Image translation and rotation are becoming essential operations in many application areas such as image processing, computer graphics and pattern recognition. Conventional translation moves image from pixels to pixels and conventional rotation usually comprises of computation-intensive CORDIC operations. Traditionally, images are represented on a square pixel structure. In this paper, we perform reversible and fast image translation and rotation based on a hexagonal structure. An image represented on the hexagonal structure is a collection of hexagonal pixels of equal size. The hexagonal structure provides a more flexible and efficient way to perform image translation and rotation without losing image information. As there is not yet any available hardware for capturing image and for displaying image on a hexagonal structure, we apply a newly developed virtual hexagonal structure. The virtual hexagonal structure retains image resolution during the process of image transformations, and almost does not introduce distortion. Furthermore, images can be smoothly and easily transferred between the traditional square structure and the hexagonal structure.