From 12ec4e8284afb30ed894d9926362141cdfb24b96 Mon Sep 17 00:00:00 2001
From: Keuin <keuinx@gmail.com>
Date: Tue, 3 May 2022 15:59:11 +0800
Subject: Refactor: do not invert ri in constructor of material_dielectric.
 Rewrite material_dielectric::scatter to stop using vec3::refract and switch
 to ri instead of ri_inv.

---
 material_dielectric.cpp | 56 ++++++++++++++++++++++++++++++-------------------
 material_dielectric.h   |  4 ++--
 2 files changed, 37 insertions(+), 23 deletions(-)

diff --git a/material_dielectric.cpp b/material_dielectric.cpp
index 61e34ec..d44ab87 100644
--- a/material_dielectric.cpp
+++ b/material_dielectric.cpp
@@ -8,29 +8,43 @@
 bool material_dielectric::scatter(ray3d &r, const object &hit_obj, double hit_t, random_uv_gen_3d &ruvg) const {
     const auto hit_p = r.at(hit_t);
     assert(hit_obj.is_on(hit_p));
-    auto n = hit_obj.normal_vector(hit_p);
-    auto ri_ = ri_inv;
-    auto cos1 = dot(r.direction(), n); // -cos(a1)
-    if (cos1 > 0) {
-        // the ray is started from the object's inner,
-        // use normal vector and ri on the surface's inner side
-        n = -n;
-        ri_ = 1.0 / ri_;
+    auto nv = hit_obj.normal_vector(hit_p);
+    const auto n1 = r.direction(); // incoming ray, unit vector
+    const bool outside = dot(nv, n1) < 0; // if the ray hits the outside of the surface
+    double rel_ri; // relative ri, source_ri/target_ri
+    if (!outside) {
+        nv = -nv; // use normal vector pointing to the inner
+        rel_ri = ri;
     } else {
-        cos1 = -cos1;
+        rel_ri = 1.0 / ri;
     }
-    vec3d r2;
-    // determine reflection or refraction using Schlick's Approximation.
-    if (reflectance(cos1, ri_) > ruvg.range01_scalar()) {
-        // reflect
-        TRACELOG("    reflect (dielectric material, schlick, ri=%-10f)\n", ri_);
-        r2 = n.reflect(r.direction());
+    const auto cos_t1 = std::min(-dot(nv, n1), 1.0); // cos(theta1)
+    const auto sin_t1_s = 1 - cos_t1 * cos_t1; // sin(theta1)^2
+    const auto rel_ri_s = rel_ri * rel_ri;
+    const auto sin_t2_s = sin_t1_s * rel_ri_s;
+    double p_reflect; // probability of schlick reflection
+    bool reflect = false;
+    if (sin_t2_s > 1.0) {
+        TRACELOG("    reflect (TIR, ri=%f)\n", ri);
+        // sin(theta2)^2 > 1, no real solution
+        // TIR (total internal reflection)
+        reflect = true;
+    } else if ((p_reflect = reflectance(cos_t1, ri)) > ruvg.range01_scalar()) {
+        TRACELOG("    reflect (schlick, ri=%f, p=%f)\n", ri, p_reflect);
+        reflect = true;
+    }
+    if (reflect) {
+        r.direction(nv.reflect(n1));
+        r.source(hit_p);
+        return true;
     } else {
-        // refract
-        TRACELOG("    refract (dielectric material, schlick, ri=%-10f)\n", ri_);
-        r2 = n.refract<true>(r.direction(), ri_);
+        // normal refract
+        TRACELOG("    refract (forced, ri=%f)\n", ri);
+        const auto sin_t2 = sqrt(sin_t2_s);
+        const auto cos_t2 = sqrt(1 - sin_t2_s);
+        const auto n2 = (-cos_t2 * nv) + (n1 + cos_t1 * nv).unit_vec() * sin_t2;
+        r.direction(n2);
+        r.source(hit_p);
+        return true;
     }
-    r.direction(r2.unit_vec());
-    r.source(hit_p);
-    return true;
 }
diff --git a/material_dielectric.h b/material_dielectric.h
index 46b17da..14cd680 100644
--- a/material_dielectric.h
+++ b/material_dielectric.h
@@ -9,7 +9,7 @@
 #include "material.h"
 
 class material_dielectric : public material {
-    double ri_inv;
+    double ri; // refractive index, 1.0 for air and 1.5 for glasses
 
     static double reflectance(double cosine, double ref_idx) {
         assert(cosine > 0);
@@ -21,7 +21,7 @@ class material_dielectric : public material {
     }
 
 public:
-    explicit material_dielectric(double ri) : ri_inv{1.0 / ri} {}
+    explicit material_dielectric(double ri) : ri{ri} {}
 
     bool scatter(ray3d &r, const object &hit_obj, double hit_t, random_uv_gen_3d &ruvg) const override;
 };
-- 
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