Designing NURBS surfaces by manipulating control points directly requires too much trial and error for immersive VR applications. A more natural interface is provided by deforming a NURBS surface so that it passes through a given target point; and by repeating such deformations we can make the surface follow one or more target curves. These deformations can be achieved by modifying the pseudo-inverse matrix of the basis functions, but this matrix is often ill-conditioned. However, the application of a modified FE approach to the weights and control points provides controllable deformations, which are demonstrated across a range of example shapes.

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.