From 3d3d60695a0e30ffca60aa1cd1f1c881d62fbbcc Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Wed, 18 Jan 2023 04:05:21 -0500
Subject: [PATCH 1/9] Chapter 14: WIP.

---
 src/main/kotlin/material/material.kt | 58 ++++++++++-------------
 src/main/kotlin/shapes/cone.kt       |  8 +++-
 src/main/kotlin/shapes/cube.kt       | 10 +++-
 src/main/kotlin/shapes/cylinder.kt   |  8 +++-
 src/main/kotlin/shapes/group.kt      | 32 +++++++++++++
 src/main/kotlin/shapes/plane.kt      | 10 +++-
 src/main/kotlin/shapes/shape.kt      | 34 ++++++--------
 src/main/kotlin/shapes/sphere.kt     | 10 +++-
 src/test/kotlin/shapes/grouptest.kt  | 70 ++++++++++++++++++++++++++++
 src/test/kotlin/shapes/shapetest.kt  | 36 +++++++++++++-
 10 files changed, 211 insertions(+), 65 deletions(-)
 create mode 100644 src/main/kotlin/shapes/group.kt
 create mode 100644 src/test/kotlin/shapes/grouptest.kt

diff --git a/src/main/kotlin/material/material.kt b/src/main/kotlin/material/material.kt
index e19391c..7a1589b 100644
--- a/src/main/kotlin/material/material.kt
+++ b/src/main/kotlin/material/material.kt
@@ -11,25 +11,34 @@ import pattern.SolidPattern
 import shapes.Shape
 import kotlin.math.pow
 
-data class Material(val pattern: Pattern = SolidPattern(Color.WHITE),
-                    val ambient: Double = DEFAULT_AMBIENT,
-                    val diffuse: Double = DEFAULT_DIFFUSE,
-                    val specular: Double = DEFAULT_SPECULAR,
-                    val shininess: Double = DEFAULT_SHININESS,
-                    val reflectivity: Double = DEFAULT_REFLECTIVITY,
-                    val transparency: Double = DEFAULT_TRANSPARENCY,
-                    val refractiveIndex: Double = DEFAULT_REFRACTIVE_INDEX) {
+class Material(val pattern: Pattern = SolidPattern(Color.WHITE),
+               ambient: Number = DEFAULT_AMBIENT,
+               diffuse: Number = DEFAULT_DIFFUSE,
+               specular: Number = DEFAULT_SPECULAR,
+               shininess: Number = DEFAULT_SHININESS,
+               reflectivity: Number = DEFAULT_REFLECTIVITY,
+               transparency: Number = DEFAULT_TRANSPARENCY,
+               refractiveIndex: Number = DEFAULT_REFRACTIVE_INDEX) {
+
+    val ambient = ambient.toDouble()
+    val diffuse = diffuse.toDouble()
+    val specular = specular.toDouble()
+    val shininess = shininess.toDouble()
+    val reflectivity = reflectivity.toDouble()
+    val transparency = transparency.toDouble()
+    val refractiveIndex = refractiveIndex.toDouble()
 
     // Convenience constructor to create a material with a solid pattern.
     constructor(color: Color,
-                ambient: Double = DEFAULT_AMBIENT,
-                diffuse: Double = DEFAULT_DIFFUSE,
-                specular: Double = DEFAULT_SPECULAR,
-                shininess: Double = DEFAULT_SHININESS,
-                reflectivity: Double = DEFAULT_REFLECTIVITY,
-                transparency: Double = DEFAULT_TRANSPARENCY,
-                refractiveIndex: Double = DEFAULT_REFRACTIVE_INDEX):
-            this(SolidPattern(color), ambient, diffuse, specular, shininess, reflectivity, transparency, refractiveIndex)
+                ambient: Number = DEFAULT_AMBIENT,
+                diffuse: Number = DEFAULT_DIFFUSE,
+                specular: Number = DEFAULT_SPECULAR,
+                shininess: Number = DEFAULT_SHININESS,
+                reflectivity: Number = DEFAULT_REFLECTIVITY,
+                transparency: Number = DEFAULT_TRANSPARENCY,
+                refractiveIndex: Number = DEFAULT_REFRACTIVE_INDEX):
+            this(SolidPattern(color),
+                ambient, diffuse, specular, shininess, reflectivity, transparency, refractiveIndex)
 
     internal fun lighting(shape: Shape,
                           light: Light,
@@ -62,23 +71,6 @@ data class Material(val pattern: Pattern = SolidPattern(Color.WHITE),
         return ambient + diffuse + specular
     }
 
-    override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-        if (other !is Material) return false
-
-        if (pattern != other.pattern) return false
-        if (!almostEquals(ambient, other.ambient)) return false
-        if (!almostEquals(diffuse, other.diffuse)) return false
-        if (!almostEquals(specular, other.specular)) return false
-        if (!almostEquals(shininess, other.shininess)) return false
-
-        return true
-    }
-
-    override fun hashCode(): Int =
-        31 * (31 * (31 * (31 * pattern.hashCode() + ambient.hashCode()) +
-                diffuse.hashCode()) + specular.hashCode()) + shininess.hashCode()
-
     companion object {
         const val DEFAULT_AMBIENT = 0.1
         const val DEFAULT_DIFFUSE = 0.9
diff --git a/src/main/kotlin/shapes/cone.kt b/src/main/kotlin/shapes/cone.kt
index a56316c..f78ea66 100644
--- a/src/main/kotlin/shapes/cone.kt
+++ b/src/main/kotlin/shapes/cone.kt
@@ -12,12 +12,16 @@ class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
            val closed: Boolean = false,
            transformation: Matrix = Matrix.I,
            material: Material = Material(),
-           castsShadow: Boolean = true):
-    Shape(transformation, material, castsShadow) {
+           castsShadow: Boolean = true,
+           parent: Shape? = null):
+    Shape(transformation, material, castsShadow, parent) {
 
     val minimum = minimum.toDouble()
     val maximum = maximum.toDouble()
 
+    override fun withParent(parent: Shape?): Shape =
+        Cone(minimum, maximum, closed, transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val a = rayLocal.direction.x * rayLocal.direction.x -
                 rayLocal.direction.y * rayLocal.direction.y +
diff --git a/src/main/kotlin/shapes/cube.kt b/src/main/kotlin/shapes/cube.kt
index e874ba6..1e01ae5 100644
--- a/src/main/kotlin/shapes/cube.kt
+++ b/src/main/kotlin/shapes/cube.kt
@@ -7,8 +7,14 @@ import math.*
 import math.Intersection
 import kotlin.math.absoluteValue
 
-class Cube(transformation: Matrix = Matrix.I, material: Material = Material(), castsShadow: Boolean = true):
-    Shape(transformation, material, castsShadow) {
+class Cube(transformation: Matrix = Matrix.I,
+           material: Material = Material(),
+           castsShadow: Boolean = true,
+           parent: Shape? = null):
+    Shape(transformation, material, castsShadow, parent) {
+    override fun withParent(parent: Shape?): Shape =
+        Cube(transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val (xtMin, xtMax) = checkAxis(rayLocal.origin.x, rayLocal.direction.x)
         val (ytMin, ytMax) = checkAxis(rayLocal.origin.y, rayLocal.direction.y)
diff --git a/src/main/kotlin/shapes/cylinder.kt b/src/main/kotlin/shapes/cylinder.kt
index 5cb3ad0..412b4d7 100644
--- a/src/main/kotlin/shapes/cylinder.kt
+++ b/src/main/kotlin/shapes/cylinder.kt
@@ -12,12 +12,16 @@ class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
                val closed: Boolean = false,
                transformation: Matrix = Matrix.I,
                material: Material = Material(),
-               castsShadow: Boolean = true):
-    Shape(transformation, material, castsShadow) {
+               castsShadow: Boolean = true,
+               parent: Shape? = null):
+    Shape(transformation, material, castsShadow, parent) {
 
     val minimum = minimum.toDouble()
     val maximum = maximum.toDouble()
 
+    override fun withParent(parent: Shape?): Shape =
+        Cylinder(minimum, maximum, closed, transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val a = rayLocal.direction.x * rayLocal.direction.x + rayLocal.direction.z * rayLocal.direction.z
 
diff --git a/src/main/kotlin/shapes/group.kt b/src/main/kotlin/shapes/group.kt
new file mode 100644
index 0000000..79768f6
--- /dev/null
+++ b/src/main/kotlin/shapes/group.kt
@@ -0,0 +1,32 @@
+package shapes
+
+// By Sebastian Raaphorst, 2023.
+
+import material.Material
+import math.Intersection
+import math.Matrix
+import math.Ray
+import math.Tuple
+
+class Group(transformation: Matrix = Matrix.I,
+            children: List<Shape> = emptyList(),
+            castsShadow: Boolean = true,
+            parent: Shape? = null):
+    Shape(transformation, Material(), castsShadow, parent) {
+
+    // Make copies of all the children to backreference this as their parent.
+    val children = children.map { it.withParent(this) }
+
+    operator fun contains(s: Shape): Boolean =
+        s in children
+
+    override fun withParent(parent: Shape?): Shape =
+        Group(transformation, children, castsShadow, parent)
+
+    override fun localIntersect(rayLocal: Ray): List<Intersection> =
+        children.flatMap { it.intersect(rayLocal) }.sortedBy { it.t }
+
+    override fun localNormalAt(localPoint: Tuple): Tuple {
+        TODO("Not yet implemented")
+    }
+}
diff --git a/src/main/kotlin/shapes/plane.kt b/src/main/kotlin/shapes/plane.kt
index dc76430..0b9c159 100644
--- a/src/main/kotlin/shapes/plane.kt
+++ b/src/main/kotlin/shapes/plane.kt
@@ -6,8 +6,14 @@ import material.Material
 import math.*
 import kotlin.math.absoluteValue
 
-class Plane(transformation: Matrix = Matrix.I, material: Material = Material(), castsShadow: Boolean = true):
-    Shape(transformation, material, castsShadow) {
+class Plane(transformation: Matrix = Matrix.I,
+            material: Material = Material(),
+            castsShadow: Boolean = true,
+            parent: Shape? = null):
+    Shape(transformation, material, castsShadow, parent) {
+    override fun withParent(parent: Shape?): Shape =
+        Plane(transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         if (rayLocal.direction.y.absoluteValue < DEFAULT_PRECISION)
             return emptyList()
diff --git a/src/main/kotlin/shapes/shape.kt b/src/main/kotlin/shapes/shape.kt
index ea99aea..8b739bd 100644
--- a/src/main/kotlin/shapes/shape.kt
+++ b/src/main/kotlin/shapes/shape.kt
@@ -8,10 +8,13 @@ import math.Matrix
 import math.Ray
 import math.Tuple
 import java.util.UUID
+import kotlin.math.PI
+import kotlin.math.sqrt
 
 abstract class Shape(val transformation: Matrix,
                      val material: Material,
-                     val castsShadow: Boolean = true,
+                     val castsShadow: Boolean,
+                     val parent: Shape?,
                      private val id: UUID = UUID.randomUUID()) {
     init {
         if (!transformation.isTransformation())
@@ -19,15 +22,19 @@ abstract class Shape(val transformation: Matrix,
                     "\tShape: ${javaClass.name}\nTransformation:\n${transformation.show()}")
     }
 
+    abstract fun withParent(parent: Shape? = null): Shape
+
     // Convert a point from world space to object space.
     // Later on, we use parent here.
-    fun worldToLocal(tuple: Tuple): Tuple =
-        transformation.inverse * tuple
+    internal fun worldToLocal(tuple: Tuple): Tuple =
+        transformation.inverse * (parent?.worldToLocal(tuple) ?: tuple)
 
     // Convert a normal vector from object space to world space.
     // Later on, we will use parent here.
-    private fun normalToWorld(localNormal: Tuple): Tuple =
-        (transformation.inverse.transpose * localNormal).toVector().normalized
+    internal fun normalToWorld(localNormal: Tuple): Tuple {
+        val normal = (transformation.inverse.transpose * localNormal).toVector().normalized
+        return parent?.normalToWorld(normal) ?: normal
+    }
 
     // The intersect method transforms the ray to object space and then passes
     // it to localNormalAt, which should comprise the concrete implementation of
@@ -52,21 +59,6 @@ abstract class Shape(val transformation: Matrix,
         // Convert back to world space.
         return normalToWorld(localNormal)
     }
-    internal abstract fun localNormalAt(localPoint: Tuple): Tuple
-
-
-    // We want shapes to be considered only equal if they represent exactly the same shape.
-    override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-        if (other !is Shape) return false
 
-        if (id != other.id) return false
-        if (transformation != other.transformation) return false
-        if (material != other.material) return false
-
-        return true
-    }
-
-    override fun hashCode(): Int =
-        31 * (31 * transformation.hashCode() + material.hashCode()) + id.hashCode()
+    internal abstract fun localNormalAt(localPoint: Tuple): Tuple
 }
diff --git a/src/main/kotlin/shapes/sphere.kt b/src/main/kotlin/shapes/sphere.kt
index 73fc503..aaf06ce 100644
--- a/src/main/kotlin/shapes/sphere.kt
+++ b/src/main/kotlin/shapes/sphere.kt
@@ -9,8 +9,14 @@ import math.Ray
 import math.Tuple
 import kotlin.math.sqrt
 
-class Sphere(transformation: Matrix = Matrix.I, material: Material = Material(), castsShadow: Boolean = true):
-    Shape(transformation, material, castsShadow) {
+class Sphere(transformation: Matrix = Matrix.I,
+             material: Material = Material(),
+             castsShadow: Boolean = true,
+             parent: Shape? = null):
+    Shape(transformation, material, castsShadow, parent) {
+    override fun withParent(parent: Shape?): Shape =
+        Sphere(transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val sphereToRay = rayLocal.origin - Tuple.PZERO
 
diff --git a/src/test/kotlin/shapes/grouptest.kt b/src/test/kotlin/shapes/grouptest.kt
new file mode 100644
index 0000000..b88a3cb
--- /dev/null
+++ b/src/test/kotlin/shapes/grouptest.kt
@@ -0,0 +1,70 @@
+package shapes
+
+// By Sebastian Raaphorst, 2023.
+
+import math.Matrix
+import math.Ray
+import math.Tuple
+import org.junit.jupiter.api.Test
+import kotlin.test.*
+
+class GroupTest {
+    @Test
+    fun `New group`() {
+        val g = Group()
+        assertEquals(Matrix.I, g.transformation)
+        assertTrue(g.children.isEmpty())
+    }
+
+    @Test
+    fun `New group with test shape`() {
+        val s = ShapeTest.TestShape()
+        val g = Group(children = listOf(s))
+        assertEquals(1, g.children.size)
+        val sp = g.children[0]
+
+        // Check that s has changed and been assigned the group as a parent.
+        assertNotSame(s, sp)
+        assertEquals(g, sp.parent)
+
+        // Check that g does not contain the initial shape, but does contain the new shape.
+        assertFalse(s in g)
+        assertTrue(sp in g)
+    }
+
+    @Test
+    fun `Intersect ray with empty group`() {
+        val g = Group()
+        val r = Ray(Tuple.PZERO, Tuple.VZ)
+        val xs = g.localIntersect(r)
+        assertTrue(xs.isEmpty())
+    }
+
+    @Test
+    fun `Intersect ray with nonempty group`() {
+        val s1 = Sphere()
+        val s2 = Sphere(transformation = Matrix.translate(0, 0, -3))
+        val s3 = Sphere(transformation = Matrix.translate(5, 0, 0))
+        val g = Group(children = listOf(s1, s2, s3))
+
+        val r = Ray(Tuple.point(0, 0, -5), Tuple.VZ)
+        val xs = g.localIntersect(r)
+        assertEquals(4, xs.size)
+        val sp1 = g.children[0]
+        val sp2 = g.children[1]
+        assertSame(sp2, xs[0].shape)
+        assertSame(sp2, xs[1].shape)
+        assertSame(sp1, xs[2].shape)
+        assertSame(sp1, xs[3].shape)
+    }
+
+    @Test
+    fun `Intersect ray with transformed group`() {
+        val s = Sphere(transformation = Matrix.translate(5, 0, 0))
+        val g = Group(transformation = Matrix.scale(2, 2, 2), children = listOf(s))
+
+        val r = Ray(Tuple.point(10, 0, -10), Tuple.VZ)
+        val xs = g.intersect(r)
+        assertEquals(2, xs.size)
+    }
+}
diff --git a/src/test/kotlin/shapes/shapetest.kt b/src/test/kotlin/shapes/shapetest.kt
index 458229b..bc1ccfa 100644
--- a/src/test/kotlin/shapes/shapetest.kt
+++ b/src/test/kotlin/shapes/shapetest.kt
@@ -6,13 +6,22 @@ import material.Material
 import math.*
 import org.junit.jupiter.api.Test
 import kotlin.math.PI
+import kotlin.math.sqrt
 
 class ShapeTest {
     class TestShape(transformation: Matrix = Matrix.I,
-                    material: Material = Material()): Shape(transformation, material) {
+                    material: Material = Material(),
+                    parent: Shape? = null):
+        Shape(transformation, material, true, parent) {
         // We need to use a var here to store a ray.
         var savedRay = Ray(Tuple.PZERO, Tuple.VZERO)
 
+        override fun withParent(parent: Shape?): Shape {
+            val s = TestShape(transformation, material, parent)
+            s.savedRay = savedRay
+            return s
+        }
+
         override fun localIntersect(rayLocal: Ray): List<Intersection> {
             savedRay = rayLocal
             return emptyList()
@@ -57,4 +66,29 @@ class ShapeTest {
         val n = s.normalAt(Tuple.point(0, sqrt2by2, -sqrt2by2))
         assertAlmostEquals(Tuple.vector(0, 0.97014, -0.24254), n)
     }
+
+    @Test
+    fun `Point from world to local space`() {
+        val s = Sphere(Matrix.translate(5, 0, 0))
+        val g2 = Group(Matrix.scale(2, 2, 2), listOf(s))
+        val g1 = Group(Matrix.rotateY(PI / 2), listOf(g2))
+
+        // We have to get the new sphere to have the parent set.
+        val sNew = (g1.children[0] as Group).children[0]
+        val p = sNew.worldToLocal(Tuple.point(-2, 0, -10))
+        assertAlmostEquals(Tuple.point(0, 0, -1), p)
+    }
+
+    @Test
+    fun `Normal from local to world space`() {
+        val s = Sphere(Matrix.translate(5, 0, 0))
+        val g2 = Group(Matrix.scale(1, 2, 3), listOf(s))
+        val g1 = Group(Matrix.rotateY(PI / 2), listOf(g2))
+
+        // We have to get the new sphere to have the parent set.
+        val sNew = (g1.children[0] as Group).children[0]
+        val sqrt3by3 = sqrt(3.0) / 3
+        val n = sNew.normalToWorld(Tuple.vector(sqrt3by3, sqrt3by3, sqrt3by3))
+        assertAlmostEquals(Tuple.vector(0.28571, 0.42857, -0.85714), n)
+    }
 }

From a05102574549b8dcd6a21dc6fef2bddd13f9ea71 Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Wed, 18 Jan 2023 04:19:40 -0500
Subject: [PATCH 2/9] Chapter 14: Renaming files to Kotlin convention.

