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•Optical properties for balls, and floor: index of refraction, and shininess, transparency, diffuse, Phong, and specular constants,

•The maximum ray tree depth,

•Precalculated values for use in the program.

•Both of these groups of data items have been ‘lumped’ together in separate data structures. As mentioned before the rays are organized as a linked list. The geometric information is stored in a second structure. By using this approach it makes it very easy to pass the various classes of information around the system, without pushing large numbers of variables on the stack.

12.8.3 Bounding Volumes

• Bounding test volumes were set up, but these have proven to be ineffective in most cases where the scene is filled, their only benefit is in a nearly empty scene, where they save a ray calculation for every pixel. There are two main bounding volumes. The first volume is constructed around the set of balls. The second is constructed to represent the half of the screen which the floor will be displayed in (this could be all or none).

12.8.4 Shadows

•Within the image there are certain objects which will be in shadows. In these cases there is a reduction in the amount of light. To detect this case a ray is traced between the light, and the point of interest (the only objects which will be hit here are spheres). If the light hits any spheres, the shadow is confirmed. When a shadow is confirmed, the specular reflection, and diffuse lighting from a point source are ignored.

•To speed the checking process, the balls have been ordered by their distance from the light. The balls are checked in order, until one is hit, or the distance from the ball is greater than the distance between the point and the light.

Ball 1

d1

d2

Ball 2

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Depth Ordered Balls

• In the figure above there are a set of balls ordered by depth from the light source. If we are looking for a shadow on any point of Ball 2, we first find a vector from the point to the light. The search then begins backward from the light. If the light strikes Ball 1, then Ball 2 is in its shadow. If the light misses it then Ball 2 is not in a shadow. Say we are finding a shadow on the floor, and the floor is known to be some distance (from the light) between Ball 1 (d1) and Ball 2 (d2). The algorithm would check for collisions with Balls 1 and 2. A check would reveal that the distance for d2 is greater than the distance to the floor, and since, no balls will have been hit, it may be concluded that the floor is not in a shadow, and the search is discontinued. This can save a great deal of search time when the light is close to the floor.

12.8.5 Aliasing

• A problem with ray tracing is that features smaller than a pixel can be missed. Another problem is that features not aligned to the pixel grid become choppy. A method for solving this problem is Supersampling Anti-aliasing. This uses an approach where the pixel map is sampled normally, as well as between pixels, and the pixel values are combined.

Sample Points

Pixel Sample

Sample Points for Anti-aliasing

The black points in Figure 18 are sampled, the four points around it are used to adjust the value. This will tend to give a local averaging effect which overcomes sudden discontinuities in image space.

12.8.6 Advanced topics

•Some advanced topics include,

•Pattern and texture mapping,

•Fog and lighting effects,