From 0dd729ba24529b5a63c849b1477e1180fc99cd47 Mon Sep 17 00:00:00 2001 From: Steve Hollasch Date: Sun, 10 Mar 2024 15:56:15 -0700 Subject: [PATCH 1/3] Fix section describing total internal reflection With a sphere of index of refraction greater than the surrounding medium, there is no incoming ray that can be chosen to show total internal reflection. An incoming ray will be bent to a smaller angle relative to the surface normal, and then bent back to the original angle on exit. To illustrate total reflection, this change renders a bubble of air inside water. Glancing rays are then reflected off the surface instead of refracted. In the service of this change, I've also moved the center sphere back a bit from the left and right spheres so you can see the affected side more clearly. This will invalidate all of the other three-sphere images, which will be fixed up in #1358 (Alpha.2 milestone verify Book 1 progression). Resolves #900 --- books/RayTracingInOneWeekend.html | 68 ++++++++++++------ images/img-1.16-glass-always-refract.png | Bin 66983 -> 73441 bytes .../img-1.17-air-bubble-total-reflection.png | Bin 0 -> 73758 bytes images/img-1.17-glass-sometimes-refract.png | Bin 74879 -> 0 bytes 4 files changed, 45 insertions(+), 23 deletions(-) create mode 100644 images/img-1.17-air-bubble-total-reflection.png delete mode 100644 images/img-1.17-glass-sometimes-refract.png diff --git a/books/RayTracingInOneWeekend.html b/books/RayTracingInOneWeekend.html index cf45109e..852e0b7e 100644 --- a/books/RayTracingInOneWeekend.html +++ b/books/RayTracingInOneWeekend.html @@ -3056,7 +3056,7 @@ auto material_right = make_shared(color(0.8, 0.6, 0.2)); world.add(make_shared(point3( 0.0, -100.5, -1.0), 100.0, material_ground)); - world.add(make_shared(point3( 0.0, 0.0, -1.0), 0.5, material_center)); + world.add(make_shared(point3( 0.0, 0.0, -1.2), 0.5, material_center)); world.add(make_shared(point3(-1.0, 0.0, -1.0), 0.5, material_left)); world.add(make_shared(point3( 1.0, 0.0, -1.0), 0.5, material_right)); ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ @@ -3277,17 +3277,18 @@
-Now we'll update the scene to change the left and center spheres to glass: +Now we'll update the scene to illustrate refraction by changing the left sphere to glass, which has +an index of refraction of approximately 1.5. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ auto material_ground = make_shared(color(0.8, 0.8, 0.0)); + auto material_center = make_shared(color(0.1, 0.2, 0.5)); ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight - auto material_center = make_shared(1.5); auto material_left = make_shared(1.5); ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ auto material_right = make_shared(color(0.8, 0.6, 0.2), 1.0); ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - [Listing [two-glass]: [main.cc] Changing left and center spheres to glass] + [Listing [two-glass]: [main.cc] Changing the left sphere to glass]
@@ -3302,9 +3303,11 @@ Total Internal Reflection -------------------------- -That definitely doesn't look right. One troublesome practical issue is that when the ray is in the -material with the higher refractive index, there is no real solution to Snell’s law, and thus there -is no refraction possible. If we refer back to Snell's law and the derivation of $\sin\theta'$: +One troublesome practical issue with refraction is that there are ray angles for which no solution +is possible using Snell's law. This happens when the ray goes into a medium of lower index of +refraction, and the angle between the ray and the surface is glancing enough that ray in the new +medium refracts to an angle greater than 90°. If we refer back to Snell's law and the derivation +of $\sin\theta'$: $$ \sin\theta' = \frac{\eta}{\eta'} \cdot \sin\theta $$ @@ -3334,8 +3337,10 @@ Here all the light is reflected, and because in practice that is usually inside solid objects, it is -called “total internal reflection”. This is why sometimes the water-air boundary acts as a perfect -mirror when you are submerged. +called _total internal reflection_. This is why sometimes the water-to-air boundary acts as a +perfect mirror when you are submerged -- if you're under water looking up, you can see things above +the water, but when you are close to the surface and looking sideways, the water surface looks like +a mirror. We can solve for `sin_theta` using the trigonometric qualities: @@ -3400,25 +3405,42 @@ -
-Attenuation is always 1 -- the glass surface absorbs nothing. If we try that out with these -parameters: +Attenuation is always 1 -- the glass surface absorbs nothing. - ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ Highlight +If we render the prior scene with the new `dielectric::scatter()` function, we see … no change. Huh? + +Well, it turns out that given a sphere of material with an index of refraction greater than air, +there's no incident angle that will yield total internal reflection -- neither for rays entering the +sphere, nor for rays exiting. This is due to the geometry of spheres, as a grazing incoming ray will +always be bent to a smaller angle, and then bent back to the original angle on exit. + +So how can we illustrate total internal reflection? Well, if the sphere has an index of refraction +_less_ than the medium it's in, then we can hit it with grazing angles that end up with total +_external_ reflection. That should be good enough. + +We'll consider the world filled with water (index of refraction approximately 1.33), and change the +sphere material to air (index of refraction 1.00) -- an air bubble! To do this, change the left +sphere material's index of refraction to + + $$\frac{\text{index of refraction of air}}{\text{index of refraction of water}}$$ + + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ auto material_ground = make_shared(color(0.8, 0.8, 0.0)); auto material_center = make_shared(color(0.1, 0.2, 0.5)); - auto material_left = make_shared(1.5); - auto material_right = make_shared(color(0.8, 0.6, 0.2), 0.0); + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight + auto material_left = make_shared(1.00 / 1.33); + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ + auto material_right = make_shared(color(0.8, 0.6, 0.2), 1.0); ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - [Listing [scene-dielectric]: [main.cc] Scene with dielectric and shiny sphere] - -
+ [Listing [two-glass]: [main.cc] Left sphere is an air bubble in water]
-We get: +This change yields the following render: + + ![Image 17: Air bubble sometimes refracts, sometimes reflects + ](../images/img-1.17-air-bubble-total-reflection.png class='pixel') - ![Image 17: Glass sphere that sometimes refracts - ](../images/img-1.17-glass-sometimes-refract.png class='pixel') +Here you can see that more-or-less direct rays refract, while glancing rays reflect.
