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12.8 RAY TRACING

•This method no longer uses polygons, but relies directly on the geometrical model.

•The lines of light which make up the pixels of the picture, are back traced, and followed through reflection, refraction, and ambient light.

•This method generates a horrendous number of calculations.

•The figure on the next page shows how ray tracing is done for the first bounce, many other bounces may be performed for more realism.

•Advantages,

-Realistic texture and appearances are easy to use

-This is the only display method suited to rendering curved surfaces

-The images give photograph quality

•Disadvantages,

-Incredibly Slow due to large number of calculations

-Requires a very powerful computer

•Support technology is being produced at a tremendous rate.

•Currently used for producing pictures and videos for sales marketing, etc. Many commercials on TV are produced with this method. Used in movies, like Terminator2, the Abyss, etc.

12.8.1 Basic Ray Tracing Theory

• The theory of ray tracing has two basic concerns. Firstly, the light path is of interest, secondly the light transmitted is also of interest. These both involve interactions with real objects, thus light-object interaction must also be covered in this section. Note that in most models discussed the geometric relations are not given. Almost all of these relations are given, derived from other sources, or easily obtained with dot products.

12.8.1.1 - A Model for Diffuse Reflection of Ambient Light

• Ambient light is assumed to be evenly distributed over the entire volume of space. This naturally occurring light will provide a basic level of illumination for all objects.

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i)Find distance squared between ray origin and centre,

ii)Calculate ray distance which is closest to centre,

iii)Test if ray is outside and points away from sphere,

iv)Find square of half chord intersection distance,

v)Test if square is negative,

vi)Calculate intersection distance,

vii)Find intersection point,

viii)Calculate normal at point.

•This algorithm gives at worst 16 additions, 13 multiples, 1 root, and 3 compares.

12.8.1.4 - Collision of a Ray With a Plane:

• A method for ray plane intersection was used to find collisions with the checkerboard. This method was devised from scratch. The proof will not be given, but it involves a parametric representation of the line, which is substituted into the plane equation. The parameter value was then found, and the collision point calculated. The algorithm for Line - Plane intersection is given below:

I

Pp

Pc

A Ray Colliding with a Plane

i)The dot product between I and N is found,

ii)If the dot product is greater than, or equal to, zero then the line does not intersect the plane,

iii)The line-plane intersection parameter is calculated (the dot product may be used here),

iv)The intersection point is calculated.

•This algorithm is also based on an explicit relationship, therefore it is quite fast. In the best case there are 3 multiplies, 2 adds and 1 compare. In the worst case there are 12 multiplies, 1 divide, 10 adds/subtracts.

12.8.1.5 - Mapping a Pattern