-// exports.ray3 = require('./ray3')
+exports.ray3 = require('./ray3')
 
 exports.rect2 = require('./rect2')
 exports.rect3 = require('./rect3')
diff --git a/lib/ray3/copy.js b/lib/ray3/copy.js
new file mode 100644
index 0000000..05337d5
--- /dev/null
+++ b/lib/ray3/copy.js
@@ -0,0 +1,21 @@
+module.exports = (r) => {
+  // @affineplane.ray3.copy(r)
+  //
+  // Copy ray object.
+  //
+  // Parameters
+  //   r
+  //     a ray3
+  //
+  // Return
+  //   a ray3
+  //
+  return {
+    x: r.x,
+    y: r.y,
+    z: r.z,
+    dx: r.dx,
+    dy: r.dy,
+    dz: r.dz
+  }
+}
diff --git a/lib/ray3/index.js b/lib/ray3/index.js
new file mode 100644
index 0000000..90eb937
--- /dev/null
+++ b/lib/ray3/index.js
@@ -0,0 +1,8 @@
+// @affineplane.ray3
+//
+// Ray is like a line but extends into one direction only from the origin.
+//
+// We represent ray with object { x, y, z, dx, dy, dz }
+//
+
+exports.copy = require('./copy')
diff --git a/test/index.test.js b/test/index.test.js
index 0508a72..9dc8f1b 100644
--- a/test/index.test.js
+++ b/test/index.test.js
@@ -24,6 +24,7 @@ const units = {
   'affineplane.point2': require('./point2/index.test'),
   'affineplane.point3': require('./point3/index.test'),
   'affineplane.quat4': require('./quat4/index.test'),
+  'affineplane.ray3': require('./ray3/index.test'),
   'affineplane.rect2': require('./rect2/index.test'),
   'affineplane.rect3': require('./rect3/index.test'),
   'affineplane.rot2': require('./rot2/index.test'),
diff --git a/test/ray3/copy.test.js b/test/ray3/copy.test.js
new file mode 100644
index 0000000..05930e0
--- /dev/null
+++ b/test/ray3/copy.test.js
@@ -0,0 +1,13 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: copy ray3', (t) => {
+    const r = { x: 1, y: 2, z: 3, dx: 1, dy: 2, dz: 3 }
+    const c = ray3.copy(r)
+
+    t.deepEqual(r, c, 'same content')
+    t.notEqual(r, c, 'not same object')
+
+    t.end()
+  })
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
new file mode 100644
index 0000000..4e01003
--- /dev/null
+++ b/test/ray3/index.test.js
@@ -0,0 +1,10 @@
+// A unit for each method.
+const units = {
+  copy: require('./copy.test')
+}
+
+module.exports = (t) => {
+  Object.keys(units).forEach((unitName) => {
+    t.test('affineplane.ray3.' + unitName, units[unitName])
+  })
+}

From 48ae6d5fcc25b3340f458bc1f06c096f4d28144e Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:27:11 +0300
Subject: [PATCH 02/21] implement ray3.create

---
 lib/ray3/create.js       | 23 +++++++++++++++++++++++
 lib/ray3/index.js        |  1 +
 test/ray3/create.test.js | 13 +++++++++++++
 test/ray3/index.test.js  |  3 ++-
 4 files changed, 39 insertions(+), 1 deletion(-)
 create mode 100644 lib/ray3/create.js
 create mode 100644 test/ray3/create.test.js

diff --git a/lib/ray3/create.js b/lib/ray3/create.js
new file mode 100644
index 0000000..0bd6e3e
--- /dev/null
+++ b/lib/ray3/create.js
@@ -0,0 +1,23 @@
+module.exports = (origin, span) => {
+  // @affineplane.ray3.create(origin, span)
+  //
+  // Create a ray object from origin point and a spanning vector.
+  //
+  // Parameters
+  //   origin
+  //     a point3, the ray starting point.
+  //   span
+  //     a dir3 or vec3, the ray direction and unit length along the ray.
+  //
+  // Return
+  //   a ray3
+  //
+  return {
+    x: origin.x,
+    y: origin.y,
+    z: origin.z,
+    dx: span.x,
+    dy: span.y,
+    dz: span.z
+  }
+}
diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index 90eb937..2167757 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -6,3 +6,4 @@
 //
 
 exports.copy = require('./copy')
+exports.create = require('./create')
diff --git a/test/ray3/create.test.js b/test/ray3/create.test.js
new file mode 100644
index 0000000..4530d37
--- /dev/null
+++ b/test/ray3/create.test.js
@@ -0,0 +1,13 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: create ray3', (t) => {
+    const origin = { x: 1, y: 2, z: 3 }
+    const span = { x: 1, y: 2, z: 3 }
+    const r = ray3.create(origin, span)
+
+    t.deepEqual(r, { x: 1, y: 2, z: 3, dx: 1, dy: 2, dz: 3 }, 'same values')
+
+    t.end()
+  })
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index 4e01003..baf9ffd 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -1,6 +1,7 @@
 // A unit for each method.
 const units = {
-  copy: require('./copy.test')
+  copy: require('./copy.test'),
+  create: require('./create.test')
 }
 
 module.exports = (t) => {

From 815b229a2efdaf79bb79455b9f961b80b3d505a4 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:35:56 +0300
Subject: [PATCH 03/21] implement ray3.validate

---
 lib/ray3/index.js          |  1 +
 lib/ray3/validate.js       | 37 +++++++++++++++++++++++++++++++++++++
 test/ray3/index.test.js    |  3 ++-
 test/ray3/validate.test.js | 35 +++++++++++++++++++++++++++++++++++
 4 files changed, 75 insertions(+), 1 deletion(-)
 create mode 100644 lib/ray3/validate.js
 create mode 100644 test/ray3/validate.test.js

diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index 2167757..a852479 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -7,3 +7,4 @@
 
 exports.copy = require('./copy')
 exports.create = require('./create')
+exports.validate = require('./validate')
diff --git a/lib/ray3/validate.js b/lib/ray3/validate.js
new file mode 100644
index 0000000..e7becf1
--- /dev/null
+++ b/lib/ray3/validate.js
@@ -0,0 +1,37 @@
+module.exports = (r) => {
+  // @affineplane.ray3.validate(r)
+  //
+  // Check if object is a valid ray3.
+  //
+  // Parameter
+  //   r
+  //     an object
+  //
+  // Return
+  //   a boolean
+  //
+  if (!r) {
+    return false
+  }
+
+  if (typeof r.x !== 'number' || Number.isNaN(r.x)) {
+    return false
+  }
+  if (typeof r.y !== 'number' || Number.isNaN(r.y)) {
+    return false
+  }
+  if (typeof r.z !== 'number' || Number.isNaN(r.z)) {
+    return false
+  }
+  if (typeof r.dx !== 'number' || Number.isNaN(r.dx)) {
+    return false
+  }
+  if (typeof r.dy !== 'number' || Number.isNaN(r.dy)) {
+    return false
+  }
+  if (typeof r.dz !== 'number' || Number.isNaN(r.dz)) {
+    return false
+  }
+
+  return true
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index baf9ffd..ba0f2a9 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -1,7 +1,8 @@
 // A unit for each method.
 const units = {
   copy: require('./copy.test'),
-  create: require('./create.test')
+  create: require('./create.test'),
+  validate: require('./validate.test')
 }
 
 module.exports = (t) => {
diff --git a/test/ray3/validate.test.js b/test/ray3/validate.test.js
new file mode 100644
index 0000000..46f988d
--- /dev/null
+++ b/test/ray3/validate.test.js
@@ -0,0 +1,35 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: valid ray', (t) => {
+    t.ok(
+      ray3.validate({ x: 0, y: 1, z: 2, dx: 0, dy: 1, dz: 2 }),
+      'should be valid'
+    )
+    t.ok(
+      ray3.validate({ x: 0, y: 1, z: 2, dx: 0, dy: 1, dz: 2, r: 3 }),
+      'allow additional props'
+    )
+
+    t.end()
+  })
+
+  ts.test('case: invalid ray', (t) => {
+    t.notOk(ray3.validate(null), 'detect null')
+    t.notOk(ray3.validate({}), 'detect empty object')
+    t.notOk(
+      ray3.validate({ x: 0, y: 0, z: 0, dx: 0, dy: 0 }),
+      'detect missing prop'
+    )
+    t.notOk(
+      ray3.validate({ x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: '1' }),
+      'detect string value'
+    )
+    t.notOk(
+      ray3.validate({ x: 0, y: 0, z: NaN, dx: 0, dy: 0, dz: 0 }),
+      'detect NaN'
+    )
+
+    t.end()
+  })
+}

From b8755a847b8af21cd403c88769acc34888e44013 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:43:38 +0300
Subject: [PATCH 04/21] improve comment wording

---
 lib/helm2/almostEqual.js | 2 +-
 lib/helm3/almostEqual.js | 2 +-
 lib/vec2/almostEqual.js  | 2 +-
 lib/vec3/almostEqual.js  | 2 +-
 lib/vec4/almostEqual.js  | 2 +-
 5 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/lib/helm2/almostEqual.js b/lib/helm2/almostEqual.js
index cbce9f2..09019d5 100644
--- a/lib/helm2/almostEqual.js
+++ b/lib/helm2/almostEqual.js
@@ -41,6 +41,6 @@ module.exports = function (tr, ts, epsilon) {
   const dx = Math.abs(tr.x - ts.x)
   const dy = Math.abs(tr.y - ts.y)
 
-  // smaller-or-equal instead of smaller-than to make epsilon=0 work.
+  // smaller-or-equal instead of smaller-than to include epsilon=0.
   return da + db + dx + dy <= epsilon
 }
diff --git a/lib/helm3/almostEqual.js b/lib/helm3/almostEqual.js
index 6809389..1cd872f 100644
--- a/lib/helm3/almostEqual.js
+++ b/lib/helm3/almostEqual.js
@@ -32,6 +32,6 @@ module.exports = function (tr, ts, epsilon) {
   const dy = Math.abs(tr.y - ts.y)
   const dz = Math.abs(tr.z - ts.z)
 
-  // smaller-or-equal instead of smaller-than to make epsilon=0 work.
+  // smaller-or-equal instead of smaller-than to include epsilon=0.
   return da + db + dx + dy + dz <= epsilon
 }
diff --git a/lib/vec2/almostEqual.js b/lib/vec2/almostEqual.js
index 9062a11..8caae6e 100644
--- a/lib/vec2/almostEqual.js
+++ b/lib/vec2/almostEqual.js
@@ -24,6 +24,6 @@ module.exports = (v, w, epsilon) => {
   const dx = Math.abs(v.x - w.x)
   const dy = Math.abs(v.y - w.y)
 
-  // Use "<=" instead of "<" to make epsilon=0 work.
+  // Use "<=" instead of "<" to include epsilon=0.
   return dx + dy <= epsilon
 }
diff --git a/lib/vec3/almostEqual.js b/lib/vec3/almostEqual.js
index c794bf0..7eef7e6 100644
--- a/lib/vec3/almostEqual.js
+++ b/lib/vec3/almostEqual.js
@@ -25,6 +25,6 @@ module.exports = (v, w, epsilon) => {
   const dy = Math.abs(v.y - w.y)
   const dz = Math.abs(v.z - w.z)
 