---
 src/main/kotlin/material/{material.kt => Material.kt}           | 1 -
 src/main/kotlin/math/{color.kt => Color.kt}                     | 0
 src/main/kotlin/math/{computations.kt => Computations.kt}       | 0
 src/main/kotlin/math/{intersection.kt => Intersection.kt}       | 0
 src/main/kotlin/math/{matrix.kt => Matrix.kt}                   | 0
 src/main/kotlin/math/{ray.kt => Ray.kt}                         | 0
 src/main/kotlin/math/{shared.kt => Shared.kt}                   | 0
 src/main/kotlin/math/{transformable.kt => Transformable.kt}     | 0
 src/main/kotlin/math/{tuple.kt => Tuple.kt}                     | 0
 src/main/kotlin/output/{canvas.kt => Canvas.kt}                 | 0
 src/main/kotlin/output/{show.kt => Show.kt}                     | 0
 .../kotlin/pattern/{blendedpattern.kt => BlendedPattern.kt}     | 0
 .../kotlin/pattern/{checkerpattern.kt => CheckerPattern.kt}     | 0
 .../kotlin/pattern/{gradientpattern.kt => GradientPattern.kt}   | 0
 src/main/kotlin/pattern/{noisepattern.kt => NoisePattern.kt}    | 0
 src/main/kotlin/pattern/{pattern.kt => Pattern.kt}              | 0
 .../pattern/{perlinnoisepattern.kt => PerlinNoisePattern.kt}    | 0
 src/main/kotlin/pattern/{ringpattern.kt => RingPattern.kt}      | 0
 .../pattern/{simplexnoisepattern.kt => SimplexNoisePattern.kt}  | 0
 src/main/kotlin/pattern/{solidpattern.kt => SolidPattern.kt}    | 1 -
 .../kotlin/pattern/{stripedpattern.kt => StripedPattern.kt}     | 0
 src/main/kotlin/scene/{camera.kt => Camera.kt}                  | 0
 src/main/kotlin/scene/{world.kt => World.kt}                    | 2 --
 src/main/kotlin/shapes/{cone.kt => Cone.kt}                     | 0
 src/main/kotlin/shapes/{cube.kt => Cube.kt}                     | 0
 src/main/kotlin/shapes/{cylinder.kt => Cylinder.kt}             | 0
 src/main/kotlin/shapes/{group.kt => Group.kt}                   | 0
 src/main/kotlin/shapes/{plane.kt => Plane.kt}                   | 0
 src/main/kotlin/shapes/{shape.kt => Shape.kt}                   | 2 --
 src/main/kotlin/shapes/{sphere.kt => Sphere.kt}                 | 0
 src/test/kotlin/light/{pointlighttest.kt => PointLightTest.kt}  | 0
 src/test/kotlin/material/{materialtest.kt => MaterialTest.kt}   | 0
 src/test/kotlin/math/{colortest.kt => ColorTest.kt}             | 0
 .../kotlin/math/{intersectiontest.kt => IntersectionTest.kt}    | 0
 src/test/kotlin/math/{matrixtest.kt => MatrixTest.kt}           | 0
 src/test/kotlin/math/{raytest.kt => RayTest.kt}                 | 0
 src/test/kotlin/math/{sharedtest.kt => SharedTest.kt}           | 0
 src/test/kotlin/math/{tupletest.kt => TupleTest.kt}             | 0
 src/test/kotlin/output/{canvastest.kt => CanvasTest.kt}         | 2 +-
 .../pattern/{blendedpatterntest.kt => BlendedPatternTest.kt}    | 2 ++
 .../pattern/{checkerpatterntest.kt => CheckerPatternTest.kt}    | 0
 .../pattern/{gradientpatterntest.kt => GradientPatternTest.kt}  | 0
 src/test/kotlin/pattern/{patterntest.kt => PatternTest.kt}      | 0
 .../kotlin/pattern/{ringpatterntest.kt => RingPatternTest.kt}   | 0
 .../kotlin/pattern/{solidpatterntest.kt => SolidPatternTest.kt} | 0
 .../pattern/{stripedpatterntest.kt => StripedPatternTest.kt}    | 0
 src/test/kotlin/scene/{cameratest.kt => CameraTest.kt}          | 0
 src/test/kotlin/scene/{worldtest.kt => WorldTest.kt}            | 0
 src/test/kotlin/shapes/{conetest.kt => ConeTest.kt}             | 0
 src/test/kotlin/shapes/{cubetest.kt => CubeTest.kt}             | 0
 src/test/kotlin/shapes/{cylindertest.kt => CylinderTest.kt}     | 0
 src/test/kotlin/shapes/{grouptest.kt => GroupTest.kt}           | 0
 src/test/kotlin/shapes/{planetest.kt => PlaneTest.kt}           | 0
 src/test/kotlin/shapes/{shapetest.kt => ShapeTest.kt}           | 0
 src/test/kotlin/shapes/{spheretest.kt => SphereTest.kt}         | 0
 55 files changed, 3 insertions(+), 7 deletions(-)
 rename src/main/kotlin/material/{material.kt => Material.kt} (99%)
 rename src/main/kotlin/math/{color.kt => Color.kt} (100%)
 rename src/main/kotlin/math/{computations.kt => Computations.kt} (100%)
 rename src/main/kotlin/math/{intersection.kt => Intersection.kt} (100%)
 rename src/main/kotlin/math/{matrix.kt => Matrix.kt} (100%)
 rename src/main/kotlin/math/{ray.kt => Ray.kt} (100%)
 rename src/main/kotlin/math/{shared.kt => Shared.kt} (100%)
 rename src/main/kotlin/math/{transformable.kt => Transformable.kt} (100%)
 rename src/main/kotlin/math/{tuple.kt => Tuple.kt} (100%)
 rename src/main/kotlin/output/{canvas.kt => Canvas.kt} (100%)
 rename src/main/kotlin/output/{show.kt => Show.kt} (100%)
 rename src/main/kotlin/pattern/{blendedpattern.kt => BlendedPattern.kt} (100%)
 rename src/main/kotlin/pattern/{checkerpattern.kt => CheckerPattern.kt} (100%)
 rename src/main/kotlin/pattern/{gradientpattern.kt => GradientPattern.kt} (100%)
 rename src/main/kotlin/pattern/{noisepattern.kt => NoisePattern.kt} (100%)
 rename src/main/kotlin/pattern/{pattern.kt => Pattern.kt} (100%)
 rename src/main/kotlin/pattern/{perlinnoisepattern.kt => PerlinNoisePattern.kt} (100%)
 rename src/main/kotlin/pattern/{ringpattern.kt => RingPattern.kt} (100%)
 rename src/main/kotlin/pattern/{simplexnoisepattern.kt => SimplexNoisePattern.kt} (100%)
 rename src/main/kotlin/pattern/{solidpattern.kt => SolidPattern.kt} (96%)
 rename src/main/kotlin/pattern/{stripedpattern.kt => StripedPattern.kt} (100%)
 rename src/main/kotlin/scene/{camera.kt => Camera.kt} (100%)
 rename src/main/kotlin/scene/{world.kt => World.kt} (99%)
 rename src/main/kotlin/shapes/{cone.kt => Cone.kt} (100%)
 rename src/main/kotlin/shapes/{cube.kt => Cube.kt} (100%)
 rename src/main/kotlin/shapes/{cylinder.kt => Cylinder.kt} (100%)
 rename src/main/kotlin/shapes/{group.kt => Group.kt} (100%)
 rename src/main/kotlin/shapes/{plane.kt => Plane.kt} (100%)
 rename src/main/kotlin/shapes/{shape.kt => Shape.kt} (98%)
 rename src/main/kotlin/shapes/{sphere.kt => Sphere.kt} (100%)
 rename src/test/kotlin/light/{pointlighttest.kt => PointLightTest.kt} (100%)
 rename src/test/kotlin/material/{materialtest.kt => MaterialTest.kt} (100%)
 rename src/test/kotlin/math/{colortest.kt => ColorTest.kt} (100%)
 rename src/test/kotlin/math/{intersectiontest.kt => IntersectionTest.kt} (100%)
 rename src/test/kotlin/math/{matrixtest.kt => MatrixTest.kt} (100%)
 rename src/test/kotlin/math/{raytest.kt => RayTest.kt} (100%)
 rename src/test/kotlin/math/{sharedtest.kt => SharedTest.kt} (100%)
 rename src/test/kotlin/math/{tupletest.kt => TupleTest.kt} (100%)
 rename src/test/kotlin/output/{canvastest.kt => CanvasTest.kt} (98%)
 rename src/test/kotlin/pattern/{blendedpatterntest.kt => BlendedPatternTest.kt} (98%)
 rename src/test/kotlin/pattern/{checkerpatterntest.kt => CheckerPatternTest.kt} (100%)
 rename src/test/kotlin/pattern/{gradientpatterntest.kt => GradientPatternTest.kt} (100%)
 rename src/test/kotlin/pattern/{patterntest.kt => PatternTest.kt} (100%)
 rename src/test/kotlin/pattern/{ringpatterntest.kt => RingPatternTest.kt} (100%)
 rename src/test/kotlin/pattern/{solidpatterntest.kt => SolidPatternTest.kt} (100%)
 rename src/test/kotlin/pattern/{stripedpatterntest.kt => StripedPatternTest.kt} (100%)
 rename src/test/kotlin/scene/{cameratest.kt => CameraTest.kt} (100%)
 rename src/test/kotlin/scene/{worldtest.kt => WorldTest.kt} (100%)
 rename src/test/kotlin/shapes/{conetest.kt => ConeTest.kt} (100%)
 rename src/test/kotlin/shapes/{cubetest.kt => CubeTest.kt} (100%)
 rename src/test/kotlin/shapes/{cylindertest.kt => CylinderTest.kt} (100%)
 rename src/test/kotlin/shapes/{grouptest.kt => GroupTest.kt} (100%)
 rename src/test/kotlin/shapes/{planetest.kt => PlaneTest.kt} (100%)
 rename src/test/kotlin/shapes/{shapetest.kt => ShapeTest.kt} (100%)
 rename src/test/kotlin/shapes/{spheretest.kt => SphereTest.kt} (100%)

diff --git a/src/main/kotlin/material/material.kt b/src/main/kotlin/material/Material.kt
similarity index 99%
rename from src/main/kotlin/material/material.kt
rename to src/main/kotlin/material/Material.kt
index 7a1589b..8d24fc6 100644
--- a/src/main/kotlin/material/material.kt
+++ b/src/main/kotlin/material/Material.kt
@@ -5,7 +5,6 @@ package material
 import light.Light
 import math.Color
 import math.Tuple
-import math.almostEquals
 import pattern.Pattern
 import pattern.SolidPattern
 import shapes.Shape
diff --git a/src/main/kotlin/math/color.kt b/src/main/kotlin/math/Color.kt
similarity index 100%
rename from src/main/kotlin/math/color.kt
rename to src/main/kotlin/math/Color.kt
diff --git a/src/main/kotlin/math/computations.kt b/src/main/kotlin/math/Computations.kt
similarity index 100%
rename from src/main/kotlin/math/computations.kt
rename to src/main/kotlin/math/Computations.kt
diff --git a/src/main/kotlin/math/intersection.kt b/src/main/kotlin/math/Intersection.kt
similarity index 100%
rename from src/main/kotlin/math/intersection.kt
rename to src/main/kotlin/math/Intersection.kt
diff --git a/src/main/kotlin/math/matrix.kt b/src/main/kotlin/math/Matrix.kt
similarity index 100%
rename from src/main/kotlin/math/matrix.kt
rename to src/main/kotlin/math/Matrix.kt
diff --git a/src/main/kotlin/math/ray.kt b/src/main/kotlin/math/Ray.kt
similarity index 100%
rename from src/main/kotlin/math/ray.kt
rename to src/main/kotlin/math/Ray.kt
diff --git a/src/main/kotlin/math/shared.kt b/src/main/kotlin/math/Shared.kt
similarity index 100%
rename from src/main/kotlin/math/shared.kt
rename to src/main/kotlin/math/Shared.kt
diff --git a/src/main/kotlin/math/transformable.kt b/src/main/kotlin/math/Transformable.kt
similarity index 100%
rename from src/main/kotlin/math/transformable.kt
rename to src/main/kotlin/math/Transformable.kt
diff --git a/src/main/kotlin/math/tuple.kt b/src/main/kotlin/math/Tuple.kt
similarity index 100%
rename from src/main/kotlin/math/tuple.kt
rename to src/main/kotlin/math/Tuple.kt
diff --git a/src/main/kotlin/output/canvas.kt b/src/main/kotlin/output/Canvas.kt
similarity index 100%
rename from src/main/kotlin/output/canvas.kt
rename to src/main/kotlin/output/Canvas.kt
diff --git a/src/main/kotlin/output/show.kt b/src/main/kotlin/output/Show.kt
similarity index 100%
rename from src/main/kotlin/output/show.kt
rename to src/main/kotlin/output/Show.kt
diff --git a/src/main/kotlin/pattern/blendedpattern.kt b/src/main/kotlin/pattern/BlendedPattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/blendedpattern.kt
rename to src/main/kotlin/pattern/BlendedPattern.kt
diff --git a/src/main/kotlin/pattern/checkerpattern.kt b/src/main/kotlin/pattern/CheckerPattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/checkerpattern.kt
rename to src/main/kotlin/pattern/CheckerPattern.kt
diff --git a/src/main/kotlin/pattern/gradientpattern.kt b/src/main/kotlin/pattern/GradientPattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/gradientpattern.kt
rename to src/main/kotlin/pattern/GradientPattern.kt
diff --git a/src/main/kotlin/pattern/noisepattern.kt b/src/main/kotlin/pattern/NoisePattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/noisepattern.kt
rename to src/main/kotlin/pattern/NoisePattern.kt
diff --git a/src/main/kotlin/pattern/pattern.kt b/src/main/kotlin/pattern/Pattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/pattern.kt
rename to src/main/kotlin/pattern/Pattern.kt
diff --git a/src/main/kotlin/pattern/perlinnoisepattern.kt b/src/main/kotlin/pattern/PerlinNoisePattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/perlinnoisepattern.kt
rename to src/main/kotlin/pattern/PerlinNoisePattern.kt
diff --git a/src/main/kotlin/pattern/ringpattern.kt b/src/main/kotlin/pattern/RingPattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/ringpattern.kt
rename to src/main/kotlin/pattern/RingPattern.kt
diff --git a/src/main/kotlin/pattern/simplexnoisepattern.kt b/src/main/kotlin/pattern/SimplexNoisePattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/simplexnoisepattern.kt
rename to src/main/kotlin/pattern/SimplexNoisePattern.kt
diff --git a/src/main/kotlin/pattern/solidpattern.kt b/src/main/kotlin/pattern/SolidPattern.kt
similarity index 96%
rename from src/main/kotlin/pattern/solidpattern.kt
rename to src/main/kotlin/pattern/SolidPattern.kt
index 4084c1f..f6550d2 100644
--- a/src/main/kotlin/pattern/solidpattern.kt
+++ b/src/main/kotlin/pattern/SolidPattern.kt
@@ -3,7 +3,6 @@ package pattern
 // By Sebastian Raaphorst, 2023.
 
 import math.Color
-import math.Matrix
 import math.Tuple
 
 class SolidPattern(val color: Color): Pattern() {
diff --git a/src/main/kotlin/pattern/stripedpattern.kt b/src/main/kotlin/pattern/StripedPattern.kt
similarity index 100%
rename from src/main/kotlin/pattern/stripedpattern.kt
rename to src/main/kotlin/pattern/StripedPattern.kt
diff --git a/src/main/kotlin/scene/camera.kt b/src/main/kotlin/scene/Camera.kt
similarity index 100%
rename from src/main/kotlin/scene/camera.kt
rename to src/main/kotlin/scene/Camera.kt
diff --git a/src/main/kotlin/scene/world.kt b/src/main/kotlin/scene/World.kt
similarity index 99%
rename from src/main/kotlin/scene/world.kt
rename to src/main/kotlin/scene/World.kt
index 4bfa04b..9f78a13 100644
--- a/src/main/kotlin/scene/world.kt
+++ b/src/main/kotlin/scene/World.kt
@@ -4,8 +4,6 @@ import light.Light
 import light.PointLight
 import material.Material
 import math.*
-import pattern.Pattern
-import shapes.Plane
 import shapes.Shape
 import shapes.Sphere
 import kotlin.math.sqrt
diff --git a/src/main/kotlin/shapes/cone.kt b/src/main/kotlin/shapes/Cone.kt
similarity index 100%
rename from src/main/kotlin/shapes/cone.kt
rename to src/main/kotlin/shapes/Cone.kt
diff --git a/src/main/kotlin/shapes/cube.kt b/src/main/kotlin/shapes/Cube.kt
similarity index 100%
rename from src/main/kotlin/shapes/cube.kt
rename to src/main/kotlin/shapes/Cube.kt
diff --git a/src/main/kotlin/shapes/cylinder.kt b/src/main/kotlin/shapes/Cylinder.kt
similarity index 100%
rename from src/main/kotlin/shapes/cylinder.kt
rename to src/main/kotlin/shapes/Cylinder.kt
diff --git a/src/main/kotlin/shapes/group.kt b/src/main/kotlin/shapes/Group.kt
similarity index 100%
rename from src/main/kotlin/shapes/group.kt
rename to src/main/kotlin/shapes/Group.kt
diff --git a/src/main/kotlin/shapes/plane.kt b/src/main/kotlin/shapes/Plane.kt
similarity index 100%
rename from src/main/kotlin/shapes/plane.kt
rename to src/main/kotlin/shapes/Plane.kt
diff --git a/src/main/kotlin/shapes/shape.kt b/src/main/kotlin/shapes/Shape.kt
similarity index 98%
rename from src/main/kotlin/shapes/shape.kt
rename to src/main/kotlin/shapes/Shape.kt
index 8b739bd..d6aa6b4 100644
--- a/src/main/kotlin/shapes/shape.kt
+++ b/src/main/kotlin/shapes/Shape.kt
@@ -8,8 +8,6 @@ import math.Matrix
 import math.Ray
 import math.Tuple
 import java.util.UUID
-import kotlin.math.PI
-import kotlin.math.sqrt
 
 abstract class Shape(val transformation: Matrix,
                      val material: Material,
diff --git a/src/main/kotlin/shapes/sphere.kt b/src/main/kotlin/shapes/Sphere.kt
similarity index 100%
rename from src/main/kotlin/shapes/sphere.kt
rename to src/main/kotlin/shapes/Sphere.kt
diff --git a/src/test/kotlin/light/pointlighttest.kt b/src/test/kotlin/light/PointLightTest.kt
similarity index 100%
rename from src/test/kotlin/light/pointlighttest.kt
rename to src/test/kotlin/light/PointLightTest.kt
diff --git a/src/test/kotlin/material/materialtest.kt b/src/test/kotlin/material/MaterialTest.kt
similarity index 100%
rename from src/test/kotlin/material/materialtest.kt
rename to src/test/kotlin/material/MaterialTest.kt
diff --git a/src/test/kotlin/math/colortest.kt b/src/test/kotlin/math/ColorTest.kt
similarity index 100%
rename from src/test/kotlin/math/colortest.kt
rename to src/test/kotlin/math/ColorTest.kt
diff --git a/src/test/kotlin/math/intersectiontest.kt b/src/test/kotlin/math/IntersectionTest.kt
similarity index 100%
rename from src/test/kotlin/math/intersectiontest.kt
rename to src/test/kotlin/math/IntersectionTest.kt
diff --git a/src/test/kotlin/math/matrixtest.kt b/src/test/kotlin/math/MatrixTest.kt
similarity index 100%
rename from src/test/kotlin/math/matrixtest.kt
rename to src/test/kotlin/math/MatrixTest.kt
diff --git a/src/test/kotlin/math/raytest.kt b/src/test/kotlin/math/RayTest.kt
similarity index 100%
rename from src/test/kotlin/math/raytest.kt
rename to src/test/kotlin/math/RayTest.kt
diff --git a/src/test/kotlin/math/sharedtest.kt b/src/test/kotlin/math/SharedTest.kt
similarity index 100%
rename from src/test/kotlin/math/sharedtest.kt
rename to src/test/kotlin/math/SharedTest.kt
diff --git a/src/test/kotlin/math/tupletest.kt b/src/test/kotlin/math/TupleTest.kt
similarity index 100%
rename from src/test/kotlin/math/tupletest.kt
rename to src/test/kotlin/math/TupleTest.kt
diff --git a/src/test/kotlin/output/canvastest.kt b/src/test/kotlin/output/CanvasTest.kt
similarity index 98%
rename from src/test/kotlin/output/canvastest.kt
rename to src/test/kotlin/output/CanvasTest.kt
index 98a400c..f497a49 100644
--- a/src/test/kotlin/output/canvastest.kt
+++ b/src/test/kotlin/output/CanvasTest.kt
@@ -6,7 +6,7 @@ import math.Color
 import org.junit.jupiter.api.Test
 import kotlin.test.assertEquals
 
