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PROFESSOR: All right.

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We're going to get
started now.

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For those of you who don't know
me, I'm Josh Slocum, one

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of your TAs.

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And today's lecture is going to
be a primer on ray tracing

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to help you get started
on the final project.

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So first, we're going to start
with a little background.

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Tell you about ray tracing.

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Ray tracing is essentially
a physics simulation.

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You simulate the way photons
bounce around and interact

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with materials.

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And from that, you generate
an image of a scene.

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It's extremely parallel because
you can trace a whole

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bunch of photons bouncing
around at the same time.

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And it has a huge capacity
for photorealism.

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So like this sample seen here,
you have all sorts of

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reflections and light working in
ways that you don't see in

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a normal rendering program.

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The final project, as you know
if you've read the handout, is

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going to be groups of two
or three people each.

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And you'll be given a working
ray tracer program.

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A very slow one, but
one that works.

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And your objective is to make
it run as fast as possible.

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You can do pretty much anything
you want with a few

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restrictions we'll
talk about later.

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You can make algorithmic
improvements, parallelize it,

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change the way the rendering
works slightly.

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All sorts of things.

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Pretty much anything
you can think of.

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The only deliverables for the
final project are the

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preliminary report due next
week, in which you'll have to

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show us that you've profiled the
project, tell us what hot

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spots you've identified, and
ideas you have for speeding up

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the ray tracer, as well
as any actual work

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you've already done.

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The final project comes with two
built-in scenes that can

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be ray traced.

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Scene one, this one here,
is rendered much

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faster than scene two.

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And you're going to want to
work on that one first.

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And then, there's scene two,
which is slightly different.

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It has water and one
less sphere.

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These are the restrictions
on what you can do

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for the final project.

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The purpose of these
restrictions is basically just

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to make sure that everyone's
ray tracer is

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doing the same thing.

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So you're all working on the
same problem, and you're not

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achieving speed ups by
simplifying out some

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functionality of the program.

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Does anyone have any questions
about the final project

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before I move on?

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All right.

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Go ahead.

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AUDIENCE: [INAUDIBLE]

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we're going to do a third scene
similar to the first

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two, right?

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PROFESSOR: Oh.

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Yeah.

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In order to make sure that
you're following these rules,

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we're going to test your ray
tracer on one or more other

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scenes and make sure that
they render properly.

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But these are the two scenes
that you will be benchmarked

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on for your performance grade.

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All right.

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Next, we're going to go over how
ray tracing works and the

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big concepts used in the ray
tracer you'll be working on.

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So the basic idea behind the
rendering is you're going to

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construct a geometric model of
the scene you want to render,

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and so it will be made
of polygons,

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or spheres, or planes.

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And then within that model, you
insert a grid of pixels.

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They'll form the image you're
going to render.

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And then, you just project the
scene onto the grid of pixels,

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and you have some image.

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The way you do this with ray
tracing is you use a method

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called ray casting where you
take some camera and cast rays

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through each pixel
onto the scene.

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And then, whatever color object
the ray hits is the

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color that that pixel gets
shaded in the scene.

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This method of tracing rays is
called backwards ray tracing,

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because you're going in opposite
direction that

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photons go in when you're
actually observing something.

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So if this was an actual
scene, you'd have light

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bouncing here and
into you're eye.

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Whereas what you're doing is
you're tracing backwards from

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the eye to the object.

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Ray casting--

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this image here is
a ray image--

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is very primitive.

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It doesn't really
get you much.

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So what you can do is you
can improve your physics

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simulation by adding a whole
bunch more things on top of

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it, like shadows, and
reflections, and global

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illumination.

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All sorts of fun stuff.

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So if you want to start
simulating shadows, and

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reflections, and defraction, you
need to start recursively

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casting rays, which is
called ray tracing.

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So when your ray bounces off of
an object, you can cast a

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reflection ray at the same
angle mirrored from the

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perpendicular of the object and
see what color object that

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ray hits, and then, shade this
object with that color.