-  // Use "<=" instead of "<" to make epsilon=0 work.
+  // Use "<=" instead of "<" to include epsilon=0.
   return dx + dy + dz <= epsilon
 }
diff --git a/lib/vec4/almostEqual.js b/lib/vec4/almostEqual.js
index 37c2ea8..a644c56 100644
--- a/lib/vec4/almostEqual.js
+++ b/lib/vec4/almostEqual.js
@@ -26,6 +26,6 @@ module.exports = (v, w, epsilon) => {
   const dz = Math.abs(v.z - w.z)
   const dw = Math.abs(v.w - w.w)
 
-  // Use "<=" instead of "<" to make epsilon=0 work.
+  // Use "<=" instead of "<" to include epsilon=0.
   return dx + dy + dz + dw <= epsilon
 }

From 83410608c1c611e8974a979ab3ea0c66a6fd0f16 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:43:55 +0300
Subject: [PATCH 05/21] implement ray3.almostEqual

---
 lib/ray3/almostEqual.js       | 34 +++++++++++++++++++++++++++++++
 lib/ray3/index.js             |  1 +
 test/ray3/almostEqual.test.js | 38 +++++++++++++++++++++++++++++++++++
 test/ray3/index.test.js       |  1 +
 4 files changed, 74 insertions(+)
 create mode 100644 lib/ray3/almostEqual.js
 create mode 100644 test/ray3/almostEqual.test.js

diff --git a/lib/ray3/almostEqual.js b/lib/ray3/almostEqual.js
new file mode 100644
index 0000000..7d09581
--- /dev/null
+++ b/lib/ray3/almostEqual.js
@@ -0,0 +1,34 @@
+const EPSILON = require('../epsilon')
+const abs = Math.abs
+
+module.exports = (r, rr, epsilon) => {
+  // @affineplane.ray3.almostEqual(r, rr[, epsilon])
+  //
+  // Test if rays are almost equal by the margin of epsilon.
+  //
+  // Parameters
+  //   r
+  //     a ray3
+  //   rr
+  //     a ray3
+  //   epsilon
+  //     Optional number, default to affineplane.epsilon.
+  //     Set to 0 for strict comparison.
+  //
+  // Return
+  //   a boolean
+  //
+  if (typeof epsilon !== 'number') {
+    epsilon = EPSILON
+  }
+
+  const dx = abs(r.x - rr.x)
+  const dy = abs(r.y - rr.y)
+  const dz = abs(r.z - rr.z)
+  const ddx = abs(r.dx - rr.dx)
+  const ddy = abs(r.dy - rr.dy)
+  const ddz = abs(r.dz - rr.dz)
+
+  // Use "<=" instead of "<" to include epsilon=0.
+  return dx + dy + dz + ddx + ddy + ddz <= epsilon
+}
diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index a852479..f25331b 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -5,6 +5,7 @@
 // We represent ray with object { x, y, z, dx, dy, dz }
 //
 
+exports.almostEqual = require('./almostEqual')
 exports.copy = require('./copy')
 exports.create = require('./create')
 exports.validate = require('./validate')
diff --git a/test/ray3/almostEqual.test.js b/test/ray3/almostEqual.test.js
new file mode 100644
index 0000000..e4c4f8b
--- /dev/null
+++ b/test/ray3/almostEqual.test.js
@@ -0,0 +1,38 @@
+const affineplane = require('../../index')
+const ray3 = affineplane.ray3
+
+module.exports = (ts) => {
+  ts.test('case: almost equal ray', (t) => {
+    t.ok(
+      ray3.almostEqual(
+        { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 0 },
+        { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 0 }
+      ),
+      'zero ray'
+    )
+    t.ok(
+      ray3.almostEqual(
+        { x: 1, y: 2, z: 3, dx: 1, dy: 2, dz: 3 },
+        { x: 1, y: 2, z: 3, dx: 1, dy: 2, dz: 3, r: 4 }
+      ),
+      'allow additional properties'
+    )
+    t.notOk(
+      ray3.almostEqual(
+        { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 0 },
+        { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 1 }
+      ),
+      'different rays'
+    )
+    t.ok(
+      ray3.almostEqual(
+        { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 0 },
+        { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 1 },
+        1
+      ),
+      'different rays but within tolerance'
+    )
+
+    t.end()
+  })
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index ba0f2a9..a27f097 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -1,5 +1,6 @@
 // A unit for each method.
 const units = {
+  almostEqual: require('./almostEqual.test'),
   copy: require('./copy.test'),
   create: require('./create.test'),
   validate: require('./validate.test')

From 7ec063c0c022a668537be2d67f068b196c2b47c3 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:52:02 +0300
Subject: [PATCH 06/21] implement ray3 .getOrigin .getVector

---
 lib/ray3/getOrigin.js       | 19 +++++++++++++++++++
 lib/ray3/getVector.js       | 18 ++++++++++++++++++
 lib/ray3/index.js           |  2 ++
 test/ray3/getOrigin.test.js | 12 ++++++++++++
 test/ray3/getVector.test.js | 12 ++++++++++++
 test/ray3/index.test.js     |  2 ++
 6 files changed, 65 insertions(+)
 create mode 100644 lib/ray3/getOrigin.js
 create mode 100644 lib/ray3/getVector.js
 create mode 100644 test/ray3/getOrigin.test.js
 create mode 100644 test/ray3/getVector.test.js

diff --git a/lib/ray3/getOrigin.js b/lib/ray3/getOrigin.js
new file mode 100644
index 0000000..34f4476
--- /dev/null
+++ b/lib/ray3/getOrigin.js
@@ -0,0 +1,19 @@
+module.exports = (r) => {
+  // @affineplane.ray3.getOrigin(r)
+  //
+  // Get the origin point of the ray. Note that you can also use the ray
+  // object itself as a point.
+  //
+  // Parameters
+  //   r
+  //     a ray3
+  //
+  // Return
+  //   a point3
+  //
+  return {
+    x: r.x,
+    y: r.y,
+    z: r.z
+  }
+}
diff --git a/lib/ray3/getVector.js b/lib/ray3/getVector.js
new file mode 100644
index 0000000..ef0af58
--- /dev/null
+++ b/lib/ray3/getVector.js
@@ -0,0 +1,18 @@
+module.exports = (r) => {
+  // @affineplane.ray3.getVector(r)
+  //
+  // Get the spanning vector of the ray.
+  //
+  // Parameters
+  //   r
+  //     a ray3
+  //
+  // Return
+  //   a vec3
+  //
+  return {
+    x: r.dx,
+    y: r.dy,
+    z: r.dz
+  }
+}
diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index f25331b..dc86ed1 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -8,4 +8,6 @@
 exports.almostEqual = require('./almostEqual')
 exports.copy = require('./copy')
 exports.create = require('./create')
+exports.getOrigin = require('./getOrigin')
+exports.getVector = require('./getVector')
 exports.validate = require('./validate')
diff --git a/test/ray3/getOrigin.test.js b/test/ray3/getOrigin.test.js
new file mode 100644
index 0000000..c9c6767
--- /dev/null
+++ b/test/ray3/getOrigin.test.js
@@ -0,0 +1,12 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: get ray3 origin', (t) => {
+    const r = { x: 1, y: 2, z: 3, dx: 4, dy: 5, dz: 6 }
+    const p = ray3.getOrigin(r)
+
+    t.deepEqual(p, { x: 1, y: 2, z: 3 }, 'should be a point')
+
+    t.end()
+  })
+}
diff --git a/test/ray3/getVector.test.js b/test/ray3/getVector.test.js
new file mode 100644
index 0000000..e477b29
--- /dev/null
+++ b/test/ray3/getVector.test.js
@@ -0,0 +1,12 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: get ray3 vector', (t) => {
+    const r = { x: 1, y: 2, z: 3, dx: 4, dy: 5, dz: 6 }
+    const v = ray3.getVector(r)
+
+    t.deepEqual(v, { x: 4, y: 5, z: 6 }, 'should be a vector')
+
+    t.end()
+  })
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index a27f097..8863e0d 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -3,6 +3,8 @@ const units = {
   almostEqual: require('./almostEqual.test'),
   copy: require('./copy.test'),
   create: require('./create.test'),
+  getOrigin: require('./getOrigin.test'),
+  getVector: require('./getVector.test'),
   validate: require('./validate.test')
 }
 

From 4b7cf9791f272629a11b2c34cc82f694faee03ab Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:53:30 +0300
Subject: [PATCH 07/21] lint vec3.invert

---
 lib/vec3/invert.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/vec3/invert.js b/lib/vec3/invert.js
index 5d87ed7..c02486f 100644
--- a/lib/vec3/invert.js
+++ b/lib/vec3/invert.js
@@ -1,4 +1,4 @@
-module.exports = (v, w) => {
+module.exports = (v) => {
   // @affineplane.vec3.invert(v)
   // @affineplane.vec3.negate
   //

From 53d34025a043716873fdd99170e26b7a8bcd3114 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 13:59:05 +0300
Subject: [PATCH 08/21] implement ray3.invert

---
 lib/ray3/index.js        |  2 ++
 lib/ray3/invert.js       | 22 ++++++++++++++++++++++
 test/ray3/index.test.js  |  1 +
 test/ray3/invert.test.js | 16 ++++++++++++++++
 4 files changed, 41 insertions(+)
 create mode 100644 lib/ray3/invert.js
 create mode 100644 test/ray3/invert.test.js

diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index dc86ed1..445e2c2 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -10,4 +10,6 @@ exports.copy = require('./copy')
 exports.create = require('./create')
 exports.getOrigin = require('./getOrigin')
 exports.getVector = require('./getVector')
+exports.invert = require('./invert')
+exports.negate = exports.invert
 exports.validate = require('./validate')
diff --git a/lib/ray3/invert.js b/lib/ray3/invert.js
new file mode 100644
index 0000000..1439838
--- /dev/null
+++ b/lib/ray3/invert.js
@@ -0,0 +1,22 @@
+module.exports = (r) => {
+  // @affineplane.ray3.invert(r)
+  // @affineplane.ray3.negate
+  //
+  // Get a ray with the same magnitude but to opposite direction.
+  //
+  // Parameters:
+  //   r
+  //     a ray3
+  //
+  // Return
+  //   a ray3
+  //
+  return {
+    x: r.x,
+    y: r.y,
+    z: r.z,
+    dx: -r.dx,
+    dy: -r.dy,
+    dz: -r.dz
+  }
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index 8863e0d..422d47f 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -5,6 +5,7 @@ const units = {
   create: require('./create.test'),
   getOrigin: require('./getOrigin.test'),
   getVector: require('./getVector.test'),
+  invert: require('./invert.test'),
   validate: require('./validate.test')
 }
 
diff --git a/test/ray3/invert.test.js b/test/ray3/invert.test.js
new file mode 100644
index 0000000..ac48055
--- /dev/null
+++ b/test/ray3/invert.test.js
@@ -0,0 +1,16 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: negate ray', (t) => {
+    const r = { x: 1, y: 2, z: 3, dx: 4, dy: 5, dz: 6 }
+    t.deepEqual(
+      ray3.invert(r),
+      { x: 1, y: 2, z: 3, dx: -4, dy: -5, dz: -6 },
+      'should negate only span'
+    )
+
+    t.deepEqual(ray3.negate(r), ray3.invert(r), 'should have alias')
+
+    t.end()
+  })
+}

