Abstract: In order to generate the high-resolution 3D images and to construct many kinds of A-level curved surfaces, a new method of freeform surface construction was proposed on the basis of hexagonal grid subdivision theory. Under the geometrical reasoning constraint conditions of the graphs vertex, the geographic reasoning technique was improved. The combination of the FFD method for freeform construction and the derived surface construction method was realized. The result shows that, by using the new method, the 3D images can be efficiently constructed with well realistric and dynamic effects.