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You can also cast a refracted
ray, and use Snell's a lot to

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tell which direction it goes
in and do the same thing.

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And then, you can cast a shadow
ray at all the light

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sources in the scene.

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And if the shadow ray hits an
object before hitting the

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light source, then you know
that this object is in the

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shade and make it darker.

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And obviously, you have to limit
the recursion depth for

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your recursive tracing, because
otherwise, you'll

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never finish rendering.

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So, first way of improving
lighting is to start using

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direct illumination, which is
you have a light source at the

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top of the scene.

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And when you hit something like
a wall here, you then

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bounce a ray at the
light source.

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And depending on how far this
intersection A is from the

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light source, you shade either
brighter or darker.

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So it might be hard to see in
this light, but the wall gets

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darker the further away
it is from the light.

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And then, you do shadows the
same way, except at point B

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here, the rate it bounces from
the ground hits this ball.

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And so, point B is
in the shade.

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Now, you can improve on shadows
by making what's

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called soft shadows.

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Soft shadows are shadows
that form a gradient

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from darker to lighter.

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They happen when you have a
light source that's not a

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point light.

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So if you look at the shadows
around you in the room, you'll

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see there are gradients,
not just a

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solid block of darkness.

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And the way you achieve that
is when you get an

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intersection, when your ray
intersects a point, you cast

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multiple shadow rays at
different points along the

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light source.

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And depending on how many of
these rays hit something

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before hitting the light
source, you shade some

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proportion of the light being
casted, or the light coming

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from this light source.

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So you can see point D here,
none of the rays hit the light

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source, and so, it's in
a very dark area.

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Whereas point C, one of the rays
hits the light source,

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and so it's in a slightly
brighter area.

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And then reflection and
refraction work very similarly

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to shadows, except instead of
bouncing from here to the

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light source, you bounce off
this metal ball at the angle

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of reflection.

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And you bounce through this
glass ball using the angle of

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refraction.

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You can calculate using
Snell's law.

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Any questions before
we move on?

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All right.

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So as you can see pretty clearly
in this image, there's

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still some problems.

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The ceiling is completely
black.

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Shadows are mostly black.

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And there's no light being
transmitted through this glass

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00:10:00,100 --> 00:10:02,810
ball either into the
shadow here.

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00:10:02,810 --> 00:10:05,730
So there's definitely some
improvements we can make on

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00:10:05,730 --> 00:10:08,310
our physics simulation.

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00:10:08,310 --> 00:10:11,100
The first thing we're going to
look at is called global

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illumination, which is pretty
much any sort of illumination

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that doesn't come directly
from light sources.

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Now the reason this sort of
illumination is important is

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that there's actually a lot of
light that gets bounced around

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the room that doesn't
come directly

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from the light source.

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Like that white wall, if I shine
this laser pointer at

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it, as you can see, there's
still a lot of light

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00:10:38,730 --> 00:10:40,580
bouncing off of it.

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It's not all being absorbed.

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So what you can do is you can
take your ray intersection,

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and you can use what's called
the Monte Carlo method, which

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is you take a whole bunch of
random samples and interpolate

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00:11:00,330 --> 00:11:05,020
those samples to get some value
that approximates what

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the illuminant should be here.

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00:11:07,550 --> 00:11:09,950
The problem with that, though,
is that when you trace

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backwards, you get this
exponential explosion of

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recursively cast rays.

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And you have no guarantee that
any of these paths will ever

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00:11:19,940 --> 00:11:22,860
get to this light source.

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So what you have to do is trace
forwards, so you start

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at the light source, and you
cast photons in random

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00:11:32,500 --> 00:11:38,040
directions and let them bounce
all around the scene until

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they get absorbed.

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00:11:39,750 --> 00:11:44,600
Now, when a photon bounces, a
bunch of light gets absorbed.

