From 3deef4d969dd50ddf540b80fe43ef16af5c17169 Mon Sep 17 00:00:00 2001
From: Nat Lasseter <user@4574.co.uk>
Date: Mon, 24 Jun 2024 22:51:51 +0100
Subject: Chapter 11

---
 hittable.go |  6 ++++--
 material.go | 46 ++++++++++++++++++++++++++++++++++++++++++++--
 rtiaw.go    |  4 +++-
 vec3.go     |  9 +++++++++
 4 files changed, 60 insertions(+), 5 deletions(-)

diff --git a/hittable.go b/hittable.go
index 42599ab..ac5e996 100644
--- a/hittable.go
+++ b/hittable.go
@@ -11,12 +11,14 @@ type HitRecord struct {
   P Vec3
   N Vec3
   T float64
+  F bool
   Mat Material
 }
 
 func (rec *HitRecord) SetFaceNormal(r Ray, out_n Vec3) {
-  if r.Direction.Dot(out_n) < 0 {
-    rec.N = out_n
+  rec.F = r.Direction.Dot(out_n) < 0;
+  if rec.F {
+    rec.N = out_n;
   } else {
     rec.N = out_n.Neg();
   }
diff --git a/material.go b/material.go
index 66ea256..62a0467 100644
--- a/material.go
+++ b/material.go
@@ -1,5 +1,9 @@
 package main
 
+import (
+  maths "math"
+)
+
 //Material
 
 type Material interface {
@@ -7,7 +11,7 @@ type Material interface {
   Scatter(r Ray, hit HitRecord) Ray
 }
 
-//Lambertian
+//Lambertian < Material
 
 type Lambertian struct {
   Albedo Vec3
@@ -25,7 +29,7 @@ func (l Lambertian) Scatter(r Ray, hit HitRecord) Ray {
   return Ray{hit.P, scat_dir, true};
 }
 
-//Metal
+//Metal < Material
 
 type Metal struct {
   Albedo Vec3
@@ -42,3 +46,41 @@ func (m Metal) Scatter(r Ray, hit HitRecord) Ray {
   valid := refl.Dot(hit.N) > 0;
   return Ray{hit.P, refl, valid};
 }
+
+//Dielectric < Material
+
+type Dielectric struct {
+  RefractionIndex float64
+}
+
+func (d Dielectric) Attenuation() Vec3 {
+  return SplatVec3(1);
+}
+
+func (d Dielectric) Scatter(r Ray, hit HitRecord) Ray {
+  ri := d.RefractionIndex;
+  if hit.F {
+    ri = 1.0 / ri;
+  }
+
+  unit_dir := r.Direction.Unit();
+  cos_theta := maths.Min(unit_dir.Neg().Dot(hit.N), 1.0);
+  sin_theta := maths.Sqrt(1.0 - maths.Pow(cos_theta, 2));
+
+  cannot_refract := ri * sin_theta > 1.0;
+
+  var dir Vec3;
+  if cannot_refract || schlick_reflect(cos_theta, ri) {
+    dir = unit_dir.Reflect(hit.N);
+  } else {
+    dir = unit_dir.Refract(hit.N, ri);
+  }
+
+  return Ray{hit.P, dir, true};
+}
+
+func schlick_reflect(cos_theta float64, ri float64) bool {
+  r0 := maths.Pow((1 - ri) / (1 + ri), 2);
+  approx := r0 + (1 - r0) * maths.Pow(1 - cos_theta, 5);
+  return approx > Interval{0, 1}.Sample();
+}
diff --git a/rtiaw.go b/rtiaw.go
index d95501d..1427fbf 100644
--- a/rtiaw.go
+++ b/rtiaw.go
@@ -11,13 +11,15 @@ func main() {
 
   mat_ground := Lambertian{Vec3{0.8, 0.8, 0}};
   mat_centre := Lambertian{Vec3{0.1, 0.2, 0.5}};
-  mat_left   := Metal{Vec3{0.8, 0.8, 0.8}, 0.3};
+  mat_left   := Dielectric{1.5};
+  mat_bubble := Dielectric{1.0 / 1.5};
   mat_right  := Metal{Vec3{0.8, 0.6, 0.2}, 1.0};
 
   var world Hittables;
   world.Add(Sphere{Vec3{ 0,   -100.5, -1  }, 100  , mat_ground});
   world.Add(Sphere{Vec3{ 0,      0  , -1.2},   0.5, mat_centre});
   world.Add(Sphere{Vec3{-1.0,    0  , -1  },   0.5, mat_left});
+  world.Add(Sphere{Vec3{-1.0,    0  , -1  },   0.4, mat_bubble});
   world.Add(Sphere{Vec3{ 1.0,    0  , -1  },   0.5, mat_right});
 
   cam := NewCamera(400, 16.0/9.0, 100, 50);
diff --git a/vec3.go b/vec3.go
index a540b7c..f590625 100644
--- a/vec3.go
+++ b/vec3.go
@@ -95,3 +95,12 @@ func RandomVec3OnUnitSphere() (v Vec3) {
 func (v Vec3) Reflect(n Vec3) Vec3 {
   return v.Sub(SplatVec3(2 * v.Dot(n)).Mul(n));
 }
+
+func (v Vec3) Refract(n Vec3, eta_ratio float64) Vec3 {
+  cos_theta := maths.Min(v.Neg().Dot(n), 1.0);
+  r_out_perp := SplatVec3(eta_ratio).
+               Mul(v.Add(SplatVec3(cos_theta).Mul(n)));
+  rops := -maths.Sqrt(maths.Abs(1.0 - r_out_perp.MagSqr()));
+  r_out_parr := SplatVec3(rops).Mul(n);
+  return r_out_perp.Add(r_out_parr);
+}
-- 
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