In ray tracing given objects (surfaces) are visualized as being seen from a given point. The two main options which are in general specified by the user are the eye point and the light sources. Then an imaginary grid of pixels is placed in a view plane between the eye and the objects. A ray follows a path from the viewpoint, through a pixel, and to the object. When a ray intersects an object, the color and orientation of the surface it encounters determine the color and intensity of the pixel. This information is used to color the pixels on the screen. Two main calculations which must be made are the determination of the (first) intersection of the ray with the surface and the determination of the normal vector to the surface at this intersection. As both of these calculations can be done very easily for implicitly represented surfaces, the ray tracing is a field in which implicit surfaces can find a large application. The Linz group realized a comparison of the ray tracing of surfaces given in parametric and implicit representation. For this aim the same software "POV-Ray 3.5" was used for the both representations. As an example, we considered both implicit and parametric representations of a quartic surface, and compared the results when tracing this surface. The result of the ray tracing is shown below for both the implicit representation (left) and the parametric representation (right). Both resulting pictures are [640x480] pixels and about the same quality.
Published June 24, 2005