-class TestCanvas {
+class CanvasTest {
     @Test
     fun `Create a Canvas`() {
         val c = Canvas(10, 20)
diff --git a/src/test/kotlin/pattern/blendedpatterntest.kt b/src/test/kotlin/pattern/BlendedPatternTest.kt
similarity index 98%
rename from src/test/kotlin/pattern/blendedpatterntest.kt
rename to src/test/kotlin/pattern/BlendedPatternTest.kt
index d7940a9..427cb38 100644
--- a/src/test/kotlin/pattern/blendedpatterntest.kt
+++ b/src/test/kotlin/pattern/BlendedPatternTest.kt
@@ -1,5 +1,7 @@
 package pattern
 
+// By Sebastian Raaphorst, 2023.
+
 import math.Color
 import math.Matrix
 import math.Tuple
diff --git a/src/test/kotlin/pattern/checkerpatterntest.kt b/src/test/kotlin/pattern/CheckerPatternTest.kt
similarity index 100%
rename from src/test/kotlin/pattern/checkerpatterntest.kt
rename to src/test/kotlin/pattern/CheckerPatternTest.kt
diff --git a/src/test/kotlin/pattern/gradientpatterntest.kt b/src/test/kotlin/pattern/GradientPatternTest.kt
similarity index 100%
rename from src/test/kotlin/pattern/gradientpatterntest.kt
rename to src/test/kotlin/pattern/GradientPatternTest.kt
diff --git a/src/test/kotlin/pattern/patterntest.kt b/src/test/kotlin/pattern/PatternTest.kt
similarity index 100%
rename from src/test/kotlin/pattern/patterntest.kt
rename to src/test/kotlin/pattern/PatternTest.kt
diff --git a/src/test/kotlin/pattern/ringpatterntest.kt b/src/test/kotlin/pattern/RingPatternTest.kt
similarity index 100%
rename from src/test/kotlin/pattern/ringpatterntest.kt
rename to src/test/kotlin/pattern/RingPatternTest.kt
diff --git a/src/test/kotlin/pattern/solidpatterntest.kt b/src/test/kotlin/pattern/SolidPatternTest.kt
similarity index 100%
rename from src/test/kotlin/pattern/solidpatterntest.kt
rename to src/test/kotlin/pattern/SolidPatternTest.kt
diff --git a/src/test/kotlin/pattern/stripedpatterntest.kt b/src/test/kotlin/pattern/StripedPatternTest.kt
similarity index 100%
rename from src/test/kotlin/pattern/stripedpatterntest.kt
rename to src/test/kotlin/pattern/StripedPatternTest.kt
diff --git a/src/test/kotlin/scene/cameratest.kt b/src/test/kotlin/scene/CameraTest.kt
similarity index 100%
rename from src/test/kotlin/scene/cameratest.kt
rename to src/test/kotlin/scene/CameraTest.kt
diff --git a/src/test/kotlin/scene/worldtest.kt b/src/test/kotlin/scene/WorldTest.kt
similarity index 100%
rename from src/test/kotlin/scene/worldtest.kt
rename to src/test/kotlin/scene/WorldTest.kt
diff --git a/src/test/kotlin/shapes/conetest.kt b/src/test/kotlin/shapes/ConeTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/conetest.kt
rename to src/test/kotlin/shapes/ConeTest.kt
diff --git a/src/test/kotlin/shapes/cubetest.kt b/src/test/kotlin/shapes/CubeTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/cubetest.kt
rename to src/test/kotlin/shapes/CubeTest.kt
diff --git a/src/test/kotlin/shapes/cylindertest.kt b/src/test/kotlin/shapes/CylinderTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/cylindertest.kt
rename to src/test/kotlin/shapes/CylinderTest.kt
diff --git a/src/test/kotlin/shapes/grouptest.kt b/src/test/kotlin/shapes/GroupTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/grouptest.kt
rename to src/test/kotlin/shapes/GroupTest.kt
diff --git a/src/test/kotlin/shapes/planetest.kt b/src/test/kotlin/shapes/PlaneTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/planetest.kt
rename to src/test/kotlin/shapes/PlaneTest.kt
diff --git a/src/test/kotlin/shapes/shapetest.kt b/src/test/kotlin/shapes/ShapeTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/shapetest.kt
rename to src/test/kotlin/shapes/ShapeTest.kt
diff --git a/src/test/kotlin/shapes/spheretest.kt b/src/test/kotlin/shapes/SphereTest.kt
similarity index 100%
rename from src/test/kotlin/shapes/spheretest.kt
rename to src/test/kotlin/shapes/SphereTest.kt

From ecda5573b7a57d8188a285093a17c1c8763e761a Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Thu, 19 Jan 2023 00:13:53 -0500
Subject: [PATCH 3/9] Chapter 14: Bounding boxes added.

---
 src/main/kotlin/apps/ch07_world.kt        |   8 +-
 src/main/kotlin/apps/ch08_shadowpuppet.kt |   8 +-
 src/main/kotlin/apps/ch09_world.kt        |   8 +-
 src/main/kotlin/apps/ch10_world.kt        |   8 +-
 src/main/kotlin/apps/ch11_world.kt        |   8 +-
 src/main/kotlin/apps/ch12_world.kt        |   9 +-
 src/main/kotlin/apps/ch13_world.kt        |   8 +-
 src/main/kotlin/math/BoundingBox.kt       | 104 ++++++++++++++++++++++
 src/main/kotlin/shapes/Cone.kt            |   7 ++
 src/main/kotlin/shapes/Cube.kt            |  25 ++----
 src/main/kotlin/shapes/Cylinder.kt        |   4 +
 src/main/kotlin/shapes/Group.kt           |  29 ++++--
 src/main/kotlin/shapes/Plane.kt           |   7 ++
 src/main/kotlin/shapes/Shape.kt           |  19 ++--
 src/main/kotlin/shapes/Sphere.kt          |   8 +-
 src/test/kotlin/shapes/CubeTest.kt        |   3 +-
 src/test/kotlin/shapes/GroupTest.kt       |  12 +--
 src/test/kotlin/shapes/ShapeTest.kt       |  18 ++++
 18 files changed, 238 insertions(+), 55 deletions(-)
 create mode 100644 src/main/kotlin/math/BoundingBox.kt

diff --git a/src/main/kotlin/apps/ch07_world.kt b/src/main/kotlin/apps/ch07_world.kt
index 0ea515b..9682c75 100644
--- a/src/main/kotlin/apps/ch07_world.kt
+++ b/src/main/kotlin/apps/ch07_world.kt
@@ -12,6 +12,7 @@ import scene.World
 import shapes.Sphere
 import java.io.File
 import kotlin.math.PI
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val multipleLights = false
@@ -87,6 +88,9 @@ fun main() {
         Camera(1000, 500, PI / 3, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch07_world.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch07_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
diff --git a/src/main/kotlin/apps/ch08_shadowpuppet.kt b/src/main/kotlin/apps/ch08_shadowpuppet.kt
index 49b48df..659fb95 100644
--- a/src/main/kotlin/apps/ch08_shadowpuppet.kt
+++ b/src/main/kotlin/apps/ch08_shadowpuppet.kt
@@ -12,6 +12,7 @@ import scene.World
 import shapes.Sphere
 import java.io.File
 import kotlin.math.PI
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val wrist = run {
@@ -77,6 +78,9 @@ fun main() {
         Camera(1200, 600, PI/6, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch08_shadowpuppet.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch08_shadowpuppet.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
diff --git a/src/main/kotlin/apps/ch09_world.kt b/src/main/kotlin/apps/ch09_world.kt
index 9e9889f..40e66ee 100644
--- a/src/main/kotlin/apps/ch09_world.kt
+++ b/src/main/kotlin/apps/ch09_world.kt
@@ -13,6 +13,7 @@ import shapes.Plane
 import shapes.Sphere
 import java.io.File
 import kotlin.math.PI
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val multipleLights = false
@@ -88,6 +89,9 @@ fun main() {
         Camera(1000, 500, PI / 3, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch09_world.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch09_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
diff --git a/src/main/kotlin/apps/ch10_world.kt b/src/main/kotlin/apps/ch10_world.kt
index 8995d5d..9b8c362 100644
--- a/src/main/kotlin/apps/ch10_world.kt
+++ b/src/main/kotlin/apps/ch10_world.kt
@@ -14,6 +14,7 @@ import shapes.Plane
 import shapes.Sphere
 import java.io.File
 import kotlin.math.PI
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val world = run {
@@ -95,6 +96,9 @@ fun main() {
         Camera(2500, 1250, PI /3, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch10_world.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch10_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
diff --git a/src/main/kotlin/apps/ch11_world.kt b/src/main/kotlin/apps/ch11_world.kt
index fa284e4..ac7cef1 100644
--- a/src/main/kotlin/apps/ch11_world.kt
+++ b/src/main/kotlin/apps/ch11_world.kt
@@ -16,6 +16,7 @@ import shapes.Plane
 import shapes.Sphere
 import java.io.File
 import kotlin.math.PI
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val wallMaterial = run {
@@ -113,6 +114,9 @@ fun main() {
         Camera(2400, 1200, 1.152, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch11_world.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch11_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
diff --git a/src/main/kotlin/apps/ch12_world.kt b/src/main/kotlin/apps/ch12_world.kt
index 67b7e66..898995e 100644
--- a/src/main/kotlin/apps/ch12_world.kt
+++ b/src/main/kotlin/apps/ch12_world.kt
@@ -14,6 +14,7 @@ import scene.Camera
 import scene.World
 import shapes.Cube
 import java.io.File
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val floorCeiling = run {
@@ -152,6 +153,10 @@ fun main() {
         Camera(2400, 1200, 0.7805, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch12_world.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch12_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
+
diff --git a/src/main/kotlin/apps/ch13_world.kt b/src/main/kotlin/apps/ch13_world.kt
index ba3ba00..b902bd7 100644
--- a/src/main/kotlin/apps/ch13_world.kt
+++ b/src/main/kotlin/apps/ch13_world.kt
@@ -15,6 +15,7 @@ import shapes.Cylinder
 import shapes.Plane
 import java.io.File
 import kotlin.math.PI
+import kotlin.system.measureTimeMillis
 
 fun main() {
     val flooring = run {
@@ -108,6 +109,9 @@ fun main() {
         Camera(2400, 1200, PI / 10, t)
     }
 
-    val canvas = camera.render(world)
-    canvas.toPPMFile(File("output/ch13_world.ppm"))
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch13_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
 }
diff --git a/src/main/kotlin/math/BoundingBox.kt b/src/main/kotlin/math/BoundingBox.kt
new file mode 100644
index 0000000..f9347a2
--- /dev/null
+++ b/src/main/kotlin/math/BoundingBox.kt
@@ -0,0 +1,104 @@
+package math
+
+// By Sebastian Raaphorst, 2023.
+
+import kotlin.math.max
+import kotlin.math.min
+
+data class BoundingBox(val minPoint: Tuple = MaxPoint, val maxPoint: Tuple = MinPoint) {
+    init {
+        if (!minPoint.isPoint())
+            throw IllegalArgumentException("BoundingBox minPoint is not a point: $minPoint.")
+        if (!maxPoint.isPoint())
+            throw IllegalArgumentException("BoundingBox maxPoint is not a point: $maxPoint.")
+    }
+
+    val isEmpty: Boolean by lazy {
+        minPoint.x > maxPoint.x || minPoint.y > maxPoint.y || minPoint.z > maxPoint.z
+    }
+    val isNotEmpty: Boolean by lazy {
+        !isEmpty
+    }
+
+    fun add(point: Tuple): BoundingBox {
+        if (!point.isPoint())
+            throw IllegalArgumentException("Tried to add vector to BoundingBox: $point.")
+        return BoundingBox(
+            Tuple.point(min(minPoint.x, point.x), min(minPoint.y, point.y), min(minPoint.z, point.z)),
+            Tuple.point(max(maxPoint.x, point.x), min(maxPoint.y, point.y), min(maxPoint.z, point.z))
+        )
+    }
+
+    fun merge(box: BoundingBox): BoundingBox =
+        add(box.minPoint).add(box.maxPoint)
+
+    fun transform(transformation: Matrix): BoundingBox {
+        val corners = listOf(
+            minPoint,
+            Tuple.point(maxPoint.x, minPoint.y, minPoint.z),
+            Tuple.point(maxPoint.x, minPoint.y, maxPoint.z),
+            Tuple.point(minPoint.x, minPoint.y, maxPoint.z),
+            Tuple.point(minPoint.x, maxPoint.y, minPoint.z),
+            Tuple.point(maxPoint.x, maxPoint.y, minPoint.z),
+            maxPoint,
+            Tuple.point(minPoint.x, maxPoint.y, maxPoint.z)
+        )
+
+        val transformedCorners = corners.map { transformation * it }
+
+        // Find the new minPoint and maxPoint.
+        val minX = transformedCorners.fold(Double.POSITIVE_INFINITY) { curr, p -> if (p.x < curr) p.x else curr }
+        val minY = transformedCorners.fold(Double.POSITIVE_INFINITY) { curr, p -> if (p.y < curr) p.y else curr }
+        val minZ = transformedCorners.fold(Double.POSITIVE_INFINITY) { curr, p -> if (p.z < curr) p.z else curr }
+        val maxX = transformedCorners.fold(Double.NEGATIVE_INFINITY) { curr, p -> if (p.x > curr) p.x else curr }
+        val maxY = transformedCorners.fold(Double.NEGATIVE_INFINITY) { curr, p -> if (p.y > curr) p.y else curr }
+        val maxZ = transformedCorners.fold(Double.NEGATIVE_INFINITY) { curr, p -> if (p.z > curr) p.z else curr }
+
+        return BoundingBox(Tuple.point(minX, minY, minZ), Tuple.point(maxX, maxY, maxZ))
+    }
+
+    // Check axis for AABB (axis aligned bounding box).
+    // minimum and maximum specify the minimum and maximum values on the axis for this bounding box.
+    private fun checkAxis(origin: Double, direction: Double, minimum: Double, maximum: Double): Pair<Double, Double> {
+        val tMin = (minimum - origin) / direction
+        val tMax = (maximum - origin) / direction
+        return if (tMin > tMax) Pair(tMax, tMin) else Pair(tMin, tMax)
+    }
+
+    // Check if the ray intersects this bounding box, and if it does, return the t-values.
+    internal fun intersects(rayLocal: Ray): List<Double> {
+        val (xtMin, xtMax) = checkAxis(rayLocal.origin.x, rayLocal.direction.x, minPoint.x, maxPoint.x)
+        val (ytMin, ytMax) = checkAxis(rayLocal.origin.y, rayLocal.direction.y, minPoint.y, maxPoint.y)
+        val (ztMin, ztMax) = checkAxis(rayLocal.origin.z, rayLocal.direction.z, minPoint.z, maxPoint.z)
+
+        val tMin = maxOf(xtMin, ytMin, ztMin)
+        val tMax = minOf(xtMax, ytMax, ztMax)
+
+        return if (tMin <= tMax)
+            listOf(tMin, tMax)
+        else
+            emptyList()
+    }
+    operator fun contains(point: Tuple): Boolean {
+        if (!point.isPoint())
+            throw IllegalArgumentException("BoundingBox contains passed vector: $point.")
+        return point.x >= minPoint.x && point.y >= minPoint.y && point.z >= minPoint.z &&
+                point.x <= maxPoint.x && point.y <= maxPoint.y && point.z <= maxPoint.z
+    }
+
+    operator fun contains(box: BoundingBox): Boolean =
+        contains(box.minPoint) && contains(box.maxPoint)
+
+    companion object {
+        internal val MaxPoint = Tuple.point(
+            Double.POSITIVE_INFINITY,
+            Double.POSITIVE_INFINITY,
+            Double.POSITIVE_INFINITY
+        )
+        internal val MinPoint = Tuple.point(
+            Double.NEGATIVE_INFINITY,
+            Double.NEGATIVE_INFINITY,
+            Double.NEGATIVE_INFINITY
+        )
+    }
+}
diff --git a/src/main/kotlin/shapes/Cone.kt b/src/main/kotlin/shapes/Cone.kt
index f78ea66..6f2d9cb 100644
--- a/src/main/kotlin/shapes/Cone.kt
+++ b/src/main/kotlin/shapes/Cone.kt
@@ -5,6 +5,8 @@ package shapes
 import material.Material
 import math.*
 import math.Intersection
+import kotlin.math.absoluteValue
+import kotlin.math.max
 import kotlin.math.sqrt
 
 class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
@@ -107,4 +109,9 @@ class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
             return Tuple.vector(localPoint.x, y, localPoint.z)
         }
     }
+
+    override val bounds: BoundingBox by lazy {
+        val r = max(this.minimum.absoluteValue, this.maximum.absoluteValue)
+        BoundingBox(Tuple.point(-r, minimum, -r), Tuple.point(r, maximum, r))
+    }
 }
diff --git a/src/main/kotlin/shapes/Cube.kt b/src/main/kotlin/shapes/Cube.kt
index 1e01ae5..0a764e1 100644
--- a/src/main/kotlin/shapes/Cube.kt
+++ b/src/main/kotlin/shapes/Cube.kt
@@ -15,25 +15,8 @@ class Cube(transformation: Matrix = Matrix.I,
     override fun withParent(parent: Shape?): Shape =
         Cube(transformation, material, castsShadow, parent)
 