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But not all the light.

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00:11:46,650 --> 00:11:51,090
And so, the rest of the light
keeps reflecting.

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And depending on the kind of
material, different amounts

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and colors of light
will be reflected.

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So as you can see, this
ray here bounces

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off the orange wall.

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00:12:00,060 --> 00:12:03,270
And so, orange light
gets reflected.

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00:12:03,270 --> 00:12:05,380
This ray bounces off
the blue wall.

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00:12:05,380 --> 00:12:07,280
And so, blue light
gets reflected.

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00:12:07,280 --> 00:12:10,330
And this ray bounces off this
metal ball, and so it gets

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00:12:10,330 --> 00:12:15,600
completely reflected up
towards the ceiling.

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00:12:15,600 --> 00:12:19,880
So if you remember each bounce
in something called a photon

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00:12:19,880 --> 00:12:25,190
map, then later, you can come
back and say, oh, there's so

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many photons in this area.

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00:12:29,800 --> 00:12:31,560
And that's what these
yellow circles are.

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00:12:31,560 --> 00:12:36,136
So the illuminance is going
to be approximately this.

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00:12:36,136 --> 00:12:40,870
The problem with that is unless
you're simulating an

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00:12:40,870 --> 00:12:45,090
extremely large number of
photons, you'll have an uneven

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00:12:45,090 --> 00:12:47,060
distribution.

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00:12:47,060 --> 00:12:50,650
So what you can do is you can
hybridize forwards ray tracing

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00:12:50,650 --> 00:12:52,970
and the Monte Carlo method.

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00:12:52,970 --> 00:12:56,400
So you construct your photon
map, which is represented in

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00:12:56,400 --> 00:13:00,170
this image by all the red dots
scattered everywhere.

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00:13:00,170 --> 00:13:03,150
And then you do backwards
ray tracing.

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00:13:03,150 --> 00:13:08,030
Then when you reach a point, you
randomly sample different

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00:13:08,030 --> 00:13:11,780
reflection rays and average
their illuminance to get the

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00:13:11,780 --> 00:13:13,800
illuminance at this point.

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00:13:13,800 --> 00:13:17,290
So you have blue illuminance
from the wall here.

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00:13:17,290 --> 00:13:21,720
And then light gray from here
and darker gray from here.

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00:13:21,720 --> 00:13:25,430
And the result is this sort of
pale blue, which you can't

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00:13:25,430 --> 00:13:27,880
really see in the image because
the light's bad.

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00:13:30,880 --> 00:13:35,060
Yeah, so backwards trace,
randomly sample, illumination.

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00:13:40,530 --> 00:13:44,054
And any questions
before we go on?

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00:13:54,880 --> 00:14:01,260
So it turns out even with
building a photon map and then

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00:14:01,260 --> 00:14:04,300
randomly sampling the photon
map, calculating the

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00:14:04,300 --> 00:14:07,120
irradiance can still
be very expensive.

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00:14:07,120 --> 00:14:11,390
So what we've implemented to
speed that up is what's called

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00:14:11,390 --> 00:14:14,360
an irradiance cache.

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00:14:14,360 --> 00:14:17,550
And the way the irradiance
cache works is there are

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00:14:17,550 --> 00:14:23,030
certain areas on objects that
will have pretty much the same

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00:14:23,030 --> 00:14:24,840
irradiance.

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00:14:24,840 --> 00:14:26,360
It's pretty much the same
irradiance levels.

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00:14:26,360 --> 00:14:30,300
So you can interpolate
from nearby points.

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00:14:30,300 --> 00:14:33,390
So what we do with the
irradiance cache is as the

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00:14:33,390 --> 00:14:40,670
scene is rendering, if there
is a cache miss, then we

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00:14:40,670 --> 00:14:45,050
calculate the irradiance for
some pixel which corresponds

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00:14:45,050 --> 00:14:47,290
to a point in the scene.

