More on Ray Tracing

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					More on Ray Tracing

 Glenn G. Chappell
 CHAPPELLG@member.ams.org
 U. of Alaska Fairbanks

 CS 481/681 Lecture Notes
 Wednesday, April 14, 2004
Review:
Basic Ray Tracing [1/5]
    In “normal” rendering:
         We deal with a series of objects, made of
          primitives.
         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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Review:
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
     scene.
         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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Review:
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
          computation.
    We can also do true specular reflection:
         Reflect the ray and do the ray tracing computation again.


                   Original ray
                                              Reflected ray




                                  Normal

    We can also do true refraction, for translucent objects.

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Review:
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
  questions.
 Our design is simple, robust, and
  easy to extend.
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Review:
Basic Ray Tracing [5/5]
    Classes
         Ray
           • A ray is defined by its starting position and its direction.
           • For convenience, rays know how to reflect and refract.
         Object
           • 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.
         Hit
           • 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:
Topics
    Next topics:
       A few notes.
       Hit testing.

       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
          inefficient.
         However, it is also very accurate, esp. for things like caustics.
    Quick Summary
         “Normal”
           • Main loop goes over primitives.
           • Which pixels does this primitive affect?
         Ray Tracing
           • Main loop goes over pixels.
           • What to I see when I look in this direction?
         Photon Tracing
           • Main loop goes over photons.
           • Where does this light end up?

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Ray Tracing Notes:
The Design
    Back to the ray tracer. I will add two more
     classes to the design:
         Object List
           • 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
             an object.
         Light List
           • 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.


    14 Apr 2004                   CS 481/681                              9
Hit Testing:
Introduction
    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.




    14 Apr 2004            CS 481/681                10
Hit Testing:
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
     vector V.
    We want to do a hit test with a sphere having center O
     and radius r.

                          ???
                      V
                  E


                                             O

                                         r


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Hit Testing:
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
     halfway point.
                               v
         If it exists!


                              V
                          E
                                  EO                         sqrt[|EO|2 – v2]
                                                    O

                                                r


    14 Apr 2004                        CS 481/681                              12
Hit Testing:
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!

                                     sqrt[disc]


                            V
                      E
                                EO                        sqrt[|EO|2 – v2]
                                                  O

                                                r


    14 Apr 2004                      CS 481/681                        13
Hit Testing:
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
     sphere.
         See grtobject.cpp for an implementation.




    14 Apr 2004              CS 481/681              14
Hit Testing:
Convex Polygons
    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:
Example
    Now we look at the GRT program.
       “GRT” = “Glenn’s Ray Tracer”.
       In class, we went over the source to
        grtmain.cpp, grtray.cpp,
        grtobject.cpp, grttypes.cpp.
         These files are on the web page.




    14 Apr 2004          CS 481/681            16

				
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