On the G1 continuity of piecewise Be´zier surfaces: a review with new results
Computer-Aided Design - Special Issue: Be´zier Techniques
Degree reduction of B-spline curves
Computer Aided Geometric Design
Efficient And Accurate Interference Detection For Polynomial Deformation
CA '96 Proceedings of the Computer Animation
G1 continuity conditions of adjacent NURBS surfaces
Computer Aided Geometric Design
Reconstruction of convergent G1 smooth B-spline surfaces
Computer Aided Geometric Design
Haptic sculpting of multi-resolution B-spline surfaces with shaped tools
Computer-Aided Design
Automatic mesh split-and-merge technique for multiple surface models
Proceedings of the 11th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and its Applications in Industry
Efficient energy evaluations for active B-Spline/NURBS surfaces
Computer-Aided Design
An explicit method for G3 merging of two Bézier curves
Journal of Computational and Applied Mathematics
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Although a number of different algorithms have been described in the literature for merging two or more B-spline/Bezier curves and stitching 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-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-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 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.