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00:14:47,290 --> 00:14:50,840
And then, if we then trace a
ray very near to that same

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00:14:50,840 --> 00:14:56,880
pixel, you can then interpolate
from nearby cached

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00:14:56,880 --> 00:15:03,000
irradiances and get something
that looks right.

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00:15:03,000 --> 00:15:07,800
So if you take a look at this
image, where the green dots

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00:15:07,800 --> 00:15:14,940
represent cache misses on these
big planer objects here.

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00:15:14,940 --> 00:15:17,150
There's very few cache misses.

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00:15:17,150 --> 00:15:20,650
And it's almost entirely
cache hits.

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00:15:20,650 --> 00:15:26,850
Whereas at the interface between
different objects, the

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00:15:26,850 --> 00:15:31,160
cache misses become
much more common.

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00:15:31,160 --> 00:15:34,650
But overall, the number of
irradiance calculations is

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00:15:34,650 --> 00:15:35,900
greatly reduced.

255
00:15:39,650 --> 00:15:44,400
And then, the third kind of
illumination that we implement

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00:15:44,400 --> 00:15:46,270
is called caustics.

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00:15:46,270 --> 00:15:53,220
Caustics are just light being
lensed into patterns of

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00:15:53,220 --> 00:15:58,520
brighter and darker spaces, such
as you get from a light

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00:15:58,520 --> 00:16:00,340
pointing towards a glass ball.

260
00:16:00,340 --> 00:16:03,310
Or if you ever see the sort of
wavy pattern on the bottom of

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00:16:03,310 --> 00:16:06,720
a pool, that's also
from caustics.

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00:16:06,720 --> 00:16:11,100
Caustics are also implemented
with the photon map, except

263
00:16:11,100 --> 00:16:12,660
it's created slightly
differently.

264
00:16:12,660 --> 00:16:15,770
Instead of bouncing photons
everywhere, photons are

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00:16:15,770 --> 00:16:19,070
absorbed as soon as they
hit a diffuse object.

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00:16:19,070 --> 00:16:24,840
So a photon might bounce off of
this metal sphere and then

267
00:16:24,840 --> 00:16:29,010
hit the wall, and it will
be immediately absorbed.

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00:16:29,010 --> 00:16:32,330
Whereas if it hits this sphere,
it'll bounce, and

269
00:16:32,330 --> 00:16:35,000
bounce, and then be absorbed.

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00:16:35,000 --> 00:16:41,240
So the objective of caustics
is to trace how photons are

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00:16:41,240 --> 00:16:43,750
grouped based on the optical
properties of

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00:16:43,750 --> 00:16:45,000
materials in the scene.

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00:16:47,700 --> 00:16:54,075
And then, caustics are rendered
pretty simply.

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00:16:56,740 --> 00:17:03,330
Because there's much fewer
photons than in the photon map

275
00:17:03,330 --> 00:17:05,920
for global illumination, you
don't need to use an

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00:17:05,920 --> 00:17:07,440
irradiance cache.

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00:17:07,440 --> 00:17:13,410
So you simply trace a ray to
a point and then sample the

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00:17:13,410 --> 00:17:15,359
number of photons nearby.

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00:17:15,359 --> 00:17:18,700
And you end up with something
like this if you just do

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00:17:18,700 --> 00:17:19,950
caustics shading.

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00:17:24,790 --> 00:17:29,810
So then at the end, you take
your direct illumination, and

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00:17:29,810 --> 00:17:33,380
then add it to caustics, and
then add it to global

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00:17:33,380 --> 00:17:34,800
illumination.

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00:17:34,800 --> 00:17:36,250
And you get something that
looks like this.

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00:17:40,070 --> 00:17:43,060
Any questions before we go
to the code overview?

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00:17:49,140 --> 00:17:49,610
Go ahead.

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00:17:49,610 --> 00:17:53,000
AUDIENCE: Do we weight
them equally?

