1. More on Ray Tracing Glenn G. Chappell CHAPPELLG@member.ams.org U. of Alaska Fairbanks CS 481/681 Lecture Notes Wednesday, April 14, 2004

2. 14 Apr 2004CS 481/6812 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.

3. 14 Apr 2004CS 481/6813 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. First hit Current pixel Image Scene objects

4. 14 Apr 2004CS 481/6814 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. We can also do true refraction, for translucent objects. Normal Original ray Reflected ray

5. 14 Apr 2004CS 481/6815 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.

6. 14 Apr 2004CS 481/6816 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.

7. 14 Apr 2004CS 481/6817 More on Ray Tracing: Topics Next topics: A few notes. Hit testing. Example ray-tracing code. Adding features to a ray tracer.

8. 14 Apr 2004CS 481/6818 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?

9. 14 Apr 2004CS 481/6819 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.

10. 14 Apr 2004CS 481/68110 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.

11. 14 Apr 2004CS 481/68111 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 ???

12. 14 Apr 2004CS 481/68112 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 – v 2 is the square of the distance from O to this halfway point. If it exists! V E O r EO v sqrt[|EO| 2 – v 2 ]

13. 14 Apr 2004CS 481/68113 Hit Testing: Ray-Sphere Intersection [3/4] So: disc = r 2 – [|EO| 2 – v 2 ] 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! V E O r EO sqrt[|EO| 2 – v 2 ] sqrt[disc]

14. 14 Apr 2004CS 481/68114 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.

15. 14 Apr 2004CS 481/68115 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.

16. 14 Apr 2004CS 481/68116 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.