@@ -3509,7 +3531,7 @@ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ ... world.add(make_shared(point3( 0.0, -100.5, -1.0), 100.0, material_ground)); - world.add(make_shared(point3( 0.0, 0.0, -1.0), 0.5, material_center)); + world.add(make_shared(point3( 0.0, 0.0, -1.2), 0.5, material_center)); world.add(make_shared(point3(-1.0, 0.0, -1.0), 0.5, material_left)); ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight world.add(make_shared(point3(-1.0, 0.0, -1.0), -0.4, material_left)); @@ -3776,7 +3798,7 @@ auto material_right = make_shared(color(0.8, 0.6, 0.2), 0.0); world.add(make_shared(point3( 0.0, -100.5, -1.0), 100.0, material_ground)); - world.add(make_shared(point3( 0.0, 0.0, -1.0), 0.5, material_center)); + world.add(make_shared(point3( 0.0, 0.0, -1.2), 0.5, material_center)); world.add(make_shared(point3(-1.0, 0.0, -1.0), 0.5, material_left)); world.add(make_shared(point3(-1.0, 0.0, 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zLElS6Vp@cv5AvmP79H&tf>uaJktbi@qida%$WsPsM<3uLoYNd`~qZYT&s=UQ>@WK-Hj{!bl8ZkfheJPoA7S9=%tKvMxO>r1UlpS3}>_zEfWD)zv z+TtOJ?r$rOf_~77*+>0k!iaBgFi!qfWc*H(EUM`_!;8b)C)QhrX$x^~KSE=ZolXhd z4=!yVN+_W3rM#mlP&Lh(&LDU!vviR>ZsEk3e|wkQg75aRDX3kD#Oa9Htlv(uG3heI z94nBrSZ~{+8#D|ezJL-)({}DwjtI<^@SSo7%Yn3MR5DcyWwOEd19{aod49lm@V4Lel~l(2vprm%Zs^3yw{|u{0qCN0IZ7ZKE6AO?~)c dUko^l{}1nqa{9^I@Tvd+002ovPDHLkV1id&PDcO$ From 7b82c9ecf3f4d53f464a837b16b8f3248539463f Mon Sep 17 00:00:00 2001 From: Steve Hollasch Date: Fri, 15 Mar 2024 19:27:53 -0700 Subject: [PATCH 2/3] Some additional wording tweaks --- books/RayTracingInOneWeekend.html | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/books/RayTracingInOneWeekend.html b/books/RayTracingInOneWeekend.html index 852e0b7e..edbc408a 100644 --- a/books/RayTracingInOneWeekend.html +++ b/books/RayTracingInOneWeekend.html @@ -3410,15 +3410,15 @@ If we render the prior scene with the new `dielectric::scatter()` function, we see … no change. Huh? Well, it turns out that given a sphere of material with an index of refraction greater than air, -there's no incident angle that will yield total internal reflection -- neither for rays entering the -sphere, nor for rays exiting. This is due to the geometry of spheres, as a grazing incoming ray will -always be bent to a smaller angle, and then bent back to the original angle on exit. +there's no incident angle that will yield total internal reflection -- neither at the ray-sphere +entrance point nor at the ray exit. This is due to the geometry of spheres, as a grazing incoming +ray will always be bent to a smaller angle, and then bent back to the original angle on exit. So how can we illustrate total internal reflection? Well, if the sphere has an index of refraction -_less_ than the medium it's in, then we can hit it with grazing angles that end up with total -_external_ reflection. That should be good enough. +_less_ than the medium it's in, then we can hit it with shallow grazing angles, getting total +_external_ reflection. That should be good enough to observe the effect. -We'll consider the world filled with water (index of refraction approximately 1.33), and change the +We'll model a world filled with water (index of refraction approximately 1.33), and change the sphere material to air (index of refraction 1.00) -- an air bubble! To do this, change the left sphere material's index of refraction to From cfde6a4dfe2d4c0623887ecf8a9a0375458e1a1c Mon Sep 17 00:00:00 2001 From: Steve Hollasch Date: Tue, 19 Mar 2024 20:57:04 -0700 Subject: [PATCH 3/3] Incorporate review feedback --- books/RayTracingInOneWeekend.html | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/books/RayTracingInOneWeekend.html b/books/RayTracingInOneWeekend.html index edbc408a..3ad04c22 100644 --- a/books/RayTracingInOneWeekend.html +++ b/books/RayTracingInOneWeekend.html @@ -3304,10 +3304,9 @@ Total Internal Reflection -------------------------- One troublesome practical issue with refraction is that there are ray angles for which no solution -is possible using Snell's law. This happens when the ray goes into a medium of lower index of -refraction, and the angle between the ray and the surface is glancing enough that ray in the new -medium refracts to an angle greater than 90°. If we refer back to Snell's law and the derivation -of $\sin\theta'$: +is possible using Snell's law. When a ray enters a medium of lower index of refraction at a +sufficiently glancing angle, it can refract with an angle greater than 90°. If we refer back to +Snell's law and the derivation of $\sin\theta'$: $$ \sin\theta' = \frac{\eta}{\eta'} \cdot \sin\theta $$