-    override fun localIntersect(rayLocal: Ray): List<Intersection> {
-        val (xtMin, xtMax) = checkAxis(rayLocal.origin.x, rayLocal.direction.x)
-        val (ytMin, ytMax) = checkAxis(rayLocal.origin.y, rayLocal.direction.y)
-        val (ztMin, ztMax) = checkAxis(rayLocal.origin.z, rayLocal.direction.z)
-
-        val tMin = maxOf(xtMin, ytMin, ztMin)
-        val tMax = minOf(xtMax, ytMax, ztMax)
-
-        return if (tMin <= tMax)
-            listOf(Intersection(tMin, this), Intersection(tMax, this))
-        else
-            emptyList()
-    }
-
-    private fun checkAxis(origin: Double, direction: Double): Pair<Double, Double> {
-        val tMin = (-1 - origin) / direction
-        val tMax = (1 - origin) / direction
-        return if (tMin > tMax) Pair(tMax, tMin) else Pair(tMin, tMax)
-    }
+    override fun localIntersect(rayLocal: Ray): List<Intersection> =
+        bounds.intersects(rayLocal).map { Intersection(it, this) }
 
     override fun localNormalAt(localPoint: Tuple): Tuple {
         val posX = localPoint.x.absoluteValue
@@ -45,4 +28,8 @@ class Cube(transformation: Matrix = Matrix.I,
             else -> Tuple.vector(0, 0, localPoint.z)
         }
     }
+
+    override val bounds: BoundingBox by lazy {
+        BoundingBox(Tuple.point(-1, -1, -1), Tuple.point(1, 1, 1))
+    }
 }
diff --git a/src/main/kotlin/shapes/Cylinder.kt b/src/main/kotlin/shapes/Cylinder.kt
index 412b4d7..16d9308 100644
--- a/src/main/kotlin/shapes/Cylinder.kt
+++ b/src/main/kotlin/shapes/Cylinder.kt
@@ -96,4 +96,8 @@ class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
         else
             Tuple.vector(localPoint.x, 0, localPoint.z)
     }
+
+    override val bounds: BoundingBox by lazy {
+        BoundingBox(Tuple.point(-1, minimum, -1), Tuple.point(1, maximum, 1))
+    }
 }
diff --git a/src/main/kotlin/shapes/Group.kt b/src/main/kotlin/shapes/Group.kt
index 79768f6..4666a94 100644
--- a/src/main/kotlin/shapes/Group.kt
+++ b/src/main/kotlin/shapes/Group.kt
@@ -3,10 +3,10 @@ package shapes
 // By Sebastian Raaphorst, 2023.
 
 import material.Material
+import math.*
+import math.BoundingBox.Companion.MaxPoint
+import math.BoundingBox.Companion.MinPoint
 import math.Intersection
-import math.Matrix
-import math.Ray
-import math.Tuple
 
 class Group(transformation: Matrix = Matrix.I,
             children: List<Shape> = emptyList(),
@@ -16,6 +16,12 @@ class Group(transformation: Matrix = Matrix.I,
 
     // Make copies of all the children to backreference this as their parent.
     val children = children.map { it.withParent(this) }
+    val size = children.size
+    val isEmpty = children.isEmpty()
+    val isNotEmpty = children.isNotEmpty()
+
+    operator fun get(idx: Int): Shape =
+        children[idx]
 
     operator fun contains(s: Shape): Boolean =
         s in children
@@ -23,10 +29,19 @@ class Group(transformation: Matrix = Matrix.I,
     override fun withParent(parent: Shape?): Shape =
         Group(transformation, children, castsShadow, parent)
 
+    // Only process children if the ray intersects the bounding box for this group.
     override fun localIntersect(rayLocal: Ray): List<Intersection> =
-        children.flatMap { it.intersect(rayLocal) }.sortedBy { it.t }
-
-    override fun localNormalAt(localPoint: Tuple): Tuple {
-        TODO("Not yet implemented")
+        if (bounds.intersects(rayLocal).isNotEmpty())
+            children.flatMap { it.intersect(rayLocal) }.sortedBy { it.t }
+        else
+            emptyList()
+
+    override fun localNormalAt(localPoint: Tuple): Tuple =
+        throw NotImplementedError("Groups do not have local normals.")
+
+    override val bounds: BoundingBox by lazy {
+        children.fold(BoundingBox(MaxPoint, MinPoint)) { curr, shape ->
+            curr.merge(shape.parentBounds)
+        }
     }
 }
diff --git a/src/main/kotlin/shapes/Plane.kt b/src/main/kotlin/shapes/Plane.kt
index 0b9c159..215c09b 100644
--- a/src/main/kotlin/shapes/Plane.kt
+++ b/src/main/kotlin/shapes/Plane.kt
@@ -23,4 +23,11 @@ class Plane(transformation: Matrix = Matrix.I,
 
     override fun localNormalAt(localPoint: Tuple): Tuple =
         Tuple.VY
+
+    override val bounds: BoundingBox by lazy {
+        BoundingBox(
+            Tuple.point(Double.NEGATIVE_INFINITY, 0, Double.NEGATIVE_INFINITY),
+            Tuple.point(Double.POSITIVE_INFINITY, 0, Double.POSITIVE_INFINITY)
+        )
+    }
 }
diff --git a/src/main/kotlin/shapes/Shape.kt b/src/main/kotlin/shapes/Shape.kt
index d6aa6b4..deff8e8 100644
--- a/src/main/kotlin/shapes/Shape.kt
+++ b/src/main/kotlin/shapes/Shape.kt
@@ -3,11 +3,10 @@ package shapes
 // By Sebastian Raaphorst, 2023.
 
 import material.Material
+import math.*
 import math.Intersection
-import math.Matrix
-import math.Ray
-import math.Tuple
 import java.util.UUID
+import kotlin.math.PI
 
 abstract class Shape(val transformation: Matrix,
                      val material: Material,
@@ -20,7 +19,8 @@ abstract class Shape(val transformation: Matrix,
                     "\tShape: ${javaClass.name}\nTransformation:\n${transformation.show()}")
     }
 
-    abstract fun withParent(parent: Shape? = null): Shape
+    // This method should only be invoked by Groups containing the object.
+    internal abstract fun withParent(parent: Shape? = null): Shape
 
     // Convert a point from world space to object space.
     // Later on, we use parent here.
@@ -43,7 +43,7 @@ abstract class Shape(val transformation: Matrix,
 
     internal abstract fun localIntersect(rayLocal: Ray): List<Intersection>
 
-    // normalAt transforms the point to object space and passes it to localNormalAt
+    // normalAt transforms the point from world to object (local) space and passes it to localNormalAt
     // which should comprise the concrete implementation of calculating the normal vector
     // at the point for the Shape. Then normalAt transforms it back into world space.
     internal fun normalAt(worldPoint: Tuple): Tuple {
@@ -58,5 +58,14 @@ abstract class Shape(val transformation: Matrix,
         return normalToWorld(localNormal)
     }
 
+    // Normal at a point in object (local) space.
+    // Normal should be returned in local space, and normalAt handles transforming it back to world space.
     internal abstract fun localNormalAt(localPoint: Tuple): Tuple
+
+    // Untransformed bounds for each Shape type.
+    internal abstract val bounds: BoundingBox
+
+    internal val parentBounds: BoundingBox by lazy {
+        bounds.transform(transformation)
+    }
 }
diff --git a/src/main/kotlin/shapes/Sphere.kt b/src/main/kotlin/shapes/Sphere.kt
index aaf06ce..d68b062 100644
--- a/src/main/kotlin/shapes/Sphere.kt
+++ b/src/main/kotlin/shapes/Sphere.kt
@@ -3,10 +3,8 @@ package shapes
 // By Sebastian Raaphorst, 2023.
 
 import material.Material
+import math.*
 import math.Intersection
-import math.Matrix
-import math.Ray
-import math.Tuple
 import kotlin.math.sqrt
 
 class Sphere(transformation: Matrix = Matrix.I,
@@ -38,6 +36,10 @@ class Sphere(transformation: Matrix = Matrix.I,
     override fun localNormalAt(localPoint: Tuple): Tuple =
         localPoint - Tuple.PZERO
 
+    override val bounds: BoundingBox by lazy {
+        BoundingBox(Tuple.point(-1, -1, -1), Tuple.point(1, 1, 1))
+    }
+
     companion object {
         internal fun glassSphere(transformation: Matrix = Matrix.I,
                         transparency: Double = 1.0,
diff --git a/src/test/kotlin/shapes/CubeTest.kt b/src/test/kotlin/shapes/CubeTest.kt
index 8c9003c..c52c760 100644
--- a/src/test/kotlin/shapes/CubeTest.kt
+++ b/src/test/kotlin/shapes/CubeTest.kt
@@ -58,8 +58,7 @@ class CubeTest {
             Tuple.vector(0.5345, 0.8018, 0.2673),
             -Tuple.VZ, -Tuple.VY, -Tuple.VX)
 
-        origins.zip(directions).withIndex().forEach { (idx, rayInfo) ->
-            val (origin, direction) = rayInfo
+        origins.zip(directions).forEach { (origin, direction) ->
             val r = Ray(origin, direction)
             val xs = c.localIntersect(r)
             assertEquals(0, xs.size)
diff --git a/src/test/kotlin/shapes/GroupTest.kt b/src/test/kotlin/shapes/GroupTest.kt
index b88a3cb..e037f69 100644
--- a/src/test/kotlin/shapes/GroupTest.kt
+++ b/src/test/kotlin/shapes/GroupTest.kt
@@ -5,7 +5,9 @@ package shapes
 import math.Matrix
 import math.Ray
 import math.Tuple
+import math.assertAlmostEquals
 import org.junit.jupiter.api.Test
+import kotlin.math.PI
 import kotlin.test.*
 
 class GroupTest {
@@ -13,15 +15,15 @@ class GroupTest {
     fun `New group`() {
         val g = Group()
         assertEquals(Matrix.I, g.transformation)
-        assertTrue(g.children.isEmpty())
+        assertTrue(g.isEmpty)
     }
 
     @Test
     fun `New group with test shape`() {
         val s = ShapeTest.TestShape()
         val g = Group(children = listOf(s))
-        assertEquals(1, g.children.size)
-        val sp = g.children[0]
+        assertEquals(1, g.size)
+        val sp = g[0]
 
         // Check that s has changed and been assigned the group as a parent.
         assertNotSame(s, sp)
@@ -50,8 +52,8 @@ class GroupTest {
         val r = Ray(Tuple.point(0, 0, -5), Tuple.VZ)
         val xs = g.localIntersect(r)
         assertEquals(4, xs.size)
-        val sp1 = g.children[0]
-        val sp2 = g.children[1]
+        val sp1 = g[0]
+        val sp2 = g[1]
         assertSame(sp2, xs[0].shape)
         assertSame(sp2, xs[1].shape)
         assertSame(sp1, xs[2].shape)
diff --git a/src/test/kotlin/shapes/ShapeTest.kt b/src/test/kotlin/shapes/ShapeTest.kt
index bc1ccfa..b7fdf59 100644
--- a/src/test/kotlin/shapes/ShapeTest.kt
+++ b/src/test/kotlin/shapes/ShapeTest.kt
@@ -29,6 +29,13 @@ class ShapeTest {
 
         override fun localNormalAt(localPoint: Tuple): Tuple =
             localPoint - Tuple.PZERO
+
+        override val bounds: BoundingBox by lazy {
+            BoundingBox(
+                Tuple.point(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY),
+                Tuple.point(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)
+            )
+        }
     }
 
     @Test
@@ -91,4 +98,15 @@ class ShapeTest {
         val n = sNew.normalToWorld(Tuple.vector(sqrt3by3, sqrt3by3, sqrt3by3))
         assertAlmostEquals(Tuple.vector(0.28571, 0.42857, -0.85714), n)
     }
+
+    @Test
+    fun `Normal on an object in group`() {
+        val s = Sphere(Matrix.translate(5, 0, 0))
+        val g2 = Group(Matrix.scale(1, 2, 3), listOf(s))
+        val g1 = Group(Matrix.rotateY(PI / 2), listOf(g2))
+
+        val sp = (g1.children[0] as Group).children[0]
+        val n = sp.normalAt(Tuple.point(1.7321, 1.1547, -5.5774))
+        assertAlmostEquals(Tuple.vector(0.28570, 0.42854, -0.85716), n)
+    }
 }

From 6c20bbf9c35279946b268231250dbbdb8db0fb64 Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Thu, 19 Jan 2023 01:39:57 -0500
Subject: [PATCH 4/9] Chapter 14: World rendered but not working.

---
 src/main/kotlin/apps/ch14_world.kt   |  91 ++++++++++++
 src/main/kotlin/apps/ch14_world.yaml | 205 +++++++++++++++++++++++++++
 src/main/kotlin/shapes/Cone.kt       |   3 +
 src/main/kotlin/shapes/Cube.kt       |   3 +
 src/main/kotlin/shapes/Cylinder.kt   |   3 +
 src/main/kotlin/shapes/Group.kt      |  10 ++
 src/main/kotlin/shapes/Plane.kt      |   3 +
 src/main/kotlin/shapes/Shape.kt      |   3 +
 src/main/kotlin/shapes/Sphere.kt     |   3 +
 src/test/kotlin/shapes/ShapeTest.kt  |   6 +
 10 files changed, 330 insertions(+)
 create mode 100644 src/main/kotlin/apps/ch14_world.kt
 create mode 100644 src/main/kotlin/apps/ch14_world.yaml

