This paper presents a grid-based, real-time surface modeling algorithm in which the generation of a precise 3D model is possible by considering the user's intention during the course of the spatial input. In order to create the corresponding model according to the user's input data, plausible candidates of wand traversal patterns of grid edges are defined by considering the sequential and directional characteristics of the wand input. The continuity of the connected polygonal surfaces, including the octree space partitioning, is guaranteed without the extra crack-patching algorithm and the pre-defined patterns. Furthermore, the proposed system was shown to be a suitable and effective surface generation tool for the spatial sketching system. It is not possible to implement the unusual input intention of the 3D spatial sketching system using the conventional Marching Cubes algorithm.