Merging multiple BB-spline surface patches in a virtual reality environment

Although a number of different algorithms have been described in the literature for merging two or more BB-spline/Bézier curves and stitching BB-spline surfaces, these techniques are not suitable for virtual reality applications that require the user to effortlessly combine multiple dissimilar patches in real-time to create the final object shape. This paper presents a novel approach for merging arbitrary BB-spline surfaces within a very low tolerance limit. The technique exploits blending matrices that are independent of the control point positions and, hence, can be pre-calculated prior to haptic interaction. Once determined, the pre-calculated blending matrices are used to generate discrete points on the BB-spline surface. When two or more surfaces are merged, these discrete point matrices are combined to form a single matrix that represents the resultant shape. By using the inverse of the revised blending matrices and the combined discrete point matrix, a new set of control points can be directly computed. The merged surface can be made to have C0,C1C0,C1 or higher connectivity at the joining edge. A brief study comparing the proposed merging technique with a commercially available CAD system is presented and the results show improved computational efficiency, accuracy, and robustness.