From 402eb164b4ac055a864b84af0ea42f6ca4aaa54d Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 14:34:18 +0300
Subject: [PATCH 09/21] detect zero ray3 span in validation

---
 lib/ray3/validate.js       | 22 +++++++++++++++-------
 test/ray3/validate.test.js |  8 ++++++--
 2 files changed, 21 insertions(+), 9 deletions(-)

diff --git a/lib/ray3/validate.js b/lib/ray3/validate.js
index e7becf1..1320457 100644
--- a/lib/ray3/validate.js
+++ b/lib/ray3/validate.js
@@ -1,7 +1,12 @@
+const EPSILON = require('../epsilon')
+const abs = Math.abs
+const isNaN = Number.isNaN
+
 module.exports = (r) => {
   // @affineplane.ray3.validate(r)
   //
-  // Check if object is a valid ray3.
+  // Check if object is a valid ray3. Valid ray has numeric properties
+  // x, y, z, dx, dy, dz and has non-zero spanning vector.
   //
   // Parameter
   //   r
@@ -14,22 +19,25 @@ module.exports = (r) => {
     return false
   }
 
-  if (typeof r.x !== 'number' || Number.isNaN(r.x)) {
+  if (typeof r.x !== 'number' || isNaN(r.x)) {
+    return false
+  }
+  if (typeof r.y !== 'number' || isNaN(r.y)) {
     return false
   }
-  if (typeof r.y !== 'number' || Number.isNaN(r.y)) {
+  if (typeof r.z !== 'number' || isNaN(r.z)) {
     return false
   }
-  if (typeof r.z !== 'number' || Number.isNaN(r.z)) {
+  if (typeof r.dx !== 'number' || isNaN(r.dx)) {
     return false
   }
-  if (typeof r.dx !== 'number' || Number.isNaN(r.dx)) {
+  if (typeof r.dy !== 'number' || isNaN(r.dy)) {
     return false
   }
-  if (typeof r.dy !== 'number' || Number.isNaN(r.dy)) {
+  if (typeof r.dz !== 'number' || isNaN(r.dz)) {
     return false
   }
-  if (typeof r.dz !== 'number' || Number.isNaN(r.dz)) {
+  if (abs(r.dx) + abs(r.dy) + abs(r.dz) < EPSILON) {
     return false
   }
 
diff --git a/test/ray3/validate.test.js b/test/ray3/validate.test.js
index 46f988d..4b30462 100644
--- a/test/ray3/validate.test.js
+++ b/test/ray3/validate.test.js
@@ -18,7 +18,7 @@ module.exports = (ts) => {
     t.notOk(ray3.validate(null), 'detect null')
     t.notOk(ray3.validate({}), 'detect empty object')
     t.notOk(
-      ray3.validate({ x: 0, y: 0, z: 0, dx: 0, dy: 0 }),
+      ray3.validate({ x: 0, y: 0, z: 0, dx: 1, dy: 0 }),
       'detect missing prop'
     )
     t.notOk(
@@ -26,9 +26,13 @@ module.exports = (ts) => {
       'detect string value'
     )
     t.notOk(
-      ray3.validate({ x: 0, y: 0, z: NaN, dx: 0, dy: 0, dz: 0 }),
+      ray3.validate({ x: 0, y: 0, z: NaN, dx: 1, dy: 0, dz: 0 }),
       'detect NaN'
     )
+    t.notOk(
+      ray3.validate({ x: 1, y: 1, z: 1, dx: 0, dy: 0, dz: 0 }),
+      'detect singular'
+    )
 
     t.end()
   })

From 391d490a46b2feacd21cf65a00ad01729945cb55 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 14:52:57 +0300
Subject: [PATCH 10/21] implement ray3 .transitFrom .transitTo

---
 lib/ray3/index.js             | 14 ++++++++++
 lib/ray3/transitFrom.js       | 29 ++++++++++++++++++++
 lib/ray3/transitTo.js         | 22 +++++++++++++++
 test/ray3/index.test.js       |  2 ++
 test/ray3/transitFrom.test.js | 50 +++++++++++++++++++++++++++++++++++
 test/ray3/transitTo.test.js   | 44 ++++++++++++++++++++++++++++++
 6 files changed, 161 insertions(+)
 create mode 100644 lib/ray3/transitFrom.js
 create mode 100644 lib/ray3/transitTo.js
 create mode 100644 test/ray3/transitFrom.test.js
 create mode 100644 test/ray3/transitTo.test.js

diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index 445e2c2..1f9a545 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -5,6 +5,18 @@
 // We represent ray with object { x, y, z, dx, dy, dz }
 //
 
+// @affineplane.ray3.ZERO
+//
+// Invalid ray with origin at zero and zero spanning vector.
+//
+exports.ZERO = { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 0 }
+
+// @affineplane.ray3.DEFAULT
+//
+// Default ray that has origin at zero and unit span along positive x-axis.
+//
+exports.DEFAULT = { x: 0, y: 0, z: 0, dx: 1, dy: 0, dz: 0 }
+
 exports.almostEqual = require('./almostEqual')
 exports.copy = require('./copy')
 exports.create = require('./create')
@@ -12,4 +24,6 @@ exports.getOrigin = require('./getOrigin')
 exports.getVector = require('./getVector')
 exports.invert = require('./invert')
 exports.negate = exports.invert
+exports.transitFrom = require('./transitFrom')
+exports.transitTo = require('./transitTo')
 exports.validate = require('./validate')
diff --git a/lib/ray3/transitFrom.js b/lib/ray3/transitFrom.js
new file mode 100644
index 0000000..0707c74
--- /dev/null
+++ b/lib/ray3/transitFrom.js
@@ -0,0 +1,29 @@
+module.exports = (ray, basis) => {
+  // @affineplane.ray3.transitFrom(ray, basis)
+  //
+  // Represent the ray in the reference basis without losing information.
+  //
+  // Parameters:
+  //   ray
+  //     a ray3, represented in the given basis.
+  //   basis
+  //     a plane3, represented in the reference basis.
+  //
+  // Return:
+  //   a ray3, represented in the reference basis.
+  //
+
+  // The basis is a mapping from itself to the reference basis.
+  const ba = basis.a
+  const bb = basis.b
+  const bm = Math.sqrt(ba * ba + bb * bb)
+
+  return {
+    x: ba * ray.x - bb * ray.y + basis.x,
+    y: bb * ray.x + ba * ray.y + basis.y,
+    z: bm * ray.z + basis.z,
+    dx: ba * ray.dx - bb * ray.dy,
+    dy: bb * ray.dx + ba * ray.dy,
+    dz: bm * ray.dz
+  }
+}
diff --git a/lib/ray3/transitTo.js b/lib/ray3/transitTo.js
new file mode 100644
index 0000000..28d12ee
--- /dev/null
+++ b/lib/ray3/transitTo.js
@@ -0,0 +1,22 @@
+const invert = require('../helm3/invert')
+const transitFrom = require('./transitFrom')
+
+module.exports = (ray, basis) => {
+  // @affineplane.ray3.transitTo(ray, basis)
+  //
+  // Represent the ray in another basis
+  // without losing information.
+  //
+  // Parameters:
+  //   ray
+  //     a ray3, represented in the reference basis.
+  //   basis
+  //     a plane3, represented in the reference basis.
+  //
+  // Return:
+  //   a ray3, represented in the given basis.
+  //
+
+  const ibasis = invert(basis)
+  return transitFrom(ray, ibasis)
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index 422d47f..ca956ab 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -6,6 +6,8 @@ const units = {
   getOrigin: require('./getOrigin.test'),
   getVector: require('./getVector.test'),
   invert: require('./invert.test'),
+  transitFrom: require('./transitFrom.test'),
+  transitTo: require('./transitTo.test'),
   validate: require('./validate.test')
 }
 
diff --git a/test/ray3/transitFrom.test.js b/test/ray3/transitFrom.test.js
new file mode 100644
index 0000000..327422c
--- /dev/null
+++ b/test/ray3/transitFrom.test.js
@@ -0,0 +1,50 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: trivial', (t) => {
+    const basis = { a: 1, b: 0, x: 0, y: 0, z: 0 }
+
+    t.deepEqual(
+      ray3.transitFrom(ray3.ZERO, basis),
+      ray3.ZERO,
+      'zero ray stays zero'
+    )
+    t.deepEqual(
+      ray3.transitFrom({ x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 }, basis),
+      { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 },
+      'ones ray'
+    )
+
+    t.end()
+  })
+
+  ts.test('case: basic', (t) => {
+    let ray, basis
+
+    ray = { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 }
+    basis = { a: 1, b: 0, x: 1, y: 1, z: 1 }
+    t.deepEqual(
+      ray3.transitFrom(ray, basis),
+      { x: 2, y: 2, z: 2, dx: 1, dy: 1, dz: 1 },
+      'translation affects only origin'
+    )
+
+    ray = { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 }
+    basis = { a: 2, b: 0, x: 1, y: 1, z: 1 }
+    t.deepEqual(
+      ray3.transitFrom(ray, basis),
+      { x: 3, y: 3, z: 3, dx: 2, dy: 2, dz: 2 },
+      'scaling affects both'
+    )
+
+    ray = { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 }
+    basis = { a: 0, b: 2, x: 1, y: 1, z: 1 }
+    t.deepEqual(
+      ray3.transitFrom(ray, basis),
+      { x: -1, y: 3, z: 3, dx: -2, dy: 2, dz: 2 },
+      'rotation affects both'
+    )
+
+    t.end()
+  })
+}
diff --git a/test/ray3/transitTo.test.js b/test/ray3/transitTo.test.js
new file mode 100644
index 0000000..d9e1cad
--- /dev/null
+++ b/test/ray3/transitTo.test.js
@@ -0,0 +1,44 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: trivial trasitTo', (t) => {
+    const basis = { a: 1, b: 0, x: 0, y: 0, z: 0 }
+
+    t.deepEqual(
+      ray3.transitTo(ray3.ZERO, basis),
+      ray3.ZERO,
+      'identity basis should not affect zero ray'
+    )
+
+    const ray = { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 }
+    t.deepEqual(
+      ray3.transitTo(ray, basis),
+      ray,
+      'identity basis should not affect ray'
+    )
+
+    t.end()
+  })
+
+  ts.test('case: basic transitTo', (t) => {
+    let ray, basis
+
+    ray = { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 }
+    basis = { a: 1, b: 0, x: 1, y: 1, z: 1 }
+    t.deepEqual(
+      ray3.transitTo(ray, basis),
+      { x: 0, y: 0, z: 0, dx: 1, dy: 1, dz: 1 },
+      'translation does not affect ray direction'
+    )
+
+    ray = { x: 3, y: 3, z: 3, dx: 2, dy: 2, dz: 2 }
+    basis = { a: 2, b: 0, x: 1, y: 1, z: 1 }
+    t.deepEqual(
+      ray3.transitTo(ray, basis),
+      { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: 1 },
+      'scaling preserves ray direction'
+    )
+
+    t.end()
+  })
+}

