Papers by Keyword: B-Spline Surface

Abstract: To increase the utility rate of machine, the sculptured surface machining method was researched to use in the spiral bevel gear tooth surface manufacturing with the industrial CNC milling machine. The three dimentional tooth surface points are required to design tool path planning in the SSM method. For obtaining the arbitrary point of tooth surface, the uniform bicubic B-spline tooth surface was reconstructed by cutting simulation and fitting programs. The discrepancies between fitted and theoretical points of tooth surface were provided with CAD/CAM platform. According to the results, the tool path planning of sculptured tooth surface machining can be designed and realized further.

Abstract: The approximate merging of two adjacent B-spline surfaces into a B-spline surface is the core problem in data communication. A novel algorithm is presented in this paper to solve this problem. In this algorithm, we compute the merging error using L₂ norm instead of the Euclidean norm, the process of merging is minimizing the approximate error and we only need solve a system of linear equations to get the final merging surface. In order to reduce the merging error, we add a weighed function on objective function to start the next merger; this function adds greater weight on where error is larger. After the next merger, the merging error will be significantly reduced. Finally, some examples are given to demonstrate the effectiveness and validity of the proposed algorithm.

Abstract: When remanufacturing complex surface parts, such as twisted blade, it is difficult to obtain an accurate model. An iterative Genetic-algorithm-based-surface reconstruction method for repair of twisted blade is presented. Genetic algorithm is applied in parametrizing data points and computing knot vectors. Then, the control points of the fitting B-spline surface are calculated by least-squares approximation through either SVD or LU methods. It shows that the accuracy of the method is improved significantly when three different twisted blades surfaces are verified by using the method.

Abstract: According to characteristic of garment mannequin, this paper puts forward the method of grid surface modeling for three-dimensional human body. Based on the analysis of fitting theory of B-spline curve and surface, it is presented that B-spline curve and surface is used for three-dimensional human modeling. The concrete processes of establishment of three-dimensional human body model are introduced. The results show that the three-dimensional human model which has been successfully achieved can satisfy the requirement of automatic measurement system.

Abstract: This paper presents an efficient method for deforming B-spline surfaces, based on the surface energy minimization. Firstly, using an analogy between the B-spline surface patch and the thin-plate element of the finite element method, and applying external forces on the surface with some given geometric constraints, the forces can locate on part of the surface or the surface. Then, the energy of the B-spline surface can change with the change of the forces. Finally, a new B-spline surface is generated by solving an optimization problem of change of the energy. The forces can be a single force, a distributed force and set of isolated force. The method can accomplish easily local deformation and total deformation of the B-spline surface.

Abstract: B-spline surfaces are widely suitable for the computer-aided geometric design (CAGD) and the modified geometry is one of the important technologies in CAGD. According to variations and weighting coefficients of single or multiple control vertices, the control vertices are modified by the method of weighted constrained optimization, the method of least squares was used for the optimal positions of control vertices on surfaces, and finally the modified B-spline surfaces are worked out by use of the variations of control vertices which had been calculated. The proposed approach not only can realize several modified geometry and deformation, but also is convenient for interaction design. The efficiency of the proposed approaches is illustrated by a practical application.