For the modeling of multipath propagation in every wireless systems, the ray tracing method has been widely studied. However, large errors may result due to the approximation of geometrical optics in curved surfaces. This paper therefore focused on the curved surfaces and edges, which are difficult to handle in ray tracing. Examples of curved surfaces can be found in arched cross-section tunnels which are common in highway networks of mountainous areas. The traditional ray tracing method of dividing the curved surface into smaller flat plates is not so accurate as the size of smaller plates may not satisfy the geometrical optics assumption, and the reflection point which satisfies Fermat's principle may not exist. In this work, a new ray tracing method is proposed with 2 contributions. The first one is the implementation of the reflection coefficient for curved surfaces in ray tracing. The second is applying the physical optics method on the caustics region. To evaluate these methods, path gain simulation results for an arched cross-section model are compared with measurements made inside an arched tunnel. To further improve the simulation results, the effect of rough surface is introduced, and the results are again compared with measurement.

Caustics are patterns of light focused by reflective or refractive objects. Because of their visually fascinating patterns, several methods have been developed to render caustics. We propose a method for the quick rendering of caustics formed by refracted and converged light through transparent objects. First, in the preprocess, we calculate sampling rays incident on each vertex of the object, and trace the rays until they leave the object taking refraction into account. The position and direction of each ray that finally transmits the transparent object are obtained and stored in a lookup table. Next, in the rendering process, when the object is illuminated, the positions and directions of the rays leaving the object are calculated using the lookup table. This makes it possible to render refractive caustics due to transparent objects at interactive frame rates, allowing us to change the light position and direction, and translate and rotate the object.

Recently, dielectric lens antennas are paid attentions in ITS applications. Many lens shape designing methods were already developed. And electrical performances were estimated through a ray tracing method. Here, arbitral lens shapes were expressed by a system of power series. In the case of ray tracing, time-consuming three-coordinate root-finder programs were needed to find intersection points of rays on the lens surfaces. In order to calculate complicated structures such as zoned lenses and complicated rays such as multiple reflections between lens surfaces, simple ray tracing methods are requested. In this paper, a simple ray tracing method that utilizes directly designed discrete points of lens surfaces is developed. In this method, a refracted ray is automatically determined for a given incident ray. As for an intersecting point of a lens surface for an outgoing ray, the nearest point to the refracted vector is found out by employing a simple searching procedure. This method is time-saving compared to the previous three-coordinate root-finding program. Through calculated results of focal points and radiation patterns in wide angle beam steering, effectiveness of a developed method is ensured. Application of the developed ray tracing method of complicated multiple reflections are studied. Reflecting points are found out speedily by the same searching procedure. A calculated example of doubly reflected rays is obtained. Through comparing calculated and measured results of wide angle radiation patterns, effectiveness of a developed method is ensured.