From b05726885f7879c3ac3ec152d47831370cbc9a2b Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 15:28:12 +0300
Subject: [PATCH 11/21] implement ray3 .homothety

---
 lib/ray3/homothety.js       | 37 +++++++++++++++++++++++++++++++++++++
 lib/ray3/index.js           |  1 +
 test/ray3/homothety.test.js | 25 +++++++++++++++++++++++++
 test/ray3/index.test.js     |  1 +
 4 files changed, 64 insertions(+)
 create mode 100644 lib/ray3/homothety.js
 create mode 100644 test/ray3/homothety.test.js

diff --git a/lib/ray3/homothety.js b/lib/ray3/homothety.js
new file mode 100644
index 0000000..5d47601
--- /dev/null
+++ b/lib/ray3/homothety.js
@@ -0,0 +1,37 @@
+const EPSILON = require('../epsilon')
+
+module.exports = (ray, origin, ratio) => {
+  // @affineplane.ray3.homothety(ray, origin, ratio)
+  //
+  // Perform a homothety about the origin for the ray.
+  //
+  // Parameters:
+  //   ray
+  //     a ray3
+  //   origin
+  //     a point3
+  //   ratio
+  //     a number, the scaling ratio
+  //
+  // Return:
+  //   a ray3
+  //
+
+  const dx = (ray.x - origin.x)
+  const dy = (ray.y - origin.y)
+  const dz = (ray.z - origin.z)
+
+  // If the ray origin does not move, then the span should not scale.
+  if (dx * dx + dy * dy + dz * dz < EPSILON) {
+    return ray
+  }
+
+  return {
+    x: origin.x + dx * ratio,
+    y: origin.y + dy * ratio,
+    z: origin.z + dz * ratio,
+    dx: ray.dx * ratio,
+    dy: ray.dy * ratio,
+    dz: ray.dz * ratio
+  }
+}
diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index 1f9a545..acddf8e 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -22,6 +22,7 @@ exports.copy = require('./copy')
 exports.create = require('./create')
 exports.getOrigin = require('./getOrigin')
 exports.getVector = require('./getVector')
+exports.homothety = require('./homothety')
 exports.invert = require('./invert')
 exports.negate = exports.invert
 exports.transitFrom = require('./transitFrom')
diff --git a/test/ray3/homothety.test.js b/test/ray3/homothety.test.js
new file mode 100644
index 0000000..815c181
--- /dev/null
+++ b/test/ray3/homothety.test.js
@@ -0,0 +1,25 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: ray homothety', (t) => {
+    let ray, center
+
+    ray = { x: 1, y: 1, z: 1, dx: 1, dy: 0, dz: 0 }
+    center = { x: 1, y: 1, z: 1 }
+    t.deepEqual(
+      ray3.homothety(ray, center, 3),
+      { x: 1, y: 1, z: 1, dx: 1, dy: 0, dz: 0 },
+      'identical origin should not scale vector'
+    )
+
+    ray = { x: 1, y: 0, z: 0, dx: 1, dy: 0, dz: 0 }
+    center = { x: 0, y: 0, z: 0 }
+    t.deepEqual(
+      ray3.homothety(ray, center, 2),
+      { x: 2, y: 0, z: 0, dx: 2, dy: 0, dz: 0 },
+      'double about zero'
+    )
+
+    t.end()
+  })
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index ca956ab..d9a47ad 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -5,6 +5,7 @@ const units = {
   create: require('./create.test'),
   getOrigin: require('./getOrigin.test'),
   getVector: require('./getVector.test'),
+  homothety: require('./homothety.test'),
   invert: require('./invert.test'),
   transitFrom: require('./transitFrom.test'),
   transitTo: require('./transitTo.test'),

From 72e2af74807e1b6aca00e1dd0741416c901d2a5a Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 17:47:41 +0300
Subject: [PATCH 12/21] implement point3.distanceToLine

---
 lib/point3/distanceToLine.js       | 57 ++++++++++++++++++++++++++++++
 lib/point3/index.js                |  1 +
 test/point3/distanceToLine.test.js | 41 +++++++++++++++++++++
 test/point3/index.test.js          |  1 +
 4 files changed, 100 insertions(+)
 create mode 100644 lib/point3/distanceToLine.js
 create mode 100644 test/point3/distanceToLine.test.js

diff --git a/lib/point3/distanceToLine.js b/lib/point3/distanceToLine.js
new file mode 100644
index 0000000..5afcc40
--- /dev/null
+++ b/lib/point3/distanceToLine.js
@@ -0,0 +1,57 @@
+const epsilon = require('../epsilon')
+
+module.exports = (p, line) => {
+  // @affineplane.point3.distanceToLine(p, line)
+  //
+  // Compute the smallest euclidean distance between a point and a line.
+  // See also affineplane.point3.distanceToRay.
+  //
+  // Parameters
+  //   p
+  //     a point3
+  //   line
+  //     a line3
+  //
+  // Return
+  //   a number, a scalar1, a dist3, a distance
+  //
+
+  // See the commented lines for algebraic solution with function calls.
+  // After the commented lines, we have opened the function calls
+  // and removed unnecessary square roots and vectorization.
+
+  // // Get vector from line origin to the point
+  // const av = pointDiff(line.origin, p)
+  // // Project the vector to the line
+  // const bv = vectorProject(av, line.span)
+  // // Magnitudes
+  // const am = vectorMagn(av)
+  // const bm = vectorMagn(bv)
+  // // Apply pythagoras to find the distance
+  // return Math.sqrt(am * am - bm * bm)
+
+  // Extract the line
+  const lp = line.origin
+  const xs = line.span.x
+  const ys = line.span.y
+  const zs = line.span.z
+  // Get vector va from line origin to the given point.
+  const xa = p.x - lp.x
+  const ya = p.y - lp.y
+  const za = p.z - lp.z
+  // Get va's magnitude squared
+  const ma2 = xa * xa + ya * ya + za * za
+  // Project va to the line to get vector vb and get its magnitude squared.
+  const adots = xa * xs + ya * ys + za * zs
+  const sdots = xs * xs + ys * ys + zs * zs
+  let mb2
+  if (sdots < epsilon) {
+    // The line has zero span.
+    // Assume vectors perpendicular, thus vb has zero magnitude.
+    mb2 = 0
+  } else {
+    mb2 = adots * adots / sdots
+  }
+  // Apply pythagoras to find the distance
+  return Math.sqrt(ma2 - mb2)
+}
diff --git a/lib/point3/index.js b/lib/point3/index.js
index 2bba710..6133d80 100644
--- a/lib/point3/index.js
+++ b/lib/point3/index.js
@@ -17,6 +17,7 @@ exports.diff = exports.delta
 exports.difference = exports.delta
 exports.direction = require('./direction')
 exports.distance = require('./distance')
+exports.distanceToLine = require('./distanceToLine')
 exports.distanceToPlane = require('./distanceToPlane')
 exports.equal = require('./equal')
 exports.equals = exports.equal
diff --git a/test/point3/distanceToLine.test.js b/test/point3/distanceToLine.test.js
new file mode 100644
index 0000000..b8a0fd4
--- /dev/null
+++ b/test/point3/distanceToLine.test.js
@@ -0,0 +1,41 @@
+const point3 = require('../../lib/point3')
+
+module.exports = (ts) => {
+  ts.test('case: distance to line', (t) => {
+    let point, line
+
+    point = { x: 0, y: 0, z: 0 }
+    line = { origin: { x: 0, y: 0, z: 0 }, span: { x: 1, y: 0, z: 0 } }
+    t.equal(
+      point3.distanceToLine(point, line),
+      0,
+      'trivial zero distance'
+    )
+
+    point = { x: 0, y: 1, z: 0 }
+    line = { origin: { x: 0, y: 0, z: 0 }, span: { x: 1, y: 0, z: 0 } }
+    t.equal(
+      point3.distanceToLine(point, line),
+      1,
+      'simple distance along y'
+    )
+
+    point = { x: 5, y: 5, z: 0 }
+    line = { origin: { x: 10, y: 0, z: 0 }, span: { x: 0, y: 2, z: 0 } }
+    t.almostEqual(
+      point3.distanceToLine(point, line),
+      5,
+      'distance along x'
+    )
+
+    point = { x: 5, y: 5, z: 0 }
+    line = { origin: { x: 0, y: 0, z: 2 }, span: { x: 2, y: 2, z: 0 } }
+    t.almostEqual(
+      point3.distanceToLine(point, line),
+      2,
+      'distance along z'
+    )
+
+    t.end()
+  })
+}
diff --git a/test/point3/index.test.js b/test/point3/index.test.js
index b3ddf9d..87190a4 100644
--- a/test/point3/index.test.js
+++ b/test/point3/index.test.js
@@ -6,6 +6,7 @@ const units = {
   difference: require('./difference.test'),
   direction: require('./direction.test'),
   distance: require('./distance.test'),
+  distanceToLine: require('./distanceToLine.test'),
   distanceToPlane: require('./distanceToPlane.test'),
   equal: require('./equal.test'),
   fromArray: require('./fromArray.test'),

From 57990bca5a04f98b784d526262fb19eec27a5df9 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:08:44 +0300
Subject: [PATCH 13/21] implement point3.distanceToRay

---
 lib/point3/distanceToLine.js      |  1 +
 lib/point3/distanceToRay.js       | 52 ++++++++++++++++++++++++++++
 lib/point3/index.js               |  1 +
 test/point3/distanceToRay.test.js | 57 +++++++++++++++++++++++++++++++
 test/point3/index.test.js         |  1 +
 5 files changed, 112 insertions(+)
 create mode 100644 lib/point3/distanceToRay.js
 create mode 100644 test/point3/distanceToRay.test.js

diff --git a/lib/point3/distanceToLine.js b/lib/point3/distanceToLine.js
index 5afcc40..5f7590e 100644
--- a/lib/point3/distanceToLine.js
+++ b/lib/point3/distanceToLine.js
@@ -19,6 +19,7 @@ module.exports = (p, line) => {
   // See the commented lines for algebraic solution with function calls.
   // After the commented lines, we have opened the function calls
   // and removed unnecessary square roots and vectorization.
+  // Note that distanceToRay uses similar approach.
 
