| DIRECT MANIPULATION OF B-SPLINE SURFACES |
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| 作者姓名： | Wang Zhiguo Zhou Laishui Wang Xiaoping College of Mechanical and Electrical Engineering CAD/CAM Research Center Nanjing University of Aeronautics and Astronautics Nanjng China |
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| 作者单位： | Wang Zhiguo Zhou Laishui Wang Xiaoping College of Mechanical and Electrical Engineering，CAD/CAM Research Center，Nanjing University of Aeronautics and Astronautics，Nanjng 210016，China |
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| 基金项目： | This project is supported by Teaching and Research Award Program for Outstanding Young Professors in Higher Education Institute, Ministry of Education, China. |
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| 摘 要： | Engineering design and geometric modeling often require the ability to modify the shape of parametric curves and surfaces so that their shape satisfy some given geometric constraints, including point, normal vector, curve and surface. Two approaches are presented to directly manipulate the shape of B-spline surface. The former is based on the least-square, whereas the latter is based on minimizing the bending energy of surface. For each method, since unified and explicit formulae are derived to compute new control points of modified surface, these methods are simple, fast and applicable for CAD systems. Algebraic technique is used to simplify the computation of B-spline composition and multiplication. Comparisons and examples are also given.
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| 关 键 词： | 工程设计 几何模型 结合能 硬度矩阵 CAD |
DIRECT MANIPULATION OF B-SPLINE SURFACES |
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| Wang Zhiguo Zhou Laishui Wang Xiaoping College of Mechanical and Electrical Engineering,CAD/CAM Research Center,Nanjing University of Aeronautics and Astronautics,Nanjng ,China.DIRECT MANIPULATION OF B-SPLINE SURFACES[J].Chinese Journal of Mechanical Engineering,2005,18(1):103-108. |
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| Authors: | WangZhiguo ZhouLaishui WangXiaoping |
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| Abstract: | Engineering design and geometric modeling often require the ability to modify the shape of parametric curves and surfaces so that their shape satisfy some given geometric constraints, including point, normal vector, curve and surface. Two approaches are presented to directly manipulate the shape of B-spline surface. The former is based on the least-square, whereas the latter is based on minimizing the bending energy of surface. For each method, since unified and explicit formulae are derived to compute new control points of modified surface, these methods are simple, fast and applicable for CAD systems. Algebraic technique is used to simplify the computation of B-spline composition and multiplication. Comparisons and examples are also given. |
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| Keywords: | NURBS Bending energy Fairness Kronecker product Stiffness matrix |
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