High-speed and effective algorithm of volume rendering is proposed. New methods of object representation by using unified freeforms and arbitrary algebraic surfaces are suggested as well. Proposed algorithm allows to lower complexity of computations, memory and bandwidth requirements in comparison with known methods. The prototyping of hardware system allows operating in real-time with high-quality images. Proposed systems are targeted for scientific visualization, medical applications such as virtual bronchoscopy, endoscopy, and tomography, fly through a virtual patient; virtual reality-based systems and high fidelity conventional image generators. Primary goal of the project is the development of algorithm and 3D data presentations for fast volume-rendering, evaluation of developed algorithms in order to find optimal hardware architecture of real-time image generator.