diff --git a/src/main/kotlin/apps/ch14_world.kt b/src/main/kotlin/apps/ch14_world.kt
new file mode 100644
index 0000000..5a02094
--- /dev/null
+++ b/src/main/kotlin/apps/ch14_world.kt
@@ -0,0 +1,91 @@
+package apps
+
+// By Sebastian Raaphorst, 2023.
+// From https://forum.raytracerchallenge.com/thread/13/groups-scene-description
+
+import light.PointLight
+import material.Material
+import math.Color
+import math.Matrix
+import math.Tuple
+import scene.Camera
+import scene.World
+import shapes.*
+import java.io.File
+import kotlin.math.PI
+import kotlin.system.measureTimeMillis
+
+fun main() {
+    val transforms = listOf(0, PI / 3, 2 * PI / 3, PI, 4 * PI / 3, 5 * PI / 3)
+        .map(Matrix::rotateY)
+
+    val leg = run {
+        val sphere = Sphere(Matrix.translate(0, 0, -1) * Matrix.scale(0.25, 0.25, 0.25))
+        val cylinder = Cylinder(0, 1, false,
+            Matrix.translate(0, 0, -1) * Matrix.rotateY(-PI / 6) *
+            Matrix.rotateZ(-PI / 2) * Matrix.scale(0.25, 1, 0.25))
+        Group(children = listOf(sphere, cylinder))
+    }
+
+    val cap = run {
+        val trans = Matrix.rotateX(-PI / 4 ) * Matrix.scale(0.24606, 1.37002, 0.24606)
+        val cones = transforms.map {
+            Cone(-1, 0, false, it * trans)
+        }
+        Group(children = cones)
+    }
+
+    val wacky = run {
+        val legs = transforms.map(leg::withTransformation)
+        val cap1 = cap.withTransformation(Matrix.translate(0, 1, 0))
+        val cap2 = cap.withTransformation(Matrix.rotateX(PI) * Matrix.translate(0, 1, 0))
+        Group(children = legs + listOf(cap1, cap2))
+    }
+
+    val backdrop = run {
+        val t = Matrix.translate(0, 0, 100) * Matrix.rotateX(PI / 2)
+        val m = Material(Color.WHITE, ambient = 1, diffuse = 0, specular = 0)
+        Plane(t, m)
+    }
+
+    val wacky1 = run {
+        val t = Matrix.translate(-2.8, 0, 0) * Matrix.rotateX(0.4363) * Matrix.rotateY(PI / 18)
+        val m = Material(Color(0.9, 0.2, 0.4), ambient = 0.2, diffuse = 0.8, specular = 0.7, shininess = 20)
+        wacky.withTransformation(t).withMaterial(m)
+    }
+
+    val wacky2 = run {
+        val t = Matrix.rotateY(PI / 18)
+        val m = Material(Color(0.2, 0.9, 0.6), ambient = 0.2, diffuse = 0.8, specular = 0.7, shininess = 20)
+        wacky.withTransformation(t).withMaterial(m)
+    }
+
+    val wacky3 = run {
+        val t = Matrix.translate(2.8, 0, 0) * Matrix.rotateX(-0.4363) * Matrix.rotateY(-PI / 18)
+        val m = Material(Color(0.2, 0.3, 1), ambient = 0.2, diffuse = 0.8, specular = 0.7, shininess = 20)
+        wacky.withTransformation(t).withMaterial(m)
+    }
+
+    val world = run {
+        val color = Color(0.25, 0.25, 0.25)
+        val light1 = PointLight(Tuple.point(10_000, 10_000, -10_000), color)
+        val light2 = PointLight(Tuple.point(-10_000, 10_000, -10_000), color)
+        val light3 = PointLight(Tuple.point(10_000, -10_000, -10_000), color)
+        val light4 = PointLight(Tuple.point(-10_000, -10_000, -10_000), color)
+        World(listOf(backdrop, wacky1, wacky2, wacky3), listOf(light1, light2, light3, light4))
+    }
+
+    val camera = run {
+        val from = Tuple.point(0, 0, -9)
+        val to = Tuple.PZERO
+        val t = from.viewTransformationFrom(to, Tuple.VY)
+        Camera(2400, 1200, 0.9, t)
+    }
+
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch14_world.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
+}
+
diff --git a/src/main/kotlin/apps/ch14_world.yaml b/src/main/kotlin/apps/ch14_world.yaml
new file mode 100644
index 0000000..ad8053e
--- /dev/null
+++ b/src/main/kotlin/apps/ch14_world.yaml
@@ -0,0 +1,205 @@
+# ======================================================
+# group.yml
+#
+# This file describes the scene illustrated at the start
+# of chapter 14, "Groups", in "The Ray Tracer
+# Challenge"
+#
+# This scene description assumes:
+#
+# 1. Your ray tracer supports multiple light sources.
+#    If it does not, you can omit the extra light
+#    sources and bump up the existing light's intensity
+#    to [1, 1, 1].
+# 2. Child objects in a group inherit their default
+#    material from the parent group. If you haven't
+#    implemented this optional feature, you'll need
+#    arrange other means of texturing the child
+#    elements (or accept that all elements of the
+#    scene will be white).
+#
+# by Jamis Buck <jamis@jamisbuck.org>
+# ======================================================
+
+# ======================================================
+# the camera
+# ======================================================
+
+- add: camera
+  width: 300
+  height: 100
+  field-of-view: 0.9
+  from: [0, 0, -9]
+  to: [0, 0, 0]
+  up: [0, 1, 0]
+
+# ======================================================
+# light sources
+# ======================================================
+
+- add: light
+  at: [ 10000, 10000, -10000 ]
+  intensity: [ 0.25, 0.25, 0.25 ]
+- add: light
+  at: [ -10000, 10000, -10000 ]
+  intensity: [ 0.25, 0.25, 0.25 ]
+- add: light
+  at: [ 10000, -10000, -10000 ]
+  intensity: [ 0.25, 0.25, 0.25 ]
+- add: light
+  at: [ -10000, -10000, -10000 ]
+  intensity: [ 0.25, 0.25, 0.25 ]
+
+# ======================================================
+# These describe groups that will be reused within
+# the scene. (You can think of these as functions that
+# return a new instance of the given shape each time they
+# are referenced.)
+# ======================================================
+
+- define: leg
+  value:
+    add: group
+    children:
+      - add: sphere
+        transform:
+          - [ scale, 0.25, 0.25, 0.25 ]
+          - [ translate, 0, 0, -1 ]
+      - add: cylinder
+        min: 0
+        max: 1
+        closed: false
+        transform:
+          - [ scale, 0.25, 1, 0.25 ]
+          - [ rotate-z, -1.5708 ]
+          - [ rotate-y, -0.5236 ]
+          - [ translate, 0, 0, -1 ]
+
+- define: cap
+  value:
+    add: group
+    children:
+      - add: cone
+        min: -1
+        max: 0
+        closed: false
+        transform:
+          - [ scale, 0.24606, 1.37002, 0.24606 ]
+          - [ rotate-x, -0.7854 ]
+      - add: cone
+        min: -1
+        max: 0
+        closed: false
+        transform:
+          - [ scale, 0.24606, 1.37002, 0.24606 ]
+          - [ rotate-x, -0.7854 ]
+          - [ rotate-y, 1.0472 ]
+      - add: cone
+        min: -1
+        max: 0
+        closed: false
+        transform:
+          - [ scale, 0.24606, 1.37002, 0.24606 ]
+          - [ rotate-x, -0.7854 ]
+          - [ rotate-y, 2.0944 ]
+      - add: cone
+        min: -1
+        max: 0
+        closed: false
+        transform:
+          - [ scale, 0.24606, 1.37002, 0.24606 ]
+          - [ rotate-x, -0.7854 ]
+          - [ rotate-y, 3.1416 ]
+      - add: cone
+        min: -1
+        max: 0
+        closed: false
+        transform:
+          - [ scale, 0.24606, 1.37002, 0.24606 ]
+          - [ rotate-x, -0.7854 ]
+          - [ rotate-y, 4.1888 ]
+      - add: cone
+        min: -1
+        max: 0
+        closed: false
+        transform:
+          - [ scale, 0.24606, 1.37002, 0.24606 ]
+          - [ rotate-x, -0.7854 ]
+          - [ rotate-y, 5.236 ]
+
+- define: wacky
+  value:
+    add: group
+    children:
+      - add: leg
+      - add: leg
+        transform:
+          - [ rotate-y, 1.0472 ]
+      - add: leg
+        transform:
+          - [ rotate-y, 2.0944 ]
+      - add: leg
+        transform:
+          - [ rotate-y, 3.1416 ]
+      - add: leg
+        transform:
+          - [ rotate-y, 4.1888 ]
+      - add: leg
+        transform:
+          - [ rotate-y, 5.236 ]
+      - add: cap
+        transform:
+          - [ translate, 0, 1, 0 ]
+      - add: cap
+        transform:
+          - [ translate, 0, 1, 0 ]
+          - [ rotate-x, 3.1416 ]
+
+# ======================================================
+# Construct the scene itself
+# ======================================================
+
+# a white backdrop
+- add: plane
+  transform:
+    - [ rotate-x, 1.5708 ]
+    - [ translate, 0, 0, 100 ]
+  material:
+    color: [ 1, 1, 1 ]
+    ambient: 1
+    diffuse: 0
+    specular: 0
+
+- add: wacky
+  transform:
+    - [ rotate-y, 0.1745 ]
+    - [ rotate-x, 0.4363 ]
+    - [ translate, -2.8, 0, 0 ]
+  material:
+    color: [ 0.9, 0.2, 0.4 ]
+    ambient: 0.2
+    diffuse: 0.8
+    specular: 0.7
+    shininess: 20
+
+- add: wacky
+  transform:
+    - [ rotate-y, 0.1745 ]
+  material:
+    color: [ 0.2, 0.9, 0.6 ]
+    ambient: 0.2
+    diffuse: 0.8
+    specular: 0.7
+    shininess: 20
+
+- add: wacky
+  transform:
+    - [ rotate-y, -0.1745 ]
+    - [ rotate-x, -0.4363 ]
+    - [ translate, 2.8, 0, 0 ]
+  material:
+    color: [ 0.2, 0.3, 1.0 ]
+    ambient: 0.2
+    diffuse: 0.8
+    specular: 0.7
+    shininess: 20
diff --git a/src/main/kotlin/shapes/Cone.kt b/src/main/kotlin/shapes/Cone.kt
index 6f2d9cb..c00a7e8 100644
--- a/src/main/kotlin/shapes/Cone.kt
+++ b/src/main/kotlin/shapes/Cone.kt
@@ -24,6 +24,9 @@ class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
     override fun withParent(parent: Shape?): Shape =
         Cone(minimum, maximum, closed, transformation, material, castsShadow, parent)
 
+    override fun withMaterial(material: Material): Shape =
+        Cone(minimum, maximum, closed, transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val a = rayLocal.direction.x * rayLocal.direction.x -
                 rayLocal.direction.y * rayLocal.direction.y +
diff --git a/src/main/kotlin/shapes/Cube.kt b/src/main/kotlin/shapes/Cube.kt
index 0a764e1..e863d3b 100644
--- a/src/main/kotlin/shapes/Cube.kt
+++ b/src/main/kotlin/shapes/Cube.kt
@@ -15,6 +15,9 @@ class Cube(transformation: Matrix = Matrix.I,
     override fun withParent(parent: Shape?): Shape =
         Cube(transformation, material, castsShadow, parent)
 
+    override fun withMaterial(material: Material): Shape =
+        Cube(transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> =
         bounds.intersects(rayLocal).map { Intersection(it, this) }
 
diff --git a/src/main/kotlin/shapes/Cylinder.kt b/src/main/kotlin/shapes/Cylinder.kt
index 16d9308..4bc9701 100644
--- a/src/main/kotlin/shapes/Cylinder.kt
+++ b/src/main/kotlin/shapes/Cylinder.kt
@@ -22,6 +22,9 @@ class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
     override fun withParent(parent: Shape?): Shape =
         Cylinder(minimum, maximum, closed, transformation, material, castsShadow, parent)
 
+    override fun withMaterial(material: Material): Shape =
+        Cylinder(minimum, maximum, closed, transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val a = rayLocal.direction.x * rayLocal.direction.x + rayLocal.direction.z * rayLocal.direction.z
 
diff --git a/src/main/kotlin/shapes/Group.kt b/src/main/kotlin/shapes/Group.kt
index 4666a94..c1097a7 100644
--- a/src/main/kotlin/shapes/Group.kt
+++ b/src/main/kotlin/shapes/Group.kt
@@ -29,6 +29,16 @@ class Group(transformation: Matrix = Matrix.I,
     override fun withParent(parent: Shape?): Shape =
         Group(transformation, children, castsShadow, parent)
 
+    fun withTransformation(transformation: Matrix): Shape {
+        if (!transformation.isTransformation())
+            throw IllegalArgumentException("Shapes must have 4x4 transformation matrices:\n" +
+                    "\tShape: ${javaClass.name}\nTransformation:\n${transformation.show()}")
+        return Group(transformation, children, castsShadow, parent)
+    }
+
+    override fun withMaterial(material: Material): Shape =
+        Group(transformation, children.map { it.withMaterial(material) }, castsShadow, parent)
+
     // Only process children if the ray intersects the bounding box for this group.
     override fun localIntersect(rayLocal: Ray): List<Intersection> =
         if (bounds.intersects(rayLocal).isNotEmpty())
diff --git a/src/main/kotlin/shapes/Plane.kt b/src/main/kotlin/shapes/Plane.kt
index 215c09b..7ea0764 100644
--- a/src/main/kotlin/shapes/Plane.kt
+++ b/src/main/kotlin/shapes/Plane.kt
@@ -14,6 +14,9 @@ class Plane(transformation: Matrix = Matrix.I,
     override fun withParent(parent: Shape?): Shape =
         Plane(transformation, material, castsShadow, parent)
 
+    override fun withMaterial(material: Material): Shape =
+        Plane(transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         if (rayLocal.direction.y.absoluteValue < DEFAULT_PRECISION)
             return emptyList()
diff --git a/src/main/kotlin/shapes/Shape.kt b/src/main/kotlin/shapes/Shape.kt
index deff8e8..84b22eb 100644
--- a/src/main/kotlin/shapes/Shape.kt
+++ b/src/main/kotlin/shapes/Shape.kt
@@ -22,6 +22,9 @@ abstract class Shape(val transformation: Matrix,
     // This method should only be invoked by Groups containing the object.
     internal abstract fun withParent(parent: Shape? = null): Shape
 
+    // This method creates a copy of the object with the specified material.
+    abstract fun withMaterial(material: Material): Shape
+
     // Convert a point from world space to object space.
     // Later on, we use parent here.
     internal fun worldToLocal(tuple: Tuple): Tuple =
diff --git a/src/main/kotlin/shapes/Sphere.kt b/src/main/kotlin/shapes/Sphere.kt
index d68b062..51d3778 100644
--- a/src/main/kotlin/shapes/Sphere.kt
+++ b/src/main/kotlin/shapes/Sphere.kt
@@ -15,6 +15,9 @@ class Sphere(transformation: Matrix = Matrix.I,
     override fun withParent(parent: Shape?): Shape =
         Sphere(transformation, material, castsShadow, parent)
 
+    override fun withMaterial(material: Material): Shape =
+        Sphere(transformation, material, castsShadow, parent)
+
     override fun localIntersect(rayLocal: Ray): List<Intersection> {
         val sphereToRay = rayLocal.origin - Tuple.PZERO
 
diff --git a/src/test/kotlin/shapes/ShapeTest.kt b/src/test/kotlin/shapes/ShapeTest.kt
index b7fdf59..81bd4bf 100644
--- a/src/test/kotlin/shapes/ShapeTest.kt
+++ b/src/test/kotlin/shapes/ShapeTest.kt
@@ -22,6 +22,12 @@ class ShapeTest {
             return s
         }
 
+        override fun withMaterial(material: Material): Shape {
+            val s = TestShape(transformation, material, parent)
+            s.savedRay = savedRay
+            return s
+        }
+
         override fun localIntersect(rayLocal: Ray): List<Intersection> {
             savedRay = rayLocal
             return emptyList()

From 83ff57e86f36319e29d794c1678273ba23cb10ee Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Fri, 20 Jan 2023 13:57:12 -1000
Subject: [PATCH 5/9] Chapter 14: Added convenience functions and test cases on
 groups to make sure things change or do not change as expected.

---
 src/main/kotlin/shapes/Group.kt     | 67 ++++++++++++++++++++++++++--
 src/test/kotlin/shapes/GroupTest.kt | 68 +++++++++++++++++++++++++++--
 src/test/kotlin/shapes/ShapeTest.kt | 12 ++---
 3 files changed, 133 insertions(+), 14 deletions(-)

diff --git a/src/main/kotlin/shapes/Group.kt b/src/main/kotlin/shapes/Group.kt
index c1097a7..681d2ad 100644
--- a/src/main/kotlin/shapes/Group.kt
+++ b/src/main/kotlin/shapes/Group.kt
@@ -7,12 +7,14 @@ import math.*
 import math.BoundingBox.Companion.MaxPoint
 import math.BoundingBox.Companion.MinPoint
 import math.Intersection
+import kotlin.math.PI
 
 class Group(transformation: Matrix = Matrix.I,
+            material: Material = Material(),
             children: List<Shape> = emptyList(),
             castsShadow: Boolean = true,
             parent: Shape? = null):
-    Shape(transformation, Material(), castsShadow, parent) {
+    Shape(transformation, material, castsShadow, parent) {
 
     // Make copies of all the children to backreference this as their parent.
     val children = children.map { it.withParent(this) }
@@ -27,17 +29,42 @@ class Group(transformation: Matrix = Matrix.I,
         s in children
 
     override fun withParent(parent: Shape?): Shape =
-        Group(transformation, children, castsShadow, parent)
+        Group(transformation, material, children, castsShadow, parent)
 
     fun withTransformation(transformation: Matrix): Shape {
         if (!transformation.isTransformation())
             throw IllegalArgumentException("Shapes must have 4x4 transformation matrices:\n" +
                     "\tShape: ${javaClass.name}\nTransformation:\n${transformation.show()}")
-        return Group(transformation, children, castsShadow, parent)
+        return Group(transformation, material, children, castsShadow, parent)
     }
 
+    fun forEach(f: (Shape) -> Unit): Unit {
+        children.forEach(f)
+    }
+
+    fun <T> map(f: (Shape) -> T): Iterable<T> =
+        children.map(f)
+
+    fun all(predicate: (Shape) -> Boolean): Boolean =
+        children.all(predicate)
+
+    fun none(predicate: (Shape) -> Boolean): Boolean =
+        children.none(predicate)
+
+    fun any(predicate: (Shape) -> Boolean): Boolean =
+        children.any(predicate)
+
+    fun <T> zip(other: Iterable<T>): Iterable<Pair<Shape, T>> =
+        children.zip(other)
+
+    fun zip(group: Group): Iterable<Pair<Shape, Shape>> =
+        children.zip(group.children)
+
+    fun withIndex(group: Group): Iterable<IndexedValue<Shape>> =
+        children.withIndex()
+
     override fun withMaterial(material: Material): Shape =
-        Group(transformation, children.map { it.withMaterial(material) }, castsShadow, parent)
+        Group(transformation, material, children.map { it.withMaterial(material) }, castsShadow, parent)
 
     // Only process children if the ray intersects the bounding box for this group.
     override fun localIntersect(rayLocal: Ray): List<Intersection> =
@@ -55,3 +82,35 @@ class Group(transformation: Matrix = Matrix.I,
         }
     }
 }
+
+
+//fun main() {
+//    val g1 = run {
+//        val s1 = Sphere(transformation = Matrix.translate(-1, -1, -1) * Matrix.scale(0.5, 0.5, 0.5))
+//        val c1 = Cylinder(transformation = Matrix.rotateY(PI / 2) * Matrix.scale(0.33, 0.33, 0.33))
+//        Group(children = listOf(s1, c1))
+//    }
+//
+//    // g1 is no longer relevant:
+//    // 1. The children of g1g should have g1g as their parent.
+//    // 2. The parent of g1g should be g2.
+//    val g2 = Group(Matrix.scale(0.1, 0.1, 0.1), listOf(g1))
+//    val g1g = g2.children[0] as Group
+//
+//    // 1. The children of g1p should have g1p as their parent.
+//    // 2. The parent of g1p should be g2p.
+//    val g2p = g2.withTransformation(Matrix.rotateX(PI))
+//    val g1p = g2.children[0] as Group
+//
+//    // Parents
+//     Check to see if g2's children have changed but maintain the same fundamental properties as g1's children.
+//        g1.zip(g1p).forEach { (s1, s2) ->
+//            assertNotSame(s1.parent, s2.parent)
+//            assertSame(g1, s1.parent)
+//            assertSame(g1p, s2.parent)
+//        }
+//        assertSame(g2, g1.parent)
+//        assertSame(g2p, g1p.parent)
+//    println("g2: $g2, g1.parent: ${g1.parent}")
+//    println()
+//}
\ No newline at end of file
diff --git a/src/test/kotlin/shapes/GroupTest.kt b/src/test/kotlin/shapes/GroupTest.kt
index e037f69..b65863f 100644
--- a/src/test/kotlin/shapes/GroupTest.kt
+++ b/src/test/kotlin/shapes/GroupTest.kt
@@ -2,10 +2,8 @@ package shapes
 
 // By Sebastian Raaphorst, 2023.
 
