The problem of mapping a 2D texture array onto an arbitrarily oriented plane in 3D space and onto curvilinear surfaces is considered. The method of mapping a 3D texture array onto freeform and volumes is considered. High-speed and effective algorithm of volume rendering is proposed. New methods of object representation by using unified free forms 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. In this paper, we propose a texture memory management policy that substitutes the classical assignation policy of one texel per voxel, applied for the volume representation in texture space. The texture is an object (not mapped) changing the properties of another object. The feature of the texture is that any object may be the texture. A supplement to the data structure with consideration of the structure is that each object can have a reference to another object being a texture for it.