Unconstrained and constrained curve fitting for reverse engineering |
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Authors: | Wen-Der Ueng Jiing-Yih Lai Yao-Chen Tsai |
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Affiliation: | 1. Mechanical Engineering Department, Tung Nan Institute of Technology, Taiwan, Republic of China 2. Mechanical Engineering Department, National Central University, Taiwan, Republic of China
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Abstract: | Curve fitting is commonly used in reverse engineering for the reconstruction of curves from measured points, and it is critically important to provide various kinds of curve-fitting algorithms to acquire curves that satisfy different constraint conditions. We divide the curve-fitting problem into unconstrained and constrained types. For the unconstrained type, three curve-fitting algorithms are investigated: general, smooth and extended curve fitting. The general curve fitting considers only the accuracy of the fitted curve; the smooth curve fitting can control both the accuracy and the fairness of the fitted curve, while the extended curve fitting can acquire a curve longer than the range of the measured points. For the constrained type, we propose three curve-fitting conditions: fixed end-points, closed curve and continuity to adjacent curves. Detailed discussion for each of the above cases is presented. Associated examples are also provided to illustrate the feasibility of the proposed algorithms. |
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