More on Ray Tracing
Glenn G. Chappell
U. of Alaska Fairbanks
CS 481/681 Lecture Notes
Wednesday, April 14, 2004
Basic Ray Tracing [1/5]
In “normal” rendering:
We deal with a series of objects, made of
For each primitive, we determine which pixels
it affects, if any.
Ray tracing turns this around:
We deal with pixels, one by one.
For each pixel, we ask what we see (which
primitive?) when we look at it.
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Basic Ray Tracing [2/5]
The way we determine what we see when we
look at a pixel is to draw an imaginary ray from
the viewing position, through the pixel, into the
We ask which objects in the scene the ray hits.
The first hit is the one that counts.
Image Scene objects
Current pixel First hit
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Basic Ray Tracing [3/5]
What do we do when we have a hit?
We determine what color the object is at that point.
Light sources and the object’s normal may affect the
We can also do true specular reflection:
Reflect the ray and do the ray tracing computation again.
We can also do true refraction, for translucent objects.
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Basic Ray Tracing [4/5]
Our discussion was centered around
two questions to be answered:
Does a ray hit an object; if so, where?
If a ray hits an object, then, looking
along the ray, what color do we see?
We outlined a simple OO design
based on answering these
Our design is simple, robust, and
easy to extend.
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Basic Ray Tracing [5/5]
• A ray is defined by its starting position and its direction.
• For convenience, rays know how to reflect and refract.
• Knows how to answer the two questions (for itself).
• Object classes are derived from a common base class.
• The two questions are answered via virtual functions.
• Stores the result of a hit test.
• For convenience, holds: whether there was a hit, and if
so, how far along the ray, where, and the object normal
at the hit point.
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More on Ray Tracing:
A few notes.
Example ray-tracing code.
Adding features to a ray tracer.
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Ray Tracing Notes:
A Third Method
We know about “normal” rendering and ray tracing.
There is a third option: photon tracing.
Here, we trace photons forward from the light source.
Since most photons do not hit the viewer’s eye, this is very
However, it is also very accurate, esp. for things like caustics.
• Main loop goes over primitives.
• Which pixels does this primitive affect?
• Main loop goes over pixels.
• What to I see when I look in this direction?
• Main loop goes over photons.
• Where does this light end up?
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Ray Tracing Notes:
Back to the ray tracer. I will add two more
classes to the design:
• This holds the entire scene. If true specular reflection is to
be performed, an object needs to have access to
information about the other objects.
• Essentially one member function: trace a ray through the
scene and return a color.
• Needs to know what color to return if the ray does not hit
• It is easy to implement cheap-ish diffuse reflection,
shadows, etc., in a ray tracer, if the location of light-
sources is known.
• I put this in my ray tracer, but it is currently not used.
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The easiest type of 3-D object to render
with the “normal” method is a triangle.
In ray tracing, “easy” means a quick hit
test and color determination.
The easiest type of object to include in a
ray-traced scene is a sphere.
This is why most early ray-traced scenes
involved shiny balls.
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Ray-Sphere Intersection [1/4]
We look at how to do a ray-sphere intersection.
Suppose we have a ray with start position E and direction
We want to do a hit test with a sphere having center O
and radius r.
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Ray-Sphere Intersection [2/4]
The vector from E to O is EO = O – E.
Let v be the dot product of EO and V.
The value of v is the distance from E to the point halfway between
the hits, if there are any hits.
So |EO|2 – v2 is the square of the distance from O to this
If it exists!
EO sqrt[|EO|2 – v2]
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Ray-Sphere Intersection [3/4]
So: disc = r2 – [|EO|2 – v2] is the square of half the distance
between the hit points.
If the hits exist!
The quantity disc is called the discriminant.
If disc < 0, then there are no hits!
EO sqrt[|EO|2 – v2]
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Ray-Sphere Intersection [4/4]
The distances to the two hits, are v – sqrt[disc]
and v + sqrt[disc].
Based on all this, we can come up with a
relatively simple algorithm to do hit testing on a
See grtobject.cpp for an implementation.
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Of course, we would like to be able to put
polygons into a ray-traced scene. We need only
deal with convex polygons.
We need to know how to do a hit test on a
convex polygon. Here is an outline:
Find the plane the polygon lies in.
Do ray-plane intersection to find the point at which the
ray hits the plane (unless it is parallel to the plane).
Check the hit point to see if it lies in the polygon.
• This is done by looping over the edges of the polygon. For
each edge, we check whether the point lies on the inside
of the line through it.
• If the point lies on the inside of all the edges, then it is
inside the polygon, and we have a hit.
The normal is the normal of the plane.
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Ray Tracing Code:
Now we look at the GRT program.
“GRT” = “Glenn’s Ray Tracer”.
In class, we went over the source to
These files are on the web page.
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