-import math.Matrix
-import math.Ray
-import math.Tuple
-import math.assertAlmostEquals
+import material.Material
+import math.*
 import org.junit.jupiter.api.Test
 import kotlin.math.PI
 import kotlin.test.*
@@ -69,4 +67,66 @@ class GroupTest {
         val xs = g.intersect(r)
         assertEquals(2, xs.size)
     }
+
+    @Test
+    fun `Calling withXXX properties on groups`() {
+        val g1 = run {
+            val s1 = Sphere(transformation = Matrix.translate(-1, -1, -1) * Matrix.scale(0.5, 0.5, 0.5))
+            val c1 = Cylinder(transformation = Matrix.rotateY(PI / 2) * Matrix.scale(0.33, 0.33, 0.33))
+            Group(children = listOf(s1, c1))
+        }
+
+        // g1 is no longer relevant:
+        // 1. The children of g1g should have g1g as their parent.
+        // 2. The parent of g1g should be g2.
+        // 3. The transformations of g1 and g1g should still be the same.
+        val g2 = Group(Matrix.scale(0.1, 0.1, 0.1), children = listOf(g1))
+        val g1g = g2.children[0] as Group
+
+        assertSame(g2, g1g.parent)
+        g1g.forEach { assertSame(g1g, it.parent) }
+        g1.zip(g1g).forEach { (s1, s2) ->
+            assertNotSame(s1, s2)
+            assertSame(s1.transformation, s2.transformation)
+        }
+
+        // 1. The children of g1p should have g1p as their parent.
+        // 2. The parent of g1p should be g2p.
+        // 3. The transformations of g1 and g1p should still be the same.
+        val g2p = g2.withTransformation(Matrix.rotateX(PI)) as Group
+        val g1p = g2p.children[0] as Group
+
+        assertSame(g2p, g1p.parent)
+        g1p.forEach { assertSame(g1p, it.parent) }
+        g1.zip(g1p).forEach { (s1, s2) ->
+            assertNotSame(s1, s2)
+            assertSame(s1.transformation, s2.transformation)
+        }
+
+        // Setting a material on g2p should set the exact same material through g2p's children.
+        val m = Material(Color.BLUE, ambient = 0.5, specular = 0.2, shininess = 100.0)
+        val g2m = g2p.withMaterial(m) as Group
+        val g1m = g2m.children[0] as Group
+
+        assertSame(m, g2m.material)
+        assertSame(m, g1m.material)
+        g1m.forEach { assertSame(m, it.material) }
+
+        assertNotSame(m, g2.material)
+        assertNotSame(m, g2p.material)
+        assertNotSame(m, g1g.material)
+        assertNotSame(m, g1p.material)
+
+        // Make sure the transformations on the shapes have not changed.
+        g1.zip(g1g).forEach { (s1, s2) -> assertSame(s1.transformation, s2.transformation) }
+        g1.zip(g1p).forEach { (s1, s2) -> assertSame(s1.transformation, s2.transformation) }
+        g1.zip(g1m).forEach { (s1, s2) -> assertSame(s1.transformation, s2.transformation) }
+
+        // Make sure the transformations on the groups have / have not changed.
+        assertSame(g1.transformation, g1g.transformation)
+        assertSame(g1.transformation, g1p.transformation)
+        assertSame(g1.transformation, g1m.transformation)
+        assertNotSame(g2.transformation, g2p.transformation)
+        assertSame(g2m.transformation, g2p.transformation)
+    }
 }
diff --git a/src/test/kotlin/shapes/ShapeTest.kt b/src/test/kotlin/shapes/ShapeTest.kt
index 81bd4bf..82daeeb 100644
--- a/src/test/kotlin/shapes/ShapeTest.kt
+++ b/src/test/kotlin/shapes/ShapeTest.kt
@@ -83,8 +83,8 @@ class ShapeTest {
     @Test
     fun `Point from world to local space`() {
         val s = Sphere(Matrix.translate(5, 0, 0))
-        val g2 = Group(Matrix.scale(2, 2, 2), listOf(s))
-        val g1 = Group(Matrix.rotateY(PI / 2), listOf(g2))
+        val g2 = Group(Matrix.scale(2, 2, 2), children = listOf(s))
+        val g1 = Group(Matrix.rotateY(PI / 2), children = listOf(g2))
 
         // We have to get the new sphere to have the parent set.
         val sNew = (g1.children[0] as Group).children[0]
@@ -95,8 +95,8 @@ class ShapeTest {
     @Test
     fun `Normal from local to world space`() {
         val s = Sphere(Matrix.translate(5, 0, 0))
-        val g2 = Group(Matrix.scale(1, 2, 3), listOf(s))
-        val g1 = Group(Matrix.rotateY(PI / 2), listOf(g2))
+        val g2 = Group(Matrix.scale(1, 2, 3), children = listOf(s))
+        val g1 = Group(Matrix.rotateY(PI / 2), children = listOf(g2))
 
         // We have to get the new sphere to have the parent set.
         val sNew = (g1.children[0] as Group).children[0]
@@ -108,8 +108,8 @@ class ShapeTest {
     @Test
     fun `Normal on an object in group`() {
         val s = Sphere(Matrix.translate(5, 0, 0))
-        val g2 = Group(Matrix.scale(1, 2, 3), listOf(s))
-        val g1 = Group(Matrix.rotateY(PI / 2), listOf(g2))
+        val g2 = Group(Matrix.scale(1, 2, 3), children = listOf(s))
+        val g1 = Group(Matrix.rotateY(PI / 2), children = listOf(g2))
 
         val sp = (g1.children[0] as Group).children[0]
         val n = sp.normalAt(Tuple.point(1.7321, 1.1547, -5.5774))

From fe13b76dfee8642e10e208df940837f652b4ac75 Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Fri, 20 Jan 2023 15:49:06 -1000
Subject: [PATCH 6/9] Chapter 14: Narrowing down problems.

---
 src/main/kotlin/apps/ch13_groups.kt | 118 ++++++++++++++++++++++++++++
 src/main/kotlin/apps/ch14_world.kt  |   2 +-
 src/main/kotlin/math/BoundingBox.kt |   2 +
 src/main/kotlin/shapes/Group.kt     |  39 +--------
 4 files changed, 125 insertions(+), 36 deletions(-)
 create mode 100644 src/main/kotlin/apps/ch13_groups.kt

diff --git a/src/main/kotlin/apps/ch13_groups.kt b/src/main/kotlin/apps/ch13_groups.kt
new file mode 100644
index 0000000..15c8447
--- /dev/null
+++ b/src/main/kotlin/apps/ch13_groups.kt
@@ -0,0 +1,118 @@
+package apps
+
+// By Sebastian Raaphorst, 2023.
+// From https://forum.raytracerchallenge.com/thread/7/cylinders-scene-description
+
+import light.PointLight
+import material.Material
+import math.Color
+import math.Matrix
+import math.Tuple
+import pattern.CheckerPattern
+import scene.Camera
+import scene.World
+import shapes.Cylinder
+import shapes.Group
+import shapes.Plane
+import java.io.File
+import kotlin.math.PI
+import kotlin.system.measureTimeMillis
+
+fun main() {
+    val flooring = run {
+        val t = Matrix.rotateY(0.3) * Matrix.scale(0.25, 0.25, 0.25)
+        val p = CheckerPattern(Color(0.5, 0.5, 0.5), Color(0.75, 0.75, 0.75), t)
+        val m = Material(p, ambient = 0.2, diffuse = 0.9, specular = 0.0)
+        Plane(Matrix.I, m)
+    }
+
+    val cylinder = run {
+        val t = Matrix.translate(-1, 0, 1) * Matrix.scale(0.5, 1 ,0.5)
+        val m = Material(Color(0, 0, 0.6), diffuse = 0.1,
+            specular = 0.9, shininess = 300.0, reflectivity = 0.9)
+        Cylinder(0, 0.75, true, t, m)
+    }
+
+    val concentricCylinders = run {
+        val gt = Matrix.translate(1, 0, 0)
+        val m = Material(Color(1, 1, 0.3), ambient = 0.1,
+            diffuse = 0.8, specular = 0.9, shininess = 300.0)
+
+        val concentricCylinder1 = run {
+            val t = Matrix.scale(0.8, 1, 0.8)
+            Cylinder(0, 0.2, false, t)
+        }
+
+        val concentricCylinder2 = run {
+            val t = Matrix.scale(0.6, 1, 0.6)
+            Cylinder(0, 0.3, false, t)
+        }
+
+        val concentricCylinder3 = run {
+            val t = Matrix.scale(0.4, 1, 0.4)
+            Cylinder(0, 0.4, false, t)
+        }
+
+        val concentricCylinder4 = run {
+            val t = Matrix.scale(0.2, 1, 0.2)
+            Cylinder(0, 0.5, true, t)
+        }
+
+        Group(gt, m, listOf(concentricCylinder1, concentricCylinder2, concentricCylinder3, concentricCylinder4))
+    }
+
+    val decorativeCylinder1 = run {
+        val t = Matrix.translate(0, 0, -0.75) * Matrix.scale(0.05, 1, 0.05)
+        val m = Material(Color.RED, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
+        Cylinder(0, 0.3, true, t, m)
+    }
+
+    val decorativeCylinder2 = run {
+        val t = Matrix.translate(0, 0, -2.25) * Matrix.rotateY(-0.15) *
+                Matrix.translate(0, 0, 1.5) * Matrix.scale(0.05, 1, 0.05)
+        val m = Material(Color.YELLOW, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
+        Cylinder(0, 0.3, true, t, m)
+    }
+
+    val decorativeCylinder3 = run {
+        val t = Matrix.translate(0, 0, -2.25) * Matrix.rotateY(-0.3) *
+                Matrix.translate(0, 0, 1.5) * Matrix.scale(0.05, 1, 0.05)
+        val m = Material(Color.GREEN, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
+        Cylinder(0, 0.3, true, t, m)
+    }
+
+    val decorativeCylinder4 = run {
+        val t = Matrix.translate(0, 0, -2.25) * Matrix.rotateY(-0.45) *
+                Matrix.translate(0, 0, 1.5) * Matrix.scale(0.05, 1, 0.05)
+        val m = Material(Color.CYAN, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
+        Cylinder(0, 0.3, true, t, m)
+    }
+
+    val glassCylinder = run {
+        val t = Matrix.translate(0, 0, -1.5) * Matrix.scale(0.33, 1, 0.33)
+        val m = Material(Color(0.25, 0, 0), diffuse = 0.1, specular = 0.9,
+            shininess = 300.0, reflectivity = 0.9, transparency = 0.9, refractiveIndex = 1.5)
+        Cylinder(0.0001, 0.5, true, t, m)
+    }
+
+    val world = run {
+        val light = PointLight(Tuple.point(1, 6.9, -4.9))
+        World(listOf(flooring, cylinder,
+            concentricCylinders,
+            decorativeCylinder1, decorativeCylinder2, decorativeCylinder3, decorativeCylinder4,
+            glassCylinder), light)
+    }
+
+    val camera = run {
+        val from = Tuple.point(8, 3.5, -9)
+        val to = Tuple.point(0, 0.3, 0)
+        val t = from.viewTransformationFrom(to, Tuple.VY)
+        Camera(2400, 1200, PI / 10, t)
+    }
+
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch13_groups.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
+}
diff --git a/src/main/kotlin/apps/ch14_world.kt b/src/main/kotlin/apps/ch14_world.kt
index 5a02094..8577749 100644
--- a/src/main/kotlin/apps/ch14_world.kt
+++ b/src/main/kotlin/apps/ch14_world.kt
@@ -79,7 +79,7 @@ fun main() {
         val from = Tuple.point(0, 0, -9)
         val to = Tuple.PZERO
         val t = from.viewTransformationFrom(to, Tuple.VY)
-        Camera(2400, 1200, 0.9, t)
+        Camera(300, 100, 0.9, t)
     }
 
     val elapsed = measureTimeMillis {
diff --git a/src/main/kotlin/math/BoundingBox.kt b/src/main/kotlin/math/BoundingBox.kt
index f9347a2..88f71ea 100644
--- a/src/main/kotlin/math/BoundingBox.kt
+++ b/src/main/kotlin/math/BoundingBox.kt
@@ -33,6 +33,8 @@ data class BoundingBox(val minPoint: Tuple = MaxPoint, val maxPoint: Tuple = Min
         add(box.minPoint).add(box.maxPoint)
 
     fun transform(transformation: Matrix): BoundingBox {
+        if (!transformation.isTransformation())
+            throw IllegalArgumentException("Cannot transform a bounding box by a non-transform matrix.")
         val corners = listOf(
             minPoint,
             Tuple.point(maxPoint.x, minPoint.y, minPoint.z),
diff --git a/src/main/kotlin/shapes/Group.kt b/src/main/kotlin/shapes/Group.kt
index 681d2ad..58d7d3d 100644
--- a/src/main/kotlin/shapes/Group.kt
+++ b/src/main/kotlin/shapes/Group.kt
@@ -77,40 +77,9 @@ class Group(transformation: Matrix = Matrix.I,
         throw NotImplementedError("Groups do not have local normals.")
 
     override val bounds: BoundingBox by lazy {
-        children.fold(BoundingBox(MaxPoint, MinPoint)) { curr, shape ->
-            curr.merge(shape.parentBounds)
-        }
+//        children.fold(BoundingBox(MaxPoint, MinPoint)) { curr, shape ->
+//            curr.merge(shape.parentBounds)
+//        }
+        BoundingBox(MinPoint, MaxPoint)
     }
 }
-
-
-//fun main() {
-//    val g1 = run {
-//        val s1 = Sphere(transformation = Matrix.translate(-1, -1, -1) * Matrix.scale(0.5, 0.5, 0.5))
-//        val c1 = Cylinder(transformation = Matrix.rotateY(PI / 2) * Matrix.scale(0.33, 0.33, 0.33))
-//        Group(children = listOf(s1, c1))
-//    }
-//
-//    // g1 is no longer relevant:
-//    // 1. The children of g1g should have g1g as their parent.
-//    // 2. The parent of g1g should be g2.
-//    val g2 = Group(Matrix.scale(0.1, 0.1, 0.1), listOf(g1))
-//    val g1g = g2.children[0] as Group
-//
-//    // 1. The children of g1p should have g1p as their parent.
-//    // 2. The parent of g1p should be g2p.
-//    val g2p = g2.withTransformation(Matrix.rotateX(PI))
-//    val g1p = g2.children[0] as Group
-//
-//    // Parents
-//     Check to see if g2's children have changed but maintain the same fundamental properties as g1's children.
-//        g1.zip(g1p).forEach { (s1, s2) ->
-//            assertNotSame(s1.parent, s2.parent)
-//            assertSame(g1, s1.parent)
-//            assertSame(g1p, s2.parent)
-//        }
-//        assertSame(g2, g1.parent)
-//        assertSame(g2p, g1p.parent)
-//    println("g2: $g2, g1.parent: ${g1.parent}")
-//    println()
-//}
\ No newline at end of file

From 7ebc3911afb6af324924b42d8f6853dd2d2a82b3 Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Fri, 20 Jan 2023 16:59:59 -1000
Subject: [PATCH 7/9] Chapter 14: Shapes may now have null materials which
 delegate to parents or the default material.

---
 src/main/kotlin/apps/ch13_groups.kt |  2 +-
 src/main/kotlin/shapes/Cone.kt      |  5 +++--
 src/main/kotlin/shapes/Cube.kt      |  6 ++++--
 src/main/kotlin/shapes/Cylinder.kt  |  5 +++--
 src/main/kotlin/shapes/Group.kt     | 10 +++++-----
 src/main/kotlin/shapes/Plane.kt     |  6 ++++--
 src/main/kotlin/shapes/Shape.kt     | 14 +++++++++++++-
 src/main/kotlin/shapes/Sphere.kt    |  6 ++++--
 8 files changed, 37 insertions(+), 17 deletions(-)

diff --git a/src/main/kotlin/apps/ch13_groups.kt b/src/main/kotlin/apps/ch13_groups.kt
index 15c8447..4fdb6ab 100644
--- a/src/main/kotlin/apps/ch13_groups.kt
+++ b/src/main/kotlin/apps/ch13_groups.kt
@@ -58,7 +58,7 @@ fun main() {
             Cylinder(0, 0.5, true, t)
         }
 
-        Group(gt, m, listOf(concentricCylinder1, concentricCylinder2, concentricCylinder3, concentricCylinder4))
+        Group(gt, m, children=listOf(concentricCylinder1, concentricCylinder2, concentricCylinder3, concentricCylinder4))
     }
 
     val decorativeCylinder1 = run {
diff --git a/src/main/kotlin/shapes/Cone.kt b/src/main/kotlin/shapes/Cone.kt
index c00a7e8..a2481d2 100644
--- a/src/main/kotlin/shapes/Cone.kt
+++ b/src/main/kotlin/shapes/Cone.kt
@@ -13,7 +13,7 @@ class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
            maximum: Number = Double.POSITIVE_INFINITY,
            val closed: Boolean = false,
            transformation: Matrix = Matrix.I,
-           material: Material = Material(),
+           material: Material? = null,
            castsShadow: Boolean = true,
            parent: Shape? = null):
     Shape(transformation, material, castsShadow, parent) {
@@ -21,8 +21,9 @@ class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
     val minimum = minimum.toDouble()
     val maximum = maximum.toDouble()
 
+    // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
-        Cone(minimum, maximum, closed, transformation, material, castsShadow, parent)
+        Cone(minimum, maximum, closed, transformation, objMaterial, castsShadow, parent)
 
     override fun withMaterial(material: Material): Shape =
         Cone(minimum, maximum, closed, transformation, material, castsShadow, parent)
diff --git a/src/main/kotlin/shapes/Cube.kt b/src/main/kotlin/shapes/Cube.kt
index e863d3b..9fffca8 100644
--- a/src/main/kotlin/shapes/Cube.kt
+++ b/src/main/kotlin/shapes/Cube.kt
@@ -8,12 +8,14 @@ import math.Intersection
 import kotlin.math.absoluteValue
 
 class Cube(transformation: Matrix = Matrix.I,
-           material: Material = Material(),
+           material: Material? = null,
            castsShadow: Boolean = true,
            parent: Shape? = null):
     Shape(transformation, material, castsShadow, parent) {
+
+    // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
-        Cube(transformation, material, castsShadow, parent)
+        Cube(transformation, objMaterial, castsShadow, parent)
 
     override fun withMaterial(material: Material): Shape =
         Cube(transformation, material, castsShadow, parent)
diff --git a/src/main/kotlin/shapes/Cylinder.kt b/src/main/kotlin/shapes/Cylinder.kt
index 4bc9701..4632cd1 100644
--- a/src/main/kotlin/shapes/Cylinder.kt
+++ b/src/main/kotlin/shapes/Cylinder.kt
@@ -11,7 +11,7 @@ class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
                maximum: Number = Double.POSITIVE_INFINITY,
                val closed: Boolean = false,
                transformation: Matrix = Matrix.I,
-               material: Material = Material(),
+               material: Material? = null,
                castsShadow: Boolean = true,
                parent: Shape? = null):
     Shape(transformation, material, castsShadow, parent) {
@@ -19,8 +19,9 @@ class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
     val minimum = minimum.toDouble()
     val maximum = maximum.toDouble()
 
+    // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
-        Cylinder(minimum, maximum, closed, transformation, material, castsShadow, parent)
+        Cylinder(minimum, maximum, closed, transformation, objMaterial, castsShadow, parent)
 
     override fun withMaterial(material: Material): Shape =
         Cylinder(minimum, maximum, closed, transformation, material, castsShadow, parent)
diff --git a/src/main/kotlin/shapes/Group.kt b/src/main/kotlin/shapes/Group.kt
index 58d7d3d..264ba6e 100644
--- a/src/main/kotlin/shapes/Group.kt
+++ b/src/main/kotlin/shapes/Group.kt
@@ -7,17 +7,16 @@ import math.*
 import math.BoundingBox.Companion.MaxPoint
 import math.BoundingBox.Companion.MinPoint
 import math.Intersection
-import kotlin.math.PI
 
 class Group(transformation: Matrix = Matrix.I,
-            material: Material = Material(),
+            material: Material? = null,
             children: List<Shape> = emptyList(),
             castsShadow: Boolean = true,
             parent: Shape? = null):
     Shape(transformation, material, castsShadow, parent) {
 
     // Make copies of all the children to backreference this as their parent.
-    val children = children.map { it.withParent(this) }
+    val children = run { children.map { it.withParent(this) } }
     val size = children.size
     val isEmpty = children.isEmpty()
     val isNotEmpty = children.isNotEmpty()
@@ -28,8 +27,9 @@ class Group(transformation: Matrix = Matrix.I,
     operator fun contains(s: Shape): Boolean =
         s in children
 
+    // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
-        Group(transformation, material, children, castsShadow, parent)
+        Group(transformation, objMaterial, children, castsShadow, parent)
 
     fun withTransformation(transformation: Matrix): Shape {
         if (!transformation.isTransformation())
@@ -38,7 +38,7 @@ class Group(transformation: Matrix = Matrix.I,
         return Group(transformation, material, children, castsShadow, parent)
     }
 