   // // Get vector from line origin to the point
   // const av = pointDiff(line.origin, p)
diff --git a/lib/point3/distanceToRay.js b/lib/point3/distanceToRay.js
new file mode 100644
index 0000000..e322663
--- /dev/null
+++ b/lib/point3/distanceToRay.js
@@ -0,0 +1,52 @@
+const epsilon = require('../epsilon')
+
+module.exports = (p, ray) => {
+  // @affineplane.point3.distanceToRay(p, ray)
+  //
+  // Compute the smallest euclidean distance between a point and a ray.
+  // For half of the space, the closest point on the ray is the ray origin
+  // and therefore, for points inside that half, the computation reduces
+  // to the euclidean distance to the ray origin.
+  // See also affineplane.point3.distanceToLine.
+  //
+  // Parameters
+  //   p
+  //     a point3
+  //   ray
+  //     a ray3
+  //
+  // Return
+  //   a number, a scalar1, a dist3, a distance
+  //
+
+  // See distanceToLine for math derivation.
+
+  // Extract the ray spanning vector
+  const xs = ray.dx
+  const ys = ray.dy
+  const zs = ray.dz
+  // Get vector va from ray origin to the given point.
+  const xa = p.x - ray.x
+  const ya = p.y - ray.y
+  const za = p.z - ray.z
+  // Get va's magnitude squared
+  const ma2 = xa * xa + ya * ya + za * za
+  // Project va to the line to get vector vb and get its magnitude squared.
+  const adots = xa * xs + ya * ys + za * zs
+  // Determine if the point is on or behind the ray origin plane
+  if (adots <= 0) {
+    // Reduce to euclidean distance to the ray origin.
+    return Math.sqrt(ma2)
+  }
+  const sdots = xs * xs + ys * ys + zs * zs
+  let mb2
+  if (sdots < epsilon) {
+    // The line has zero span.
+    // Assume vectors perpendicular, thus vb has zero magnitude.
+    mb2 = 0
+  } else {
+    mb2 = adots * adots / sdots
+  }
+  // Apply pythagoras to find the distance
+  return Math.sqrt(ma2 - mb2)
+}
diff --git a/lib/point3/index.js b/lib/point3/index.js
index 6133d80..9b7c614 100644
--- a/lib/point3/index.js
+++ b/lib/point3/index.js
@@ -19,6 +19,7 @@ exports.direction = require('./direction')
 exports.distance = require('./distance')
 exports.distanceToLine = require('./distanceToLine')
 exports.distanceToPlane = require('./distanceToPlane')
+exports.distanceToRay = require('./distanceToRay')
 exports.equal = require('./equal')
 exports.equals = exports.equal
 exports.fromArray = require('./fromArray')
diff --git a/test/point3/distanceToRay.test.js b/test/point3/distanceToRay.test.js
new file mode 100644
index 0000000..5b70aa2
--- /dev/null
+++ b/test/point3/distanceToRay.test.js
@@ -0,0 +1,57 @@
+const point3 = require('../../lib/point3')
+
+module.exports = (ts) => {
+  ts.test('case: distance to ray', (t) => {
+    let point, ray
+
+    point = { x: 0, y: 0, z: 0 }
+    ray = { x: 0, y: 0, z: 0, dx: 1, dy: 0, dz: 0 }
+    t.equal(
+      point3.distanceToRay(point, ray),
+      0,
+      'trivial zero distance'
+    )
+
+    point = { x: -5, y: 0, z: 0 }
+    ray = { x: 0, y: 0, z: 0, dx: 1, dy: 0, dz: 0 }
+    t.equal(
+      point3.distanceToRay(point, ray),
+      5,
+      'point on the line but behind ray plane'
+    )
+
+    point = { x: 0, y: 1, z: 0 }
+    ray = { x: 0, y: 0, z: 0, dx: 1, dy: 0, dz: 0 }
+    t.equal(
+      point3.distanceToRay(point, ray),
+      1,
+      'simple distance along y'
+    )
+
+    point = { x: 0, y: 0, z: 0 }
+    ray = { x: 1, y: 2, z: 2, dx: 0, dy: 0, dz: 5 }
+    t.equal(
+      point3.distanceToRay(point, ray),
+      3,
+      'simple distance behind ray plane'
+    )
+
+    point = { x: 5, y: 5, z: 0 }
+    ray = { x: 10, y: 0, z: 0, dx: 0, dy: 2, dz: 0 }
+    t.almostEqual(
+      point3.distanceToRay(point, ray),
+      5,
+      'distance along x'
+    )
+
+    point = { x: 5, y: 5, z: 0 }
+    ray = { x: 0, y: 0, z: 2, dx: 2, dy: 2, dz: 0 }
+    t.almostEqual(
+      point3.distanceToRay(point, ray),
+      2,
+      'distance along z'
+    )
+
+    t.end()
+  })
+}
diff --git a/test/point3/index.test.js b/test/point3/index.test.js
index 87190a4..97582d6 100644
--- a/test/point3/index.test.js
+++ b/test/point3/index.test.js
@@ -8,6 +8,7 @@ const units = {
   distance: require('./distance.test'),
   distanceToLine: require('./distanceToLine.test'),
   distanceToPlane: require('./distanceToPlane.test'),
+  distanceToRay: require('./distanceToRay.test'),
   equal: require('./equal.test'),
   fromArray: require('./fromArray.test'),
   homothety: require('./homothety.test'),

From fa35db3bb80be97b2a3f5f85b73d2ce70e78cdf8 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:29:50 +0300
Subject: [PATCH 14/21] correct point3.offset docs

---
 lib/point3/offset.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/point3/offset.js b/lib/point3/offset.js
index 70a9869..ec3a383 100644
--- a/lib/point3/offset.js
+++ b/lib/point3/offset.js
@@ -5,7 +5,7 @@ module.exports = (p, dx, dy, dz) => {
   //
   // Parameters:
   //   p
-  //     a point2
+  //     a point3
   //   dx
   //     a number, the offset along x-axis
   //   dy

From 558870973910d783464788398b74405403bc5708 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:33:18 +0300
Subject: [PATCH 15/21] implement ray3.offset

---
 lib/ray3/index.js        |  1 +
 lib/ray3/offset.js       | 27 +++++++++++++++++++++++++++
 test/ray3/index.test.js  |  1 +
 test/ray3/offset.test.js | 12 ++++++++++++
 4 files changed, 41 insertions(+)
 create mode 100644 lib/ray3/offset.js
 create mode 100644 test/ray3/offset.test.js

diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index acddf8e..7048ffd 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -25,6 +25,7 @@ exports.getVector = require('./getVector')
 exports.homothety = require('./homothety')
 exports.invert = require('./invert')
 exports.negate = exports.invert
+exports.offset = require('./offset')
 exports.transitFrom = require('./transitFrom')
 exports.transitTo = require('./transitTo')
 exports.validate = require('./validate')
diff --git a/lib/ray3/offset.js b/lib/ray3/offset.js
new file mode 100644
index 0000000..4458b4e
--- /dev/null
+++ b/lib/ray3/offset.js
@@ -0,0 +1,27 @@
+module.exports = (ray, dx, dy, dz) => {
+  // @affineplane.ray3.offset(ray, dx, dy, dz)
+  //
+  // Offset a ray origin by scalars dx, dy, dz.
+  //
+  // Parameters:
+  //   ray
+  //     a ray3
+  //   dx
+  //     a number, the offset along x-axis
+  //   dy
+  //     a number, the offset along y-axis
+  //   dz
+  //     a number, the offset along z-axis
+  //
+  // Return
+  //   a ray3
+  //
+  return {
+    x: ray.x + dx,
+    y: ray.y + dy,
+    z: ray.z + dz,
+    dx: ray.dx,
+    dy: ray.dy,
+    dz: ray.dz
+  }
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index d9a47ad..39d463c 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -7,6 +7,7 @@ const units = {
   getVector: require('./getVector.test'),
   homothety: require('./homothety.test'),
   invert: require('./invert.test'),
+  offset: require('./offset.test'),
   transitFrom: require('./transitFrom.test'),
   transitTo: require('./transitTo.test'),
   validate: require('./validate.test')
diff --git a/test/ray3/offset.test.js b/test/ray3/offset.test.js
new file mode 100644
index 0000000..4d35ef1
--- /dev/null
+++ b/test/ray3/offset.test.js
@@ -0,0 +1,12 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: ray3 offset', (t) => {
+    t.deepEqual(ray3.offset(
+      { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 1 },
+      1, 1, 1
+    ), { x: 1, y: 1, z: 1, dx: 0, dy: 0, dz: 1 })
+
+    t.end()
+  })
+}

From be00d49c80dc574094162f1e26ffa81ff60a11b7 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:41:18 +0300
Subject: [PATCH 16/21] implement ray3.at

---
 lib/ray3/at.js          | 29 +++++++++++++++++++++++++++++
 lib/ray3/index.js       |  1 +
 test/ray3/at.test.js    | 21 +++++++++++++++++++++
 test/ray3/index.test.js |  1 +
 4 files changed, 52 insertions(+)
 create mode 100644 lib/ray3/at.js
 create mode 100644 test/ray3/at.test.js

diff --git a/lib/ray3/at.js b/lib/ray3/at.js
new file mode 100644
index 0000000..a813c63
--- /dev/null
+++ b/lib/ray3/at.js
@@ -0,0 +1,29 @@
+module.exports = (ray, c) => {
+  // @affineplane.ray3.at(line, c)
+  //
+  // Get a point on the ray at position c from the ray origin.
+  // For example, c=2 gives a point two ray spans away from the origin.
+  // Negative positions default to the ray origin.
+  //
+  // Parameters:
+  //   ray
+  //     a ray3
+  //   c
+  //     a number
+  //
+  // Return:
+  //   a point3
+  //
+  if (c <= 0) {
+    return {
+      x: ray.x,
+      y: ray.y,
+      z: ray.z
+    }
+  }
+  return {
+    x: ray.x + c * ray.dx,
+    y: ray.y + c * ray.dy,
+    z: ray.z + c * ray.dz
+  }
+}
diff --git a/lib/ray3/index.js b/lib/ray3/index.js
index 7048ffd..0c72ec3 100644
--- a/lib/ray3/index.js
+++ b/lib/ray3/index.js
@@ -18,6 +18,7 @@ exports.ZERO = { x: 0, y: 0, z: 0, dx: 0, dy: 0, dz: 0 }
 exports.DEFAULT = { x: 0, y: 0, z: 0, dx: 1, dy: 0, dz: 0 }
 
 exports.almostEqual = require('./almostEqual')
+exports.at = require('./at')
 exports.copy = require('./copy')
 exports.create = require('./create')
 exports.getOrigin = require('./getOrigin')
diff --git a/test/ray3/at.test.js b/test/ray3/at.test.js
new file mode 100644
index 0000000..12afa30
--- /dev/null
+++ b/test/ray3/at.test.js
@@ -0,0 +1,21 @@
+const ray3 = require('../../lib/ray3')
+
+module.exports = (ts) => {
+  ts.test('case: basic ray at', (t) => {
+    const ray = { x: 1, y: 1, z: 1, dx: 1, dy: 1, dz: -1 }
+
+    t.deepEqual(
+      ray3.at(ray, 3),
+      { x: 4, y: 4, z: -2 },
+      'three spans away from origin'
+    )
+
+    t.deepEqual(
+      ray3.at(ray, -3),
+      { x: 1, y: 1, z: 1 },
+      'negative position at origin'
+    )
+
+    t.end()
+  })
+}
diff --git a/test/ray3/index.test.js b/test/ray3/index.test.js
index 39d463c..82598e3 100644
--- a/test/ray3/index.test.js
+++ b/test/ray3/index.test.js
@@ -1,6 +1,7 @@
 // A unit for each method.
 const units = {
   almostEqual: require('./almostEqual.test'),
+  at: require('./at.test'),
   copy: require('./copy.test'),
   create: require('./create.test'),
   getOrigin: require('./getOrigin.test'),

