Caustics are patterns of light formed by reflection or refraction of light from objects, and several methods have been developed to render caustics because of their visually beautiful patterns. This paper proposes a method for the rapid rendering of caustics formed by refracted light through transparent objects. First, a preprocess is used to generate sampling rays incident on each vertex of the object, and, taking refraction into account, to trace the rays until they leave the object. The position and direction of each ray that finally leaves the transparent object are obtained and stored in a lookup table. Next, in the rendering process, when the object is illuminated, the position and direction 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 even if the direction of the light changes and the object is translated or rotated.