Merging multiple B B -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 B B -spline/Bzier curves and stitching B B -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 B B -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 B B -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,C1 C 0 , C 1 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.
virtual reality blending matrices modeling and simulation merging of b b -spline surfaces b b b b b