B-spline surface fitting to random points with bounded boundary conditions

Authors:
Kuo-Jen Chen;Yao-Chen Tsai;Jiing-Yih Lai;Wen-Der Ueng
Affiliations:
Department of Mechanical Engineering, National Central University, Taiwan, ROC.;Department of Mechanical Engineering, National Central University, Taiwan, ROC.;Department of Mechanical Engineering, National Central University, Taiwan, ROC.;Department of Mechanical Engineering, Tungnan University, Taiwan, ROC
Venue:
International Journal of Computer Applications in Technology
Year:
2007

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Abstract

Two algorithms for the surface fitting of random points are developed. The first algorithm is employed to pass through four given boundary curves, while the second algorithm is employed to achieve an extended bound. The fitted surface is essentially a B-spline surface where the control points and the parametric values of each measured point are unknown. Two kinds of base surfaces are proposed for the initialisation of the parametric values. An objective function, including