From 5ac7556edfbd2a9335fd1a7db5ab2bd835f68c9a Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:54:33 +0300
Subject: [PATCH 17/21] document UNIT and ZERO constants in various geometries

---
 lib/box2/index.js    | 10 ++++++++++
 lib/box3/index.js    | 10 ++++++++++
 lib/circle3/index.js | 10 ++++++++++
 lib/point2/index.js  |  4 ++++
 lib/point3/index.js  |  4 ++++
 lib/sphere2/index.js | 10 ++++++++++
 lib/sphere3/index.js | 10 ++++++++++
 lib/vec2/index.js    |  5 +++++
 lib/vec3/index.js    |  5 +++++
 lib/vec4/index.js    |  5 +++++
 10 files changed, 73 insertions(+)

diff --git a/lib/box2/index.js b/lib/box2/index.js
index a05f6cb..e2f769b 100644
--- a/lib/box2/index.js
+++ b/lib/box2/index.js
@@ -9,7 +9,17 @@
 // - `x,y` provide origin position in the reference basis.
 // - `w,h` provide box size on the reference basis.
 //
+
+// @affineplane.box2.UNIT
+//
+// An origin-centered box with unit width and height.
+//
 exports.UNIT = { a: 1, b: 0, x: -0.5, y: -0.5, w: 1, h: 1 }
+
+// @affineplane.box2.ZERO
+//
+// A zero-size box.
+//
 exports.ZERO = { a: 1, b: 0, x: 0, y: 0, w: 0, h: 0 }
 
 exports.almostEqual = require('./almostEqual')
diff --git a/lib/box3/index.js b/lib/box3/index.js
index 1b151cd..a5bf0e7 100644
--- a/lib/box3/index.js
+++ b/lib/box3/index.js
@@ -9,7 +9,17 @@
 // - `x,y,z` provide origin position in the reference basis.
 // - `w,h,d` provide box size on the reference basis.
 //
+
+// @affineplane.box3.UNIT
+//
+// An origin-centered box with unit width, height, and depth.
+//
 exports.UNIT = { a: 1, b: 0, x: -0.5, y: -0.5, z: -0.5, w: 1, h: 1, d: 1 }
+
+// @affineplane.box3.ZERO
+//
+// A zero-size box.
+//
 exports.ZERO = { a: 1, b: 0, x: 0, y: 0, z: 0, w: 0, h: 0, d: 0 }
 
 exports.almostEqual = require('./almostEqual')
diff --git a/lib/circle3/index.js b/lib/circle3/index.js
index b417bab..715ce64 100644
--- a/lib/circle3/index.js
+++ b/lib/circle3/index.js
@@ -4,7 +4,17 @@
 //
 // Represented with an object `{ x, y, z, r }` for the origin and the radius.
 //
+
+// @affineplane.circle3.UNIT
+//
+// The unit circle, radius=1.
+//
 exports.UNIT = { x: 0, y: 0, z: 0, r: 1 }
+
+// @affineplane.circle3.ZERO
+//
+// A zero-radius circle.
+//
 exports.ZERO = { x: 0, y: 0, z: 0, r: 0 }
 
 exports.almostEqual = require('./almostEqual')
diff --git a/lib/point2/index.js b/lib/point2/index.js
index 21e7c94..fb6582a 100644
--- a/lib/point2/index.js
+++ b/lib/point2/index.js
@@ -8,6 +8,10 @@
 // ![A point](geometry_point.png)
 //
 
+// @affineplane.point2.ZERO
+//
+// The zero point
+//
 exports.ZERO = { x: 0, y: 0 }
 
 // exports.add
diff --git a/lib/point3/index.js b/lib/point3/index.js
index 9b7c614..c18bb43 100644
--- a/lib/point3/index.js
+++ b/lib/point3/index.js
@@ -5,6 +5,10 @@
 // translation of the plane on which they are represented.
 //
 
+// @affineplane.point3.ZERO
+//
+// The zero point
+//
 exports.ZERO = { x: 0, y: 0, z: 0 }
 
 exports.almostEqual = require('./almostEqual')
diff --git a/lib/sphere2/index.js b/lib/sphere2/index.js
index 40cd4d6..73e7310 100644
--- a/lib/sphere2/index.js
+++ b/lib/sphere2/index.js
@@ -5,7 +5,17 @@
 //
 // Represented with an object `{ x, y, r }` for the origin and the radius.
 //
+
+// @affineplane.sphere2.UNIT
+//
+// The unit circle, radius=1.
+//
 exports.UNIT = { x: 0, y: 0, r: 1 }
+
+// @affineplane.sphere2.ZERO
+//
+// A zero-radius circle.
+//
 exports.ZERO = { x: 0, y: 0, r: 0 }
 
 exports.almostEqual = require('./almostEqual')
diff --git a/lib/sphere3/index.js b/lib/sphere3/index.js
index 20c8d67..ed7990c 100644
--- a/lib/sphere3/index.js
+++ b/lib/sphere3/index.js
@@ -4,7 +4,17 @@
 //
 // Represented with an object `{ x, y, z, r }` for the origin and the radius.
 //
+
+// @affineplane.sphere3.UNIT
+//
+// The unit sphere, radius=1.
+//
 exports.UNIT = { x: 0, y: 0, z: 0, r: 1 }
+
+// @affineplane.sphere3.ZERO
+//
+// A zero-radius sphere.
+//
 exports.ZERO = { x: 0, y: 0, z: 0, r: 0 }
 
 exports.almostEqual = require('./almostEqual')
diff --git a/lib/vec2/index.js b/lib/vec2/index.js
index f9a8ee7..15c4395 100644
--- a/lib/vec2/index.js
+++ b/lib/vec2/index.js
@@ -6,6 +6,11 @@
 //
 // ![A vector](geometry_vector.png)
 //
+
+// @affineplane.vec2.ZERO
+//
+// The zero vector in 2D
+//
 exports.ZERO = { x: 0, y: 0 }
 
 // exports.distance
diff --git a/lib/vec3/index.js b/lib/vec3/index.js
index cfaada5..8f924cf 100644
--- a/lib/vec3/index.js
+++ b/lib/vec3/index.js
@@ -5,6 +5,11 @@
 // and therefore their coordinates are affected only by plane scale
 // and rotation when represented on different plane.
 //
+
+// @affineplane.vec3.ZERO
+//
+// The zero vector in 3D
+//
 exports.ZERO = { x: 0, y: 0, z: 0 }
 
 exports.add = require('./add')
diff --git a/lib/vec4/index.js b/lib/vec4/index.js
index a2e9f20..05556f3 100644
--- a/lib/vec4/index.js
+++ b/lib/vec4/index.js
@@ -2,6 +2,11 @@
 //
 // A vec4 is a 4D vector { x, y, z, w }.
 //
+
+// @affineplane.vec4.ZERO
+//
+// The zero vector in 4D
+//
 exports.ZERO = { x: 0, y: 0, z: 0, w: 0 }
 
 exports.add = require('./add')

From de34fc2ad4cb25abbc296be4fdbf558563bc3395 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:55:55 +0300
Subject: [PATCH 18/21] register ray3 for doc generation

---
 docs/generate.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/docs/generate.js b/docs/generate.js
index e432ec3..a9c7469 100644
--- a/docs/generate.js
+++ b/docs/generate.js
@@ -77,6 +77,7 @@ yamdog.generate({
       point3: '#affineplanepoint3',
       poly2: '#affineplanepoly2',
       quat4: '#affineplanequat4',
+      ray3: '#affineplaneray3',
       rot2: '#affineplanerot2',
       scalar1: '#affineplanescalar1',
       scalar2: '#affineplanescalar2',

From 9e1f910c83709dc1839e97cc409f612d6bcfa733 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:57:24 +0300
Subject: [PATCH 19/21] render docs

---
 docs/API.md | 467 +++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 466 insertions(+), 1 deletion(-)

diff --git a/docs/API.md b/docs/API.md
index e274427..a42297f 100644
--- a/docs/API.md
+++ b/docs/API.md
@@ -39,6 +39,7 @@ The functions are grouped in the following submodules.
 - [affineplane.point3](#affineplanepoint3)
 - [affineplane.poly2](#affineplanepoly2)
 - [affineplane.quat4](#affineplanequat4)
+- [affineplane.ray3](#affineplaneray3)
 - [affineplane.rect2](#affineplanerect2)
 - [affineplane.rect3](#affineplanerect3)
 - [affineplane.rot2](#affineplanerot2)
@@ -150,6 +151,8 @@ and thus can be represented in any basis without loss of information.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.box2.UNIT](#affineplanebox2unit)
+- [affineplane.box2.ZERO](#affineplanebox2zero)
 - [affineplane.box2.almostEqual](#affineplanebox2almostequal)
 - [affineplane.box2.at](#affineplanebox2at)
 - [affineplane.box2.atBox](#affineplanebox2atbox)
@@ -187,6 +190,34 @@ and thus can be represented in any basis without loss of information.
 