-    fun forEach(f: (Shape) -> Unit): Unit {
+    fun forEach(f: (Shape) -> Unit) {
         children.forEach(f)
     }
 
diff --git a/src/main/kotlin/shapes/Plane.kt b/src/main/kotlin/shapes/Plane.kt
index 7ea0764..8e34c2c 100644
--- a/src/main/kotlin/shapes/Plane.kt
+++ b/src/main/kotlin/shapes/Plane.kt
@@ -7,12 +7,14 @@ import math.*
 import kotlin.math.absoluteValue
 
 class Plane(transformation: Matrix = Matrix.I,
-            material: Material = Material(),
+            material: Material? = null,
             castsShadow: Boolean = true,
             parent: Shape? = null):
     Shape(transformation, material, castsShadow, parent) {
+
+    // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
-        Plane(transformation, material, castsShadow, parent)
+        Plane(transformation, objMaterial, castsShadow, parent)
 
     override fun withMaterial(material: Material): Shape =
         Plane(transformation, material, castsShadow, parent)
diff --git a/src/main/kotlin/shapes/Shape.kt b/src/main/kotlin/shapes/Shape.kt
index 84b22eb..cfb5d9a 100644
--- a/src/main/kotlin/shapes/Shape.kt
+++ b/src/main/kotlin/shapes/Shape.kt
@@ -9,7 +9,7 @@ import java.util.UUID
 import kotlin.math.PI
 
 abstract class Shape(val transformation: Matrix,
-                     val material: Material,
+                     material: Material? = null,
                      val castsShadow: Boolean,
                      val parent: Shape?,
                      private val id: UUID = UUID.randomUUID()) {
@@ -19,6 +19,14 @@ abstract class Shape(val transformation: Matrix,
                     "\tShape: ${javaClass.name}\nTransformation:\n${transformation.show()}")
     }
 
+    // We need to store the parameter passed in for material here in order to propagate it correctly.
+    // We will access it below: if an object does not have a material, it will try to see if it has a parent
+    // with a material.
+    protected val objMaterial = material
+
+    val material: Material
+        get() = objMaterial ?: (parent?.objMaterial ?: DefaultMaterial)
+
     // This method should only be invoked by Groups containing the object.
     internal abstract fun withParent(parent: Shape? = null): Shape
 
@@ -71,4 +79,8 @@ abstract class Shape(val transformation: Matrix,
     internal val parentBounds: BoundingBox by lazy {
         bounds.transform(transformation)
     }
+
+    companion object {
+        private val DefaultMaterial = Material()
+    }
 }
diff --git a/src/main/kotlin/shapes/Sphere.kt b/src/main/kotlin/shapes/Sphere.kt
index 51d3778..8724dc7 100644
--- a/src/main/kotlin/shapes/Sphere.kt
+++ b/src/main/kotlin/shapes/Sphere.kt
@@ -8,12 +8,14 @@ import math.Intersection
 import kotlin.math.sqrt
 
 class Sphere(transformation: Matrix = Matrix.I,
-             material: Material = Material(),
+             material: Material? = null,
              castsShadow: Boolean = true,
              parent: Shape? = null):
     Shape(transformation, material, castsShadow, parent) {
+
+    // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
-        Sphere(transformation, material, castsShadow, parent)
+        Sphere(transformation, objMaterial, castsShadow, parent)
 
     override fun withMaterial(material: Material): Shape =
         Sphere(transformation, material, castsShadow, parent)

From 6b86ac7f1dc8ce1bf13c3e0744607b3da6d26c42 Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Fri, 20 Jan 2023 17:37:54 -1000
Subject: [PATCH 8/9] Chapter 14: Fixed bounding box calculation error.

---
 src/main/kotlin/apps/ch14_world.kt  |  2 +-
 src/main/kotlin/math/BoundingBox.kt |  9 +++++++--
 src/main/kotlin/shapes/Group.kt     | 11 +++++------
 3 files changed, 13 insertions(+), 9 deletions(-)

diff --git a/src/main/kotlin/apps/ch14_world.kt b/src/main/kotlin/apps/ch14_world.kt
index 8577749..706d25a 100644
--- a/src/main/kotlin/apps/ch14_world.kt
+++ b/src/main/kotlin/apps/ch14_world.kt
@@ -79,7 +79,7 @@ fun main() {
         val from = Tuple.point(0, 0, -9)
         val to = Tuple.PZERO
         val t = from.viewTransformationFrom(to, Tuple.VY)
-        Camera(300, 100, 0.9, t)
+        Camera(1200, 400, 0.9, t)
     }
 
     val elapsed = measureTimeMillis {
diff --git a/src/main/kotlin/math/BoundingBox.kt b/src/main/kotlin/math/BoundingBox.kt
index 88f71ea..f198f8f 100644
--- a/src/main/kotlin/math/BoundingBox.kt
+++ b/src/main/kotlin/math/BoundingBox.kt
@@ -5,6 +5,9 @@ package math
 import kotlin.math.max
 import kotlin.math.min
 
+// Unless otherwise stated, a bounding box is empty, as indicated by setting the
+// 1. minPoint to INF, INF, INF
+// 2. maxPoint to -INF, -INF, -INF
 data class BoundingBox(val minPoint: Tuple = MaxPoint, val maxPoint: Tuple = MinPoint) {
     init {
         if (!minPoint.isPoint())
@@ -20,12 +23,12 @@ data class BoundingBox(val minPoint: Tuple = MaxPoint, val maxPoint: Tuple = Min
         !isEmpty
     }
 
-    fun add(point: Tuple): BoundingBox {
+    private fun add(point: Tuple): BoundingBox {
         if (!point.isPoint())
             throw IllegalArgumentException("Tried to add vector to BoundingBox: $point.")
         return BoundingBox(
             Tuple.point(min(minPoint.x, point.x), min(minPoint.y, point.y), min(minPoint.z, point.z)),
-            Tuple.point(max(maxPoint.x, point.x), min(maxPoint.y, point.y), min(maxPoint.z, point.z))
+            Tuple.point(max(maxPoint.x, point.x), max(maxPoint.y, point.y), max(maxPoint.z, point.z))
         )
     }
 
@@ -102,5 +105,7 @@ data class BoundingBox(val minPoint: Tuple = MaxPoint, val maxPoint: Tuple = Min
             Double.NEGATIVE_INFINITY,
             Double.NEGATIVE_INFINITY
         )
+
+        internal val Empty = BoundingBox(MaxPoint, MinPoint)
     }
 }
diff --git a/src/main/kotlin/shapes/Group.kt b/src/main/kotlin/shapes/Group.kt
index 264ba6e..f34a8ff 100644
--- a/src/main/kotlin/shapes/Group.kt
+++ b/src/main/kotlin/shapes/Group.kt
@@ -4,8 +4,6 @@ package shapes
 
 import material.Material
 import math.*
-import math.BoundingBox.Companion.MaxPoint
-import math.BoundingBox.Companion.MinPoint
 import math.Intersection
 
 class Group(transformation: Matrix = Matrix.I,
@@ -77,9 +75,10 @@ class Group(transformation: Matrix = Matrix.I,
         throw NotImplementedError("Groups do not have local normals.")
 
     override val bounds: BoundingBox by lazy {
-//        children.fold(BoundingBox(MaxPoint, MinPoint)) { curr, shape ->
-//            curr.merge(shape.parentBounds)
-//        }
-        BoundingBox(MinPoint, MaxPoint)
+        // At first, the bounds are a completely empty box, with:
+        // 1. minPoint at INF, INF, INF
+        // 2. maxPoint at -INF, -INF, -INF.
+        // We make the space larger from the children.
+        children.fold(BoundingBox.Empty) { curr, shape -> curr.merge(shape.parentBounds) }
     }
 }

From 8ed00a546570a1da60339c4a6dde139a6188ba61 Mon Sep 17 00:00:00 2001
From: Sebastian Raaphorst <sraaphorst@gmail.com>
Date: Fri, 20 Jan 2023 18:39:03 -1000
Subject: [PATCH 9/9] Chapter 14: Added hexagon example and major refactor of
 Cylinder and Cone into Cappable.

---
 output/ch14_world.png                         | Bin 0 -> 198686 bytes
 .../apps/{shared.kt => ch01_02_shared.kt}     |   0
 src/main/kotlin/apps/ch13_groups.kt           | 118 ----------
 src/main/kotlin/apps/ch14_hexagon.kt          |  40 ++++
 src/main/kotlin/apps/ch14_shared.kt           |  20 ++
 src/main/kotlin/apps/ch14_world.kt            |  10 +-
 src/main/kotlin/apps/ch14_world.yaml          | 205 ------------------
 src/main/kotlin/scene/Camera.kt               |   7 +-
 src/main/kotlin/shapes/Cappable.kt            |  69 ++++++
 src/main/kotlin/shapes/Cone.kt                |  59 +----
 src/main/kotlin/shapes/Cylinder.kt            |  60 +----
 11 files changed, 144 insertions(+), 444 deletions(-)
 create mode 100644 output/ch14_world.png
 rename src/main/kotlin/apps/{shared.kt => ch01_02_shared.kt} (100%)
 delete mode 100644 src/main/kotlin/apps/ch13_groups.kt
 create mode 100644 src/main/kotlin/apps/ch14_hexagon.kt
 create mode 100644 src/main/kotlin/apps/ch14_shared.kt
 delete mode 100644 src/main/kotlin/apps/ch14_world.yaml
 create mode 100644 src/main/kotlin/shapes/Cappable.kt

diff --git a/output/ch14_world.png b/output/ch14_world.png
new file mode 100644
index 0000000000000000000000000000000000000000..5f06e7e4d78abcbecb482dc7c33ffd70a2a1462b
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literal 0
HcmV?d00001

diff --git a/src/main/kotlin/apps/shared.kt b/src/main/kotlin/apps/ch01_02_shared.kt
similarity index 100%
rename from src/main/kotlin/apps/shared.kt
rename to src/main/kotlin/apps/ch01_02_shared.kt
diff --git a/src/main/kotlin/apps/ch13_groups.kt b/src/main/kotlin/apps/ch13_groups.kt
deleted file mode 100644
index 4fdb6ab..0000000
--- a/src/main/kotlin/apps/ch13_groups.kt
+++ /dev/null
@@ -1,118 +0,0 @@
-package apps
-
-// By Sebastian Raaphorst, 2023.
-// From https://forum.raytracerchallenge.com/thread/7/cylinders-scene-description
-
-import light.PointLight
-import material.Material
-import math.Color
-import math.Matrix
-import math.Tuple
-import pattern.CheckerPattern
-import scene.Camera
-import scene.World
-import shapes.Cylinder
-import shapes.Group
-import shapes.Plane
-import java.io.File
-import kotlin.math.PI
-import kotlin.system.measureTimeMillis
-
-fun main() {
-    val flooring = run {
-        val t = Matrix.rotateY(0.3) * Matrix.scale(0.25, 0.25, 0.25)
-        val p = CheckerPattern(Color(0.5, 0.5, 0.5), Color(0.75, 0.75, 0.75), t)
-        val m = Material(p, ambient = 0.2, diffuse = 0.9, specular = 0.0)
-        Plane(Matrix.I, m)
-    }
-
-    val cylinder = run {
-        val t = Matrix.translate(-1, 0, 1) * Matrix.scale(0.5, 1 ,0.5)
-        val m = Material(Color(0, 0, 0.6), diffuse = 0.1,
-            specular = 0.9, shininess = 300.0, reflectivity = 0.9)
-        Cylinder(0, 0.75, true, t, m)
-    }
-
-    val concentricCylinders = run {
-        val gt = Matrix.translate(1, 0, 0)
-        val m = Material(Color(1, 1, 0.3), ambient = 0.1,
-            diffuse = 0.8, specular = 0.9, shininess = 300.0)
-
-        val concentricCylinder1 = run {
-            val t = Matrix.scale(0.8, 1, 0.8)
-            Cylinder(0, 0.2, false, t)
-        }
-
-        val concentricCylinder2 = run {
-            val t = Matrix.scale(0.6, 1, 0.6)
-            Cylinder(0, 0.3, false, t)
-        }
-
-        val concentricCylinder3 = run {
-            val t = Matrix.scale(0.4, 1, 0.4)
-            Cylinder(0, 0.4, false, t)
-        }
-
-        val concentricCylinder4 = run {
-            val t = Matrix.scale(0.2, 1, 0.2)
-            Cylinder(0, 0.5, true, t)
-        }
-
-        Group(gt, m, children=listOf(concentricCylinder1, concentricCylinder2, concentricCylinder3, concentricCylinder4))
-    }
-
-    val decorativeCylinder1 = run {
-        val t = Matrix.translate(0, 0, -0.75) * Matrix.scale(0.05, 1, 0.05)
-        val m = Material(Color.RED, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
-        Cylinder(0, 0.3, true, t, m)
-    }
-
-    val decorativeCylinder2 = run {
-        val t = Matrix.translate(0, 0, -2.25) * Matrix.rotateY(-0.15) *
-                Matrix.translate(0, 0, 1.5) * Matrix.scale(0.05, 1, 0.05)
-        val m = Material(Color.YELLOW, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
-        Cylinder(0, 0.3, true, t, m)
-    }
-
-    val decorativeCylinder3 = run {
-        val t = Matrix.translate(0, 0, -2.25) * Matrix.rotateY(-0.3) *
-                Matrix.translate(0, 0, 1.5) * Matrix.scale(0.05, 1, 0.05)
-        val m = Material(Color.GREEN, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
-        Cylinder(0, 0.3, true, t, m)
-    }
-
-    val decorativeCylinder4 = run {
-        val t = Matrix.translate(0, 0, -2.25) * Matrix.rotateY(-0.45) *
-                Matrix.translate(0, 0, 1.5) * Matrix.scale(0.05, 1, 0.05)
-        val m = Material(Color.CYAN, ambient = 0.1, diffuse = 0.9, specular = 0.9, shininess = 300.0)
-        Cylinder(0, 0.3, true, t, m)
-    }
-
-    val glassCylinder = run {
-        val t = Matrix.translate(0, 0, -1.5) * Matrix.scale(0.33, 1, 0.33)
-        val m = Material(Color(0.25, 0, 0), diffuse = 0.1, specular = 0.9,
-            shininess = 300.0, reflectivity = 0.9, transparency = 0.9, refractiveIndex = 1.5)
-        Cylinder(0.0001, 0.5, true, t, m)
-    }
-
-    val world = run {
-        val light = PointLight(Tuple.point(1, 6.9, -4.9))
-        World(listOf(flooring, cylinder,
-            concentricCylinders,
-            decorativeCylinder1, decorativeCylinder2, decorativeCylinder3, decorativeCylinder4,
-            glassCylinder), light)
-    }
-
-    val camera = run {
-        val from = Tuple.point(8, 3.5, -9)
-        val to = Tuple.point(0, 0.3, 0)
-        val t = from.viewTransformationFrom(to, Tuple.VY)
-        Camera(2400, 1200, PI / 10, t)
-    }
-
-    val elapsed = measureTimeMillis {
-        val canvas = camera.render(world)
-        canvas.toPPMFile(File("output/ch13_groups.ppm"))
-    }
-    println("Time elapsed: ${elapsed / 1000.0} s")
-}
diff --git a/src/main/kotlin/apps/ch14_hexagon.kt b/src/main/kotlin/apps/ch14_hexagon.kt
new file mode 100644
index 0000000..2e2ab5a
--- /dev/null
+++ b/src/main/kotlin/apps/ch14_hexagon.kt
@@ -0,0 +1,40 @@
+package apps
+
+// By Sebastian Raaphorst, 2023.
+
+import light.PointLight
+import math.Matrix
+import math.Tuple
+import scene.Camera
+import scene.World
+import shapes.Group
+import java.io.File
+import kotlin.math.PI
+import kotlin.system.measureTimeMillis
+
+fun main() {
+    val hexagon = run {
+        val sides = (0 until 6).map { Matrix.rotateY(it * PI / 3) }.map {
+            side.withTransformation(it)
+        }
+        Group(Matrix.rotateX(-0.4363) * Matrix.rotateY(-PI / 18), children = sides)
+    }
+
+    val world = run {
+        val light = PointLight(Tuple.point(0, 10, -5))
+        World(listOf(hexagon), light)
+    }
+
+    val camera = run {
+        val from = Tuple.point(0, 0, -5)
+        val to = Tuple.PZERO
+        val t = from.viewTransformationFrom(to, Tuple.VY)
+        Camera(1200, 600, 1, t)
+    }
+
+    val elapsed = measureTimeMillis {
+        val canvas = camera.render(world)
+        canvas.toPPMFile(File("output/ch14_hexagon.ppm"))
+    }
+    println("Time elapsed: ${elapsed / 1000.0} s")
+}
\ No newline at end of file
diff --git a/src/main/kotlin/apps/ch14_shared.kt b/src/main/kotlin/apps/ch14_shared.kt
new file mode 100644
index 0000000..38fba0c
--- /dev/null
+++ b/src/main/kotlin/apps/ch14_shared.kt
@@ -0,0 +1,20 @@
+package apps
+
+// By Sebastian Raaphorst, 2023.
+
+import math.Matrix
+import shapes.Cylinder
+import shapes.Group
+import shapes.Sphere
+import kotlin.math.PI
+
+// The shared side of a hexagon.
+val side = run {
+    val corner = Sphere(Matrix.translate(0, 0, -1) * Matrix.scale(0.25, 0.25, 0.25))
+    val edge = Cylinder(
+        0, 1, false,
+        Matrix.translate(0, 0, -1) * Matrix.rotateY(-PI / 6)
+                * Matrix.rotateZ(-PI / 2) * Matrix.scale(0.25, 1, 0.25)
+    )
+    Group(children = listOf(corner, edge))
+}
\ No newline at end of file
diff --git a/src/main/kotlin/apps/ch14_world.kt b/src/main/kotlin/apps/ch14_world.kt
index 706d25a..3becd2e 100644
--- a/src/main/kotlin/apps/ch14_world.kt
+++ b/src/main/kotlin/apps/ch14_world.kt
@@ -19,14 +19,6 @@ fun main() {
     val transforms = listOf(0, PI / 3, 2 * PI / 3, PI, 4 * PI / 3, 5 * PI / 3)
         .map(Matrix::rotateY)
 
