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.

This paper addresses a new surface reconstruction scheme for approximating the isosurface from a set of tomographic cross sectional images. Differently from the novel Marching Cubes (MC) algorithm, our method does not extract the iso-density surface (isosurface) directly from the voxel data but calculates the iso-density point (isopoint) first. After building a coarse initial mesh approximating the ideal isosurface by the cell-boundary representation, it metamorphoses the mesh into the final isosurface by a relaxation scheme, called shrink-wrapping process. Compared with the MC algorithm, our method is robust and does not make any cracks on surface. Furthermore, since it is possible to utilize lots of additional isopoints during the surface reconstruction process by extending the adjacency definition, theoretically the resulting surface can be better in quality than the MC algorithm. According to experiments, it is proved to be very robust and efficient for isosurface reconstruction from cross sectional images.