 Source: [box2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/box2/index.js)
 
+<a name="affineplanebox2unit"></a>
+## [affineplane](#affineplane).[box2](#affineplanebox2).[UNIT](#affineplanebox2unit)
+
+An origin-centered box with unit width and height.
+
+Source: [box2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/box2/index.js)
+
+<a name="affineplanebox2zero"></a>
+## [affineplane](#affineplane).[box2](#affineplanebox2).[ZERO](#affineplanebox2zero)
+
+A zero-size box.
+
+Source: [box2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/box2/index.js)
+
+<a name="affineplanebox3unit"></a>
+## [affineplane](#affineplane).[box3](#affineplanebox3).[UNIT](#affineplanebox3unit)
+
+An origin-centered box with unit width, height, and depth.
+
+Source: [box3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/box3/index.js)
+
+<a name="affineplanebox3zero"></a>
+## [affineplane](#affineplane).[box3](#affineplanebox3).[ZERO](#affineplanebox3zero)
+
+A zero-size box.
+
+Source: [box3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/box3/index.js)
+
 <a name="affineplanebox2almostequal"></a>
 ## [affineplane](#affineplane).[box2](#affineplanebox2).[almostEqual](#affineplanebox2almostequal)(b, bb[, tolerance])
 
@@ -839,6 +870,8 @@ thus can be represented in any basis without loss of information.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.box3.UNIT](#affineplanebox3unit)
+- [affineplane.box3.ZERO](#affineplanebox3zero)
 - [affineplane.box3.almostEqual](#affineplanebox3almostequal)
 - [affineplane.box3.at](#affineplanebox3at)
 - [affineplane.box3.atBox](#affineplanebox3atbox)
@@ -1483,6 +1516,8 @@ Represented with an object `{ x, y, z, r }` for the origin and the radius.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.circle3.UNIT](#affineplanecircle3unit)
+- [affineplane.circle3.ZERO](#affineplanecircle3zero)
 - [affineplane.circle3.almostEqual](#affineplanecircle3almostequal)
 - [affineplane.circle3.area](#affineplanecircle3area)
 - [affineplane.circle3.atCenter](#affineplanecircle3atcenter)
@@ -1507,6 +1542,20 @@ Represented with an object `{ x, y, z, r }` for the origin and the radius.
 - [affineplane.circle3.validate](#affineplanecircle3validate)
 
 
+Source: [circle3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/circle3/index.js)
+
+<a name="affineplanecircle3unit"></a>
+## [affineplane](#affineplane).[circle3](#affineplanecircle3).[UNIT](#affineplanecircle3unit)
+
+The unit circle, radius=1.
+
+Source: [circle3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/circle3/index.js)
+
+<a name="affineplanecircle3zero"></a>
+## [affineplane](#affineplane).[circle3](#affineplanecircle3).[ZERO](#affineplanecircle3zero)
+
+A zero-radius circle.
+
 Source: [circle3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/circle3/index.js)
 
 <a name="affineplanecircle3almostequal"></a>
@@ -6689,6 +6738,7 @@ An affine space does not have origin; `{ x:0, y:0 }` is not an origin.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.point2.ZERO](#affineplanepoint2zero)
 - [affineplane.point2.almostEqual](#affineplanepoint2almostequal)
 - [affineplane.point2.average](#affineplanepoint2average)
 - [affineplane.point2.copy](#affineplanepoint2copy)
@@ -6721,6 +6771,13 @@ An affine space does not have origin; `{ x:0, y:0 }` is not an origin.
 - [affineplane.point2.vectorTo](#affineplanepoint2vectorto)
 
 
+Source: [point2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/point2/index.js)
+
+<a name="affineplanepoint2zero"></a>
+## [affineplane](#affineplane).[point2](#affineplanepoint2).[ZERO](#affineplanepoint2zero)
+
+The zero point
+
 Source: [point2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/point2/index.js)
 
 <a name="affineplanepoint2almostequal"></a>
@@ -7266,6 +7323,7 @@ translation of the plane on which they are represented.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.point3.ZERO](#affineplanepoint3zero)
 - [affineplane.point3.almostEqual](#affineplanepoint3almostequal)
 - [affineplane.point3.average](#affineplanepoint3average)
 - [affineplane.point3.copy](#affineplanepoint3copy)
@@ -7275,7 +7333,9 @@ translation of the plane on which they are represented.
 - [affineplane.point3.difference](#affineplanepoint3difference)
 - [affineplane.point3.direction](#affineplanepoint3direction)
 - [affineplane.point3.distance](#affineplanepoint3distance)
+- [affineplane.point3.distanceToLine](#affineplanepoint3distancetoline)
 - [affineplane.point3.distanceToPlane](#affineplanepoint3distancetoplane)
+- [affineplane.point3.distanceToRay](#affineplanepoint3distancetoray)
 - [affineplane.point3.equal](#affineplanepoint3equal)
 - [affineplane.point3.equals](#affineplanepoint3equals)
 - [affineplane.point3.fromArray](#affineplanepoint3fromarray)
@@ -7298,6 +7358,13 @@ translation of the plane on which they are represented.
 - [affineplane.point3.vectorTo](#affineplanepoint3vectorto)
 
 
+Source: [point3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/point3/index.js)
+
+<a name="affineplanepoint3zero"></a>
+## [affineplane](#affineplane).[point3](#affineplanepoint3).[ZERO](#affineplanepoint3zero)
+
+The zero point
+
 Source: [point3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/point3/index.js)
 
 <a name="affineplanepoint3almostequal"></a>
@@ -7442,6 +7509,27 @@ Euclidean distance between two points.
 
 Source: [distance.js](https://github.com/axelpale/affineplane/blob/main/lib/point3/distance.js)
 
+<a name="affineplanepoint3distancetoline"></a>
+## [affineplane](#affineplane).[point3](#affineplanepoint3).[distanceToLine](#affineplanepoint3distancetoline)(p, line)
+
+Compute the smallest euclidean distance between a point and a line.
+See also [affineplane.point3.distanceToRay](#affineplanepoint3distancetoray).
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *p*
+  - a [point3](#affineplanepoint3)
+- *line*
+  - a [line3](#affineplaneline3)
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a number, a [scalar1](#affineplanescalar1), a [dist3](#affineplanedist3), a distance
+
+
+Source: [distanceToLine.js](https://github.com/axelpale/affineplane/blob/main/lib/point3/distanceToLine.js)
+
 <a name="affineplanepoint3distancetoplane"></a>
 ## [affineplane](#affineplane).[point3](#affineplanepoint3).[distanceToPlane](#affineplanepoint3distancetoplane)(p, plane)
 
@@ -7462,6 +7550,30 @@ Euclidean distance between point and plane.
 
 Source: [distanceToPlane.js](https://github.com/axelpale/affineplane/blob/main/lib/point3/distanceToPlane.js)
 
+<a name="affineplanepoint3distancetoray"></a>
+## [affineplane](#affineplane).[point3](#affineplanepoint3).[distanceToRay](#affineplanepoint3distancetoray)(p, ray)
+
+Compute the smallest euclidean distance between a point and a ray.
+For half of the space, the closest point on the ray is the ray origin
+and therefore, for points inside that half, the computation reduces
+to the euclidean distance to the ray origin.
+See also [affineplane.point3.distanceToLine](#affineplanepoint3distancetoline).
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *p*
+  - a [point3](#affineplanepoint3)
+- *ray*
+  - a [ray3](#affineplaneray3)
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a number, a [scalar1](#affineplanescalar1), a [dist3](#affineplanedist3), a distance
+
+
+Source: [distanceToRay.js](https://github.com/axelpale/affineplane/blob/main/lib/point3/distanceToRay.js)
+
 <a name="affineplanepoint3equal"></a>
 ## [affineplane](#affineplane).[point3](#affineplanepoint3).[equal](#affineplanepoint3equal)(p, q)
 
@@ -7546,7 +7658,7 @@ Offset a point by scalars dx, dy, dz.
 <p style="margin-bottom: 0"><strong>Parameters:</strong></p>
 
 - *p*
-  - a [point2](#affineplanepoint2)
+  - a [point3](#affineplanepoint3)
 - *dx*
   - a number, the offset along x-axis
 - *dy*
@@ -8080,6 +8192,303 @@ an angle like π/2, the vector will be rotated twice that amount, π.
 
 Source: [rotateVector.js](https://github.com/axelpale/affineplane/blob/main/lib/quat4/rotateVector.js)
 
+<a name="affineplaneray3"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3)
+
+Ray is like a line but extends into one direction only from the origin.
+
+We represent ray with object `{ x, y, z, dx, dy, dz }`
+
+
+<p style="margin-bottom: 0"><strong>Contents:</strong></p>
+
+
+- [affineplane.ray3.DEFAULT](#affineplaneray3default)
+- [affineplane.ray3.ZERO](#affineplaneray3zero)
+- [affineplane.ray3.almostEqual](#affineplaneray3almostequal)
+- [affineplane.ray3.at](#affineplaneray3at)
+- [affineplane.ray3.copy](#affineplaneray3copy)
+- [affineplane.ray3.create](#affineplaneray3create)
+- [affineplane.ray3.getOrigin](#affineplaneray3getorigin)
+- [affineplane.ray3.getVector](#affineplaneray3getvector)
+- [affineplane.ray3.homothety](#affineplaneray3homothety)
+- [affineplane.ray3.invert](#affineplaneray3invert)
+- [affineplane.ray3.negate](#affineplaneray3negate)
+- [affineplane.ray3.offset](#affineplaneray3offset)
+- [affineplane.ray3.transitFrom](#affineplaneray3transitfrom)
+- [affineplane.ray3.transitTo](#affineplaneray3transitto)
+- [affineplane.ray3.validate](#affineplaneray3validate)
+
+
+Source: [ray3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/index.js)
+
+<a name="affineplaneray3default"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[DEFAULT](#affineplaneray3default)
+
+Default ray that has origin at zero and unit span along positive x-axis.
+
+Source: [ray3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/index.js)
+
+<a name="affineplaneray3zero"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[ZERO](#affineplaneray3zero)
+
+Invalid ray with origin at zero and zero spanning vector.
+
+Source: [ray3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/index.js)
+
+<a name="affineplaneray3almostequal"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[almostEqual](#affineplaneray3almostequal)(r, rr[, epsilon])
+
+Test if rays are almost equal by the margin of epsilon.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *r*
+  - a [ray3](#affineplaneray3)
+- *rr*
+  - a [ray3](#affineplaneray3)
+- *epsilon*
+  - Optional number, default to [affineplane.epsilon](#affineplaneepsilon).
+  - Set to 0 for strict comparison.
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a boolean
+
+
+Source: [almostEqual.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/almostEqual.js)
+
+<a name="affineplaneray3at"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[at](#affineplaneray3at)(line, c)
+
+Get a point on the ray at position c from the ray origin.
+For example, c=2 gives a point two ray spans away from the origin.
+Negative positions default to the ray origin.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *ray*
+  - a [ray3](#affineplaneray3)
+- *c*
+  - a number
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [point3](#affineplanepoint3)
+
+
+Source: [at.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/at.js)
+
+<a name="affineplaneray3copy"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[copy](#affineplaneray3copy)(r)
+
+Copy ray object.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *r*
+  - a [ray3](#affineplaneray3)
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3)
+
+
+Source: [copy.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/copy.js)
+
+<a name="affineplaneray3create"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[create](#affineplaneray3create)(origin, span)
+
+Create a ray object from origin point and a spanning vector.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *origin*
+  - a [point3](#affineplanepoint3), the ray starting point.
+- *span*
+  - a [dir3](#affineplanedir3) or [vec3](#affineplanevec3), the ray direction and unit length along the ray.
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3)
+
+
+Source: [create.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/create.js)
+
+<a name="affineplaneray3getorigin"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[getOrigin](#affineplaneray3getorigin)(r)
+
+Get the origin point of the ray. Note that you can also use the ray
+object itself as a point.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *r*
+  - a [ray3](#affineplaneray3)
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [point3](#affineplanepoint3)
+
+
+Source: [getOrigin.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/getOrigin.js)
+
+<a name="affineplaneray3getvector"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[getVector](#affineplaneray3getvector)(r)
+
+Get the spanning vector of the ray.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *r*
+  - a [ray3](#affineplaneray3)
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [vec3](#affineplanevec3)
+
+
+Source: [getVector.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/getVector.js)
+
+<a name="affineplaneray3homothety"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[homothety](#affineplaneray3homothety)(ray, origin, ratio)
+
+Perform a homothety about the origin for the ray.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *ray*
+  - a [ray3](#affineplaneray3)
+- *origin*
+  - a [point3](#affineplanepoint3)
+- *ratio*
+  - a number, the scaling ratio
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3)
+
+
+Source: [homothety.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/homothety.js)
+
+<a name="affineplaneray3invert"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[invert](#affineplaneray3invert)(r)
+
+Get a ray with the same magnitude but to opposite direction.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *r*
+  - a [ray3](#affineplaneray3)
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3)
+
+
+Aliases: [affineplane.ray3.negate](#affineplaneray3negate)
+
+Source: [invert.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/invert.js)
+
+<a name="affineplaneray3negate"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[negate](#affineplaneray3negate)
+
+Alias of [affineplane.ray3.invert](#affineplaneray3invert)
+
+Source: [invert.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/invert.js)
+
+<a name="affineplaneray3offset"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[offset](#affineplaneray3offset)(ray, dx, dy, dz)
+
+Offset a ray origin by scalars dx, dy, dz.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *ray*
+  - a [ray3](#affineplaneray3)
+- *dx*
+  - a number, the offset along x-axis
+- *dy*
+  - a number, the offset along y-axis
+- *dz*
+  - a number, the offset along z-axis
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3)
+
+
+Source: [offset.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/offset.js)
+
+<a name="affineplaneray3transitfrom"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[transitFrom](#affineplaneray3transitfrom)(ray, basis)
+
+Represent the ray in the reference basis without losing information.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *ray*
+  - a [ray3](#affineplaneray3), represented in the given basis.
+- *basis*
+  - a [plane3](#affineplaneplane3), represented in the reference basis.
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3), represented in the reference basis.
+
+
+Source: [transitFrom.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/transitFrom.js)
+
+<a name="affineplaneray3transitto"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[transitTo](#affineplaneray3transitto)(ray, basis)
+
+Represent the ray in another basis
+without losing information.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *ray*
+  - a [ray3](#affineplaneray3), represented in the reference basis.
+- *basis*
+  - a [plane3](#affineplaneplane3), represented in the reference basis.
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a [ray3](#affineplaneray3), represented in the given basis.
+
+
+Source: [transitTo.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/transitTo.js)
+
+<a name="affineplaneray3validate"></a>
+## [affineplane](#affineplane).[ray3](#affineplaneray3).[validate](#affineplaneray3validate)(r)
+
+Check if object is a valid [ray3](#affineplaneray3). Valid ray has numeric properties
+x, y, z, dx, dy, dz and has non-zero spanning vector.
+
+<p style="margin-bottom: 0"><strong>Parameters:</strong></p>
+
+- *r*
+  - an object
+
+
+<p style="margin-bottom: 0"><strong>Returns:</strong></p>
+
+- a boolean
+
+
+Source: [validate.js](https://github.com/axelpale/affineplane/blob/main/lib/ray3/validate.js)
+
 <a name="affineplanerect2"></a>
 ## [affineplane](#affineplane).[rect2](#affineplanerect2)
 
