This paper shows the calculation of 3D geometric information such as height, direction and distance under the constraints of a catadioptric camera system. The catadioptric camera system satisfies the single viewpoint constraints adopting hyperboloidal mirror. To calculate the 3D information with a single omni-directional image, the points are assumed to lie in perpendicular to the ground. The infinite plane is also detected as a circle from the structure of the mirror and camera. The analytic experiments verify the correctness of theory using real images taken in indoor environments like rooms or corridors. Thus, the experimental results show the applicability to calculate the 3D geometric information using single omni-directional images.