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00:17:53,000 --> 00:17:54,110
PROFESSOR: So the
question was, do

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00:17:54,110 --> 00:17:55,830
we weight them equally?

290
00:17:55,830 --> 00:18:00,150
And the answer is yes.

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00:18:00,150 --> 00:18:03,470
And you just sum
them together.

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00:18:09,290 --> 00:18:13,560
Ideally, you were clever and
constructed your ray tracer so

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00:18:13,560 --> 00:18:17,510
that they should be weighted
equally, because there's

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00:18:17,510 --> 00:18:20,080
weighting done internally,
basically.

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00:18:32,380 --> 00:18:36,630
So next, we're going to do a
quick overview of the code

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00:18:36,630 --> 00:18:39,610
that will be in your
repositories just get you

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00:18:39,610 --> 00:18:42,055
started and help you understand
how it works.

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00:18:46,080 --> 00:18:49,200
First, we're going to start by
explaining some of the classes

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00:18:49,200 --> 00:18:51,030
you'll find.

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00:18:51,030 --> 00:18:57,580
First is SceneObject, which is
the parent class for all of

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00:18:57,580 --> 00:19:00,530
the objects that will be used to
construct the scenes you'll

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00:19:00,530 --> 00:19:03,030
be rendering.

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00:19:03,030 --> 00:19:06,900
Every scene object has a ray
intersection method that's

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00:19:06,900 --> 00:19:09,830
called whenever you
trace a ray.

305
00:19:09,830 --> 00:19:14,100
And it'll return where the ray

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00:19:14,100 --> 00:19:19,700
intersection is and the object.

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00:19:19,700 --> 00:19:23,310
And SceneObject is inherited by
these objects here, which

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00:19:23,310 --> 00:19:31,120
all of the objects will
inherit from.

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00:19:31,120 --> 00:19:36,700
Then we've got the Raytracer
class, which

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00:19:36,700 --> 00:19:38,960
contains the main method.

311
00:19:38,960 --> 00:19:40,920
So it starts the program.

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00:19:40,920 --> 00:19:45,770
And it also contains methods for
constructing the scene and

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00:19:45,770 --> 00:19:50,760
then rendering the
scene once you've

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00:19:50,760 --> 00:19:53,690
constructed the scene first.

315
00:19:53,690 --> 00:19:58,150
We have the LightSource class,
which is a base class for any

316
00:19:58,150 --> 00:19:59,450
light sources.

317
00:19:59,450 --> 00:20:04,330
In our ray tracer, the only
subclass is square photon

318
00:20:04,330 --> 00:20:10,660
light, which is this light at
the top of the scene here.

319
00:20:10,660 --> 00:20:15,520
And what that does, or what the
light class does, is it

320
00:20:15,520 --> 00:20:19,990
contains methods for
constructing the photon maps

321
00:20:19,990 --> 00:20:24,900
and getting illumination from
either global, or caustic, or

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00:20:24,900 --> 00:20:27,890
direct sources.

323
00:20:27,890 --> 00:20:32,720
And then there's also the
iCache class, which

324
00:20:32,720 --> 00:20:35,610
essentially just implements
the iCache for you.

325
00:20:39,820 --> 00:20:41,070
Any questions?

326
00:20:47,600 --> 00:20:52,530
So basic execution overview.

327
00:20:52,530 --> 00:20:55,770
You have the main method
for Raytracer.

328
00:20:55,770 --> 00:20:57,910
Parses the command line.

329
00:20:57,910 --> 00:20:59,970
Constructs the scene.

330
00:20:59,970 --> 00:21:02,590
And the scene is just a
command line switch.

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00:21:02,590 --> 00:21:05,750
So if you say S1, it'll
construct scene one.

332
00:21:05,750 --> 00:21:09,780
If you say S2, it'll construct
scene two.

333
00:21:09,780 --> 00:21:12,680
Then for each light source, it
tells the light source to make

334
00:21:12,680 --> 00:21:16,800
photon maps for the global
and caustic illumination.