@@ -9552,6 +9961,8 @@ Aliases: [affineplane.circle2](#affineplanecircle2)
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.sphere2.UNIT](#affineplanesphere2unit)
+- [affineplane.sphere2.ZERO](#affineplanesphere2zero)
 - [affineplane.sphere2.almostEqual](#affineplanesphere2almostequal)
 - [affineplane.sphere2.area](#affineplanesphere2area)
 - [affineplane.sphere2.atCenter](#affineplanesphere2atcenter)
@@ -9574,6 +9985,20 @@ Aliases: [affineplane.circle2](#affineplanecircle2)
 - [affineplane.sphere2.validate](#affineplanesphere2validate)
 
 
+Source: [sphere2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/sphere2/index.js)
+
+<a name="affineplanesphere2unit"></a>
+## [affineplane](#affineplane).[sphere2](#affineplanesphere2).[UNIT](#affineplanesphere2unit)
+
+The unit circle, radius=1.
+
+Source: [sphere2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/sphere2/index.js)
+
+<a name="affineplanesphere2zero"></a>
+## [affineplane](#affineplane).[sphere2](#affineplanesphere2).[ZERO](#affineplanesphere2zero)
+
+A zero-radius circle.
+
 Source: [sphere2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/sphere2/index.js)
 
 <a name="affineplanesphere2almostequal"></a>
@@ -9985,6 +10410,8 @@ Represented with an object `{ x, y, z, r }` for the origin and the radius.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.sphere3.UNIT](#affineplanesphere3unit)
+- [affineplane.sphere3.ZERO](#affineplanesphere3zero)
 - [affineplane.sphere3.almostEqual](#affineplanesphere3almostequal)
 - [affineplane.sphere3.area](#affineplanesphere3area)
 - [affineplane.sphere3.atCenter](#affineplanesphere3atcenter)
@@ -10011,6 +10438,20 @@ Represented with an object `{ x, y, z, r }` for the origin and the radius.
 - [affineplane.sphere3.volume](#affineplanesphere3volume)
 
 
+Source: [sphere3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/sphere3/index.js)
+
+<a name="affineplanesphere3unit"></a>
+## [affineplane](#affineplane).[sphere3](#affineplanesphere3).[UNIT](#affineplanesphere3unit)
+
+The unit sphere, radius=1.
+
+Source: [sphere3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/sphere3/index.js)
+
+<a name="affineplanesphere3zero"></a>
+## [affineplane](#affineplane).[sphere3](#affineplanesphere3).[ZERO](#affineplanesphere3zero)
+
+A zero-radius sphere.
+
 Source: [sphere3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/sphere3/index.js)
 
 <a name="affineplanesphere3almostequal"></a>
@@ -10504,6 +10945,7 @@ position vectors.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.vec2.ZERO](#affineplanevec2zero)
 - [affineplane.vec2.add](#affineplanevec2add)
 - [affineplane.vec2.almostEqual](#affineplanevec2almostequal)
 - [affineplane.vec2.average](#affineplanevec2average)
@@ -10544,6 +10986,27 @@ position vectors.
 
 Source: [vec2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/vec2/index.js)
 
+<a name="affineplanevec2zero"></a>
+## [affineplane](#affineplane).[vec2](#affineplanevec2).[ZERO](#affineplanevec2zero)
+
+The zero vector in 2D
+
+Source: [vec2/index.js](https://github.com/axelpale/affineplane/blob/main/lib/vec2/index.js)
+
+<a name="affineplanevec3zero"></a>
+## [affineplane](#affineplane).[vec3](#affineplanevec3).[ZERO](#affineplanevec3zero)
+
+The zero vector in 3D
+
+Source: [vec3/index.js](https://github.com/axelpale/affineplane/blob/main/lib/vec3/index.js)
+
+<a name="affineplanevec4zero"></a>
+## [affineplane](#affineplane).[vec4](#affineplanevec4).[ZERO](#affineplanevec4zero)
+
+The zero vector in 4D
+
+Source: [vec4/index.js](https://github.com/axelpale/affineplane/blob/main/lib/vec4/index.js)
+
 <a name="affineplanevec2add"></a>
 ## [affineplane](#affineplane).[vec2](#affineplanevec2).[add](#affineplanevec2add)(v, w)
 
@@ -11241,6 +11704,7 @@ and rotation when represented on different plane.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.vec3.ZERO](#affineplanevec3zero)
 - [affineplane.vec3.add](#affineplanevec3add)
 - [affineplane.vec3.almostEqual](#affineplanevec3almostequal)
 - [affineplane.vec3.average](#affineplanevec3average)
@@ -12033,6 +12497,7 @@ A [vec4](#affineplanevec4) is a 4D vector { x, y, z, w }.
 <p style="margin-bottom: 0"><strong>Contents:</strong></p>
 
 
+- [affineplane.vec4.ZERO](#affineplanevec4zero)
 - [affineplane.vec4.add](#affineplanevec4add)
 - [affineplane.vec4.almostEqual](#affineplanevec4almostequal)
 - [affineplane.vec4.create](#affineplanevec4create)

From 59fe0c41a2ab2f0e0ad69f4a01e1fa0822b9a2f1 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 18:59:31 +0300
Subject: [PATCH 20/21] list ray3 in readme

---
 README.md | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 968cc2f..f607d2f 100644
--- a/README.md
+++ b/README.md
@@ -37,9 +37,10 @@ Shapes with position in space:
 - [plane3](https://axelpale.github.io/affineplane/docs/API.html#affineplaneplane3), an xy-plane in 3D, `{a,b,x,y,z}`
 - [point2](https://axelpale.github.io/affineplane/docs/API.html#affineplanepoint2), a location in 2D, `{x,y}`
 - [point3](https://axelpale.github.io/affineplane/docs/API.html#affineplanepoint3), a location in 3D, `{x,y,z}`
+- [ray3](https://axelpale.github.io/affineplane/docs/API.html#affineplaneray3), a ray in 3D, `{x,y,z,dx,dy,dz}`
 - [scalar1](https://axelpale.github.io/affineplane/docs/API.html#affineplanescalar1), a first-order measure (length), `s`
 - [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), `s`
+- [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}]`
 - [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}`

From ad23e5c10306dd75bd3e9ac485c2c21a21c67d69 Mon Sep 17 00:00:00 2001
From: Akseli Palen <akseli.palen@gmail.com>
Date: Sat, 29 Apr 2023 19:01:15 +0300
Subject: [PATCH 21/21] bump v2.16.0

---
 docs/API.md    | 2 +-
 lib/version.js | 2 +-
 package.json   | 7 +++++--
 3 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/docs/API.md b/docs/API.md
index a42297f..df93342 100644
--- a/docs/API.md
+++ b/docs/API.md
@@ -1,5 +1,5 @@
 <a name="top"></a>
-# Affineplane API Documentation v2.15.0
+# Affineplane API Documentation v2.16.0
 
 Welcome to affineplane API reference documentation. These docs are generated with [yamdog](https://axelpale.github.io/yamdog/).
 
diff --git a/lib/version.js b/lib/version.js
index 9ac6ec2..5679a40 100644
--- a/lib/version.js
+++ b/lib/version.js
@@ -1,2 +1,2 @@
 // Generated by genversion.
-module.exports = '2.15.0'
+module.exports = '2.16.0'
diff --git a/package.json b/package.json
index f38a00f..b4df288 100644
--- a/package.json
+++ b/package.json
@@ -1,6 +1,6 @@
 {
   "name": "affineplane",
-  "version": "2.15.0",
+  "version": "2.16.0",
   "description": "Affine geometry library for 2D and 3D spaces",
   "keywords": [
     "affine",
@@ -21,7 +21,10 @@
     "similarity",
     "helmert",
     "perspective",
-    "projection"
+    "projection",
+    "segment",
+    "line",
+    "ray"
   ],
   "homepage": "https://github.com/axelpale/affineplane",
   "main": "index.js",