-    val leg = run {
-        val sphere = Sphere(Matrix.translate(0, 0, -1) * Matrix.scale(0.25, 0.25, 0.25))
-        val cylinder = Cylinder(0, 1, false,
-            Matrix.translate(0, 0, -1) * Matrix.rotateY(-PI / 6) *
-            Matrix.rotateZ(-PI / 2) * Matrix.scale(0.25, 1, 0.25))
-        Group(children = listOf(sphere, cylinder))
-    }
-
     val cap = run {
         val trans = Matrix.rotateX(-PI / 4 ) * Matrix.scale(0.24606, 1.37002, 0.24606)
         val cones = transforms.map {
@@ -36,7 +28,7 @@ fun main() {
     }
 
     val wacky = run {
-        val legs = transforms.map(leg::withTransformation)
+        val legs = transforms.map(side::withTransformation)
         val cap1 = cap.withTransformation(Matrix.translate(0, 1, 0))
         val cap2 = cap.withTransformation(Matrix.rotateX(PI) * Matrix.translate(0, 1, 0))
         Group(children = legs + listOf(cap1, cap2))
diff --git a/src/main/kotlin/apps/ch14_world.yaml b/src/main/kotlin/apps/ch14_world.yaml
deleted file mode 100644
index ad8053e..0000000
--- a/src/main/kotlin/apps/ch14_world.yaml
+++ /dev/null
@@ -1,205 +0,0 @@
-# ======================================================
-# group.yml
-#
-# This file describes the scene illustrated at the start
-# of chapter 14, "Groups", in "The Ray Tracer
-# Challenge"
-#
-# This scene description assumes:
-#
-# 1. Your ray tracer supports multiple light sources.
-#    If it does not, you can omit the extra light
-#    sources and bump up the existing light's intensity
-#    to [1, 1, 1].
-# 2. Child objects in a group inherit their default
-#    material from the parent group. If you haven't
-#    implemented this optional feature, you'll need
-#    arrange other means of texturing the child
-#    elements (or accept that all elements of the
-#    scene will be white).
-#
-# by Jamis Buck <jamis@jamisbuck.org>
-# ======================================================
-
-# ======================================================
-# the camera
-# ======================================================
-
-- add: camera
-  width: 300
-  height: 100
-  field-of-view: 0.9
-  from: [0, 0, -9]
-  to: [0, 0, 0]
-  up: [0, 1, 0]
-
-# ======================================================
-# light sources
-# ======================================================
-
-- add: light
-  at: [ 10000, 10000, -10000 ]
-  intensity: [ 0.25, 0.25, 0.25 ]
-- add: light
-  at: [ -10000, 10000, -10000 ]
-  intensity: [ 0.25, 0.25, 0.25 ]
-- add: light
-  at: [ 10000, -10000, -10000 ]
-  intensity: [ 0.25, 0.25, 0.25 ]
-- add: light
-  at: [ -10000, -10000, -10000 ]
-  intensity: [ 0.25, 0.25, 0.25 ]
-
-# ======================================================
-# These describe groups that will be reused within
-# the scene. (You can think of these as functions that
-# return a new instance of the given shape each time they
-# are referenced.)
-# ======================================================
-
-- define: leg
-  value:
-    add: group
-    children:
-      - add: sphere
-        transform:
-          - [ scale, 0.25, 0.25, 0.25 ]
-          - [ translate, 0, 0, -1 ]
-      - add: cylinder
-        min: 0
-        max: 1
-        closed: false
-        transform:
-          - [ scale, 0.25, 1, 0.25 ]
-          - [ rotate-z, -1.5708 ]
-          - [ rotate-y, -0.5236 ]
-          - [ translate, 0, 0, -1 ]
-
-- define: cap
-  value:
-    add: group
-    children:
-      - add: cone
-        min: -1
-        max: 0
-        closed: false
-        transform:
-          - [ scale, 0.24606, 1.37002, 0.24606 ]
-          - [ rotate-x, -0.7854 ]
-      - add: cone
-        min: -1
-        max: 0
-        closed: false
-        transform:
-          - [ scale, 0.24606, 1.37002, 0.24606 ]
-          - [ rotate-x, -0.7854 ]
-          - [ rotate-y, 1.0472 ]
-      - add: cone
-        min: -1
-        max: 0
-        closed: false
-        transform:
-          - [ scale, 0.24606, 1.37002, 0.24606 ]
-          - [ rotate-x, -0.7854 ]
-          - [ rotate-y, 2.0944 ]
-      - add: cone
-        min: -1
-        max: 0
-        closed: false
-        transform:
-          - [ scale, 0.24606, 1.37002, 0.24606 ]
-          - [ rotate-x, -0.7854 ]
-          - [ rotate-y, 3.1416 ]
-      - add: cone
-        min: -1
-        max: 0
-        closed: false
-        transform:
-          - [ scale, 0.24606, 1.37002, 0.24606 ]
-          - [ rotate-x, -0.7854 ]
-          - [ rotate-y, 4.1888 ]
-      - add: cone
-        min: -1
-        max: 0
-        closed: false
-        transform:
-          - [ scale, 0.24606, 1.37002, 0.24606 ]
-          - [ rotate-x, -0.7854 ]
-          - [ rotate-y, 5.236 ]
-
-- define: wacky
-  value:
-    add: group
-    children:
-      - add: leg
-      - add: leg
-        transform:
-          - [ rotate-y, 1.0472 ]
-      - add: leg
-        transform:
-          - [ rotate-y, 2.0944 ]
-      - add: leg
-        transform:
-          - [ rotate-y, 3.1416 ]
-      - add: leg
-        transform:
-          - [ rotate-y, 4.1888 ]
-      - add: leg
-        transform:
-          - [ rotate-y, 5.236 ]
-      - add: cap
-        transform:
-          - [ translate, 0, 1, 0 ]
-      - add: cap
-        transform:
-          - [ translate, 0, 1, 0 ]
-          - [ rotate-x, 3.1416 ]
-
-# ======================================================
-# Construct the scene itself
-# ======================================================
-
-# a white backdrop
-- add: plane
-  transform:
-    - [ rotate-x, 1.5708 ]
-    - [ translate, 0, 0, 100 ]
-  material:
-    color: [ 1, 1, 1 ]
-    ambient: 1
-    diffuse: 0
-    specular: 0
-
-- add: wacky
-  transform:
-    - [ rotate-y, 0.1745 ]
-    - [ rotate-x, 0.4363 ]
-    - [ translate, -2.8, 0, 0 ]
-  material:
-    color: [ 0.9, 0.2, 0.4 ]
-    ambient: 0.2
-    diffuse: 0.8
-    specular: 0.7
-    shininess: 20
-
-- add: wacky
-  transform:
-    - [ rotate-y, 0.1745 ]
-  material:
-    color: [ 0.2, 0.9, 0.6 ]
-    ambient: 0.2
-    diffuse: 0.8
-    specular: 0.7
-    shininess: 20
-
-- add: wacky
-  transform:
-    - [ rotate-y, -0.1745 ]
-    - [ rotate-x, -0.4363 ]
-    - [ translate, 2.8, 0, 0 ]
-  material:
-    color: [ 0.2, 0.3, 1.0 ]
-    ambient: 0.2
-    diffuse: 0.8
-    specular: 0.7
-    shininess: 20
diff --git a/src/main/kotlin/scene/Camera.kt b/src/main/kotlin/scene/Camera.kt
index 449e6f8..cad7979 100644
--- a/src/main/kotlin/scene/Camera.kt
+++ b/src/main/kotlin/scene/Camera.kt
@@ -9,13 +9,16 @@ import output.Canvas
 import kotlin.math.tan
 
 // Map a 3D scene onto a 2D canvas.
-data class Camera(val hSize: Int, val vSize: Int, val fov: Double, val transformation: Matrix = Matrix.I) {
+class Camera(private val hSize: Int,
+             private val vSize: Int,
+             fov: Number,
+             internal val transformation: Matrix = Matrix.I) {
     init {
         if (!transformation.isTransformation())
             throw IllegalArgumentException("Illegal camera transformation:\n${transformation.show()}")
     }
 
-    private val halfView = tan(fov / 2.0)
+    private val halfView = tan(fov.toDouble() / 2.0)
     private val aspect = hSize.toDouble() / vSize.toDouble()
     private val halfWidth = if (aspect >= 1) halfView else halfView * aspect
     private val halfHeight = if (aspect >= 1) halfView / aspect else halfView
diff --git a/src/main/kotlin/shapes/Cappable.kt b/src/main/kotlin/shapes/Cappable.kt
new file mode 100644
index 0000000..05af572
--- /dev/null
+++ b/src/main/kotlin/shapes/Cappable.kt
@@ -0,0 +1,69 @@
+package shapes
+
+// By Sebastian Raaphorst, 2023.
+
+import material.Material
+import math.almostEquals
+import math.Intersection
+import math.Matrix
+import math.Ray
+import kotlin.math.sqrt
+
+// An object like a Cylinder or Cone that can be limited in length and cappable.
+abstract class Cappable(
+    internal val minimum: Double = Double.NEGATIVE_INFINITY,
+    internal val maximum: Double = Double.POSITIVE_INFINITY,
+    internal val closed: Boolean = false,
+    transformation: Matrix = Matrix.I,
+    material: Material? = null,
+    castsShadow: Boolean = true,
+    parent: Shape? = null
+    ): Shape (transformation, material, castsShadow, parent) {
+
+    private fun checkCap(rayLocal: Ray, radius: Double, t: Double): Boolean {
+        val x = rayLocal.origin.x + t * rayLocal.direction.x
+        val z = rayLocal.origin.z + t * rayLocal.direction.z
+        return x * x + z * z <= radius * radius
+    }
+
+    internal fun intersectCaps(rayLocal: Ray, minRadius: Double, maxRadius: Double): List<Intersection> {
+        if (!closed or almostEquals(0, rayLocal.direction.y))
+            return emptyList()
+
+        val tMin = (minimum - rayLocal.origin.y) / rayLocal.direction.y
+        val tMax = (maximum - rayLocal.origin.y) / rayLocal.direction.y
+
+        return when(Pair(checkCap(rayLocal, minRadius, tMin), checkCap(rayLocal, maxRadius, tMax))) {
+            Pair(true, true) -> listOf(Intersection(tMin, this), Intersection(tMax, this))
+            Pair(true, false) -> listOf(Intersection(tMin, this))
+            Pair(false, true) -> listOf(Intersection(tMax, this))
+            else -> emptyList()
+        }
+    }
+
+    internal fun intersectBody(rayLocal: Ray, a: Double, b: Double, c: Double): List<Intersection> {
+        val disc = b * b - 4 * a * c
+
+        if (disc < 0)
+            emptyList<Intersection>()
+
+        val sqrtDisc = sqrt(disc)
+        val (t0, t1) = run {
+            val t0Tmp = (-b - sqrtDisc) / (2 * a)
+            val t1Tmp = (-b + sqrtDisc) / (2 * a)
+            if (t0Tmp <= t1Tmp) Pair(t0Tmp, t1Tmp) else Pair(t1Tmp, t0Tmp)
+        }
+
+        // Check for intersections with the body of the cone.
+        val y0 = rayLocal.origin.y + t0 * rayLocal.direction.y
+        val y1 = rayLocal.origin.y + t1 * rayLocal.direction.y
+        val t0Int = minimum < y0 && y0 < maximum
+        val t1Int = minimum < y1 && y1 < maximum
+        return when (Pair(t0Int, t1Int)) {
+            Pair(true, true) -> listOf(Intersection(t0, this), Intersection(t1, this))
+            Pair(true, false) -> listOf(Intersection(t0, this))
+            Pair(false, true) -> listOf(Intersection(t1, this))
+            else -> emptyList()
+        }
+    }
+}
diff --git a/src/main/kotlin/shapes/Cone.kt b/src/main/kotlin/shapes/Cone.kt
index a2481d2..efa209f 100644
--- a/src/main/kotlin/shapes/Cone.kt
+++ b/src/main/kotlin/shapes/Cone.kt
@@ -11,15 +11,12 @@ import kotlin.math.sqrt
 
 class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
            maximum: Number = Double.POSITIVE_INFINITY,
-           val closed: Boolean = false,
+           closed: Boolean = false,
            transformation: Matrix = Matrix.I,
            material: Material? = null,
            castsShadow: Boolean = true,
            parent: Shape? = null):
-    Shape(transformation, material, castsShadow, parent) {
-
-    val minimum = minimum.toDouble()
-    val maximum = maximum.toDouble()
+    Cappable(minimum.toDouble(), maximum.toDouble(), closed, transformation, material, castsShadow, parent) {
 
     // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
@@ -43,62 +40,14 @@ class Cone(minimum: Number = Double.NEGATIVE_INFINITY,
         val xs1 = if (almostEquals(0.0, a)) {
             if (almostEquals(0.0, b)) emptyList()
             else listOf(Intersection(-c / (2 * b), this))
-        }
-        else {
-            val disc = b * b - 4 * a * c
-
-            if (disc < 0)
-                emptyList<Intersection>()
-
-            val sqrtDisc = sqrt(disc)
-            val (t0, t1) = run {
-                val t0Tmp = (-b - sqrtDisc) / (2 * a)
-                val t1Tmp = (-b + sqrtDisc) / (2 * a)
-                if (t0Tmp <= t1Tmp) Pair(t0Tmp, t1Tmp) else Pair(t1Tmp, t0Tmp)
-            }
-
-            // Check for intersections with the body of the cylinder.
-            val y0 = rayLocal.origin.y + t0 * rayLocal.direction.y
-            val y1 = rayLocal.origin.y + t1 * rayLocal.direction.y
-            val t0Int = minimum < y0 && y0 < maximum
-            val t1Int = minimum < y1 && y1 < maximum
-            when (Pair(t0Int, t1Int)) {
-                Pair(true, true) -> listOf(Intersection(t0, this), Intersection(t1, this))
-                Pair(true, false) -> listOf(Intersection(t0, this))
-                Pair(false, true) -> listOf(Intersection(t1, this))
-                else -> emptyList()
-            }
-        }
+        } else intersectBody(rayLocal, a, b, c)
 
         // Check for intersections with the caps of the cylinder, if appropriate.
-        val xs2 = intersectCaps(rayLocal)
+        val xs2 = intersectCaps(rayLocal, minimum, maximum)
 
         return xs1 + xs2
     }
 
-    // Helper function to check to see if intersection at t is within a radius of 1
-    // (i.e. radius of cylinder) from the y-axis.
-    private fun checkCap(ray: Ray, t: Double, y: Double): Boolean {
-        val x = ray.origin.x + t * ray.direction.x
-        val z = ray.origin.z + t * ray.direction.z
-        return x * x + z * z <= y * y
-    }
-
-    // Return any intersections with the caps of a closed cylinder.
-    private fun intersectCaps(ray: Ray): List<Intersection> {
-        if (!closed or almostEquals(0, ray.direction.y))
-            return emptyList()
-
-        val tMin = (minimum - ray.origin.y) / ray.direction.y
-        val tMax = (maximum - ray.origin.y) / ray.direction.y
-        return when(Pair(checkCap(ray, tMin, minimum), checkCap(ray, tMax, maximum))) {
-            Pair(true, true) -> listOf(Intersection(tMin, this), Intersection(tMax, this))
-            Pair(true, false) -> listOf(Intersection(tMin, this))
-            Pair(false, true) -> listOf(Intersection(tMax, this))
-            else -> emptyList()
-        }
-    }
-
     override fun localNormalAt(localPoint: Tuple): Tuple {
         val dist = localPoint.x * localPoint.x + localPoint.z * localPoint.z
 
diff --git a/src/main/kotlin/shapes/Cylinder.kt b/src/main/kotlin/shapes/Cylinder.kt
index 4632cd1..09a3d1c 100644
--- a/src/main/kotlin/shapes/Cylinder.kt
+++ b/src/main/kotlin/shapes/Cylinder.kt
@@ -5,19 +5,15 @@ package shapes
 import material.Material
 import math.*
 import math.Intersection
-import kotlin.math.sqrt
 
 class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
                maximum: Number = Double.POSITIVE_INFINITY,
-               val closed: Boolean = false,
+               closed: Boolean = false,
                transformation: Matrix = Matrix.I,
                material: Material? = null,
                castsShadow: Boolean = true,
                parent: Shape? = null):
-    Shape(transformation, material, castsShadow, parent) {
-
-    val minimum = minimum.toDouble()
-    val maximum = maximum.toDouble()
+    Cappable(minimum.toDouble(), maximum.toDouble(), closed, transformation, material, castsShadow, parent) {
 
     // Note due to Kotlin semantics, we have to use objMaterial here.
     override fun withParent(parent: Shape?): Shape =
@@ -31,64 +27,18 @@ class Cylinder(minimum: Number = Double.NEGATIVE_INFINITY,
 
         // Only check for intersections with the body of the cylinder if a is not near 0.
         val xs1 = if (almostEquals(0.0, a)) emptyList()
-            else {
-
+        else {
             val b = 2 * rayLocal.origin.x * rayLocal.direction.x + 2 * rayLocal.origin.z * rayLocal.direction.z
             val c = rayLocal.origin.x * rayLocal.origin.x + rayLocal.origin.z * rayLocal.origin.z - 1
-            val disc = b * b - 4 * a * c
-
-            if (disc < 0)
-                emptyList<Intersection>()
-
-            val sqrtDisc = sqrt(disc)
-            val (t0, t1) = run {
-                val t0Tmp = (-b - sqrtDisc) / (2 * a)
-                val t1Tmp = (-b + sqrtDisc) / (2 * a)
-                if (t0Tmp <= t1Tmp) Pair(t0Tmp, t1Tmp) else Pair(t1Tmp, t0Tmp)
-            }
-
-            // Check for intersections with the body of the cylinder.
-            val y0 = rayLocal.origin.y + t0 * rayLocal.direction.y
-            val y1 = rayLocal.origin.y + t1 * rayLocal.direction.y
-            val t0Int = minimum < y0 && y0 < maximum
-            val t1Int = minimum < y1 && y1 < maximum
-            when (Pair(t0Int, t1Int)) {
-                Pair(true, true) -> listOf(Intersection(t0, this), Intersection(t1, this))
-                Pair(true, false) -> listOf(Intersection(t0, this))
-                Pair(false, true) -> listOf(Intersection(t1, this))
-                else -> emptyList()
-            }
+            intersectBody(rayLocal, a, b, c)
         }
 
         // Check for intersections with the caps of the cylinder, if appropriate.
-        val xs2 = intersectCaps(rayLocal)
+        val xs2 = intersectCaps(rayLocal, 1.0, 1.0)
 
         return xs1 + xs2
     }
 
-    // Helper function to check to see if intersection at t is within a radius of 1
-    // (i.e. radius of cylinder) from the y-axis.
-    private fun checkCap(ray: Ray, t: Double): Boolean {
-        val x = ray.origin.x + t * ray.direction.x
-        val z = ray.origin.z + t * ray.direction.z
-        return x * x + z * z <= 1
-    }
-
-    // Return any intersections with the caps of a closed cylinder.
-    private fun intersectCaps(ray: Ray): List<Intersection> {
-        if (!closed or almostEquals(0, ray.direction.y))
-            return emptyList()
-
-        val tMin = (minimum - ray.origin.y) / ray.direction.y
-        val tMax = (maximum - ray.origin.y) / ray.direction.y
-        return when(Pair(checkCap(ray, tMin), checkCap(ray, tMax))) {
-            Pair(true, true) -> listOf(Intersection(tMin, this), Intersection(tMax, this))
-            Pair(true, false) -> listOf(Intersection(tMin, this))
-            Pair(false, true) -> listOf(Intersection(tMax, this))
-            else -> emptyList()
-        }
-    }
-
     override fun localNormalAt(localPoint: Tuple): Tuple {
         val dist = localPoint.x * localPoint.x + localPoint.z * localPoint.z