335
00:21:16,800 --> 00:21:19,058
GUEST SPEAKER: I should mention
that we actually moved

336
00:21:19,058 --> 00:21:22,502
the main functionality
into [INAUDIBLE]

337
00:21:22,502 --> 00:21:23,486
so you can replace the data.

338
00:21:23,486 --> 00:21:25,454
You don't have to touch that.

339
00:21:25,454 --> 00:21:28,160
It just constructs the scene,
so that we can then add a

340
00:21:28,160 --> 00:21:29,390
scene [INAUDIBLE] from that.

341
00:21:29,390 --> 00:21:31,100
So you shouldn't need
to do that.

342
00:21:31,100 --> 00:21:31,670
PROFESSOR: OK.

343
00:21:31,670 --> 00:21:37,020
So that's changed then.

344
00:21:37,020 --> 00:21:40,890
Then, main calls the render
function of Raytracer.

345
00:21:40,890 --> 00:21:43,800
What the render function
does--

346
00:21:43,800 --> 00:21:45,760
excuse me, method does--

347
00:21:45,760 --> 00:21:49,720
is it casts a ray for each
pixel in the scene you're

348
00:21:49,720 --> 00:21:55,440
going to render, finds the
nearest intersection, and then

349
00:21:55,440 --> 00:21:58,760
computes the shading at that
intersection by recursively

350
00:21:58,760 --> 00:22:02,730
bouncing rays and [? painting ?]
the illuminance

351
00:22:02,730 --> 00:22:03,980
cache for illumination.

352
00:22:07,670 --> 00:22:11,720
And that's basically what
the Raytracer does.

353
00:22:11,720 --> 00:22:13,900
It's pretty simple.

354
00:22:13,900 --> 00:22:18,740
So we're also going to quickly
go over how the light source

355
00:22:18,740 --> 00:22:23,810
traces photons for direct
and global illumination.

356
00:22:23,810 --> 00:22:30,320
The difference is kind of
settled, but pretty important.

357
00:22:30,320 --> 00:22:36,160
With global illumination, you
want some total number of

358
00:22:36,160 --> 00:22:38,710
photons to be put in the map.

359
00:22:38,710 --> 00:22:45,380
And you put a photon in the
map whenever it hits some

360
00:22:45,380 --> 00:22:46,630
diffuse surface.

361
00:22:50,460 --> 00:22:55,040
And then, that photon then
continues bouncing around

362
00:22:55,040 --> 00:22:56,290
until it's absorbed.

363
00:22:58,380 --> 00:23:01,660
For caustic illumination,
it's pretty similar.

364
00:23:01,660 --> 00:23:04,640
You have some set number
of photons you want to

365
00:23:04,640 --> 00:23:06,400
get into the map.

366
00:23:06,400 --> 00:23:10,410
You cast a ray in some
random direction.

367
00:23:10,410 --> 00:23:15,960
And then, the ray intersects
with a diffuse material.

368
00:23:15,960 --> 00:23:18,990
You store the intersection
in the photon map.

369
00:23:18,990 --> 00:23:19,850
And then you break.

370
00:23:19,850 --> 00:23:21,811
You don't keep bouncing
the photons around.

371
00:23:24,900 --> 00:23:29,500
So that's basically it for
the code overview.

372
00:23:29,500 --> 00:23:33,070
This slide has some resources
that you can use if you want

373
00:23:33,070 --> 00:23:34,770
to learn more about
ray tracing.

374
00:23:37,370 --> 00:23:40,080
Some of these will explain
concepts that we haven't

375
00:23:40,080 --> 00:23:42,840
implemented.

376
00:23:42,840 --> 00:23:45,710
They're an interesting read,
but not needed if you don't

377
00:23:45,710 --> 00:23:48,210
want to read them.

378
00:23:48,210 --> 00:23:57,260
And also, there's no standard
way of doing global

379
00:23:57,260 --> 00:24:00,090
illumination or direct
illumination.

380
00:24:00,090 --> 00:24:03,750
So you may come across resources
that do things

381
00:24:03,750 --> 00:24:07,320
slightly different than our
reference implementation.

382
00:24:07,320 --> 00:24:09,740
That doesn't mean either
one is wrong.

383
00:24:09,740 --> 00:24:12,480
But you should be aware that
there will almost certainly be

384
00:24:12,480 --> 00:24:13,730
differences.

385
00:24:25,020 --> 00:24:28,338
Does anyone have
any questions?

386
00:24:28,338 --> 00:24:28,792
Go ahead.

387
00:24:28,792 --> 00:24:30,154
AUDIENCE: So we can use one
of those alternatives?

388
00:24:30,154 --> 00:24:32,190
PROFESSOR: Can you say
that louder please?

389
00:24:32,190 --> 00:24:33,820
AUDIENCE: So we can use one
of those alternatives?

390
00:24:36,920 --> 00:24:39,290
PROFESSOR: These aren't
implementations.

391
00:24:39,290 --> 00:24:41,920
They're descriptions of
how ray tracing works.

392
00:24:44,590 --> 00:24:48,920
You should not change your
code to work in this way.

393
00:24:48,920 --> 00:24:52,040
These are just to help with
clarification if you want to

394
00:24:52,040 --> 00:24:54,620
learn more about what's being
done in the code.

395
00:24:57,796 --> 00:24:58,282
Go ahead.

396
00:24:58,282 --> 00:24:59,740
AUDIENCE: [INAUDIBLE PHRASE]

397
00:24:59,740 --> 00:25:06,544
what specifically are we allowed
to change for the

398
00:25:06,544 --> 00:25:08,280
[INAUDIBLE]?

399
00:25:08,280 --> 00:25:10,230
PROFESSOR: So what
specifically are

400
00:25:10,230 --> 00:25:11,003
you allowed to change?

401
00:25:11,003 --> 00:25:13,280
AUDIENCE: Yeah.

402
00:25:13,280 --> 00:25:14,530
Which ever one's smaller
[INAUDIBLE PHRASE].

403
00:25:18,240 --> 00:25:22,280
PROFESSOR: Anything not
prohibited by these rules,

404
00:25:22,280 --> 00:25:28,390
which are paraphrased from the
project handout, you can do.

405
00:25:28,390 --> 00:25:31,650
So basically, as long as you're
still performing the

406
00:25:31,650 --> 00:25:36,756
same essential calculations,
you're fine.

407
00:25:36,756 --> 00:25:37,254
Hmm?

408
00:25:37,254 --> 00:25:40,574
GUEST SPEAKER: I would say the
criteria for correctness is to

409
00:25:40,574 --> 00:25:42,860
look at the images, and
say that they look

410
00:25:42,860 --> 00:25:43,160
more or less the same.

411
00:25:43,160 --> 00:25:46,060
They don't give you a pixel
by pixel accurate.

412
00:25:46,060 --> 00:25:51,020
This isn't a graphics class
that actually does that.

413
00:25:51,020 --> 00:25:56,000
This should be almost
like a [INAUDIBLE].

414
00:25:56,000 --> 00:25:58,180
PROFESSOR: They should visually
look the same.

415
00:26:03,970 --> 00:26:12,160
If you find some approximation
that looks almost the same and

416
00:26:12,160 --> 00:26:15,880
runs 100 times faster,
go for it.

417
00:26:15,880 --> 00:26:19,570
You can't say, for example,
simplify your ray tracer

418
00:26:19,570 --> 00:26:21,720
though by saying, OK, we're
only going to be able to

419
00:26:21,720 --> 00:26:23,380
render these two scenes,
but we'll be able to

420
00:26:23,380 --> 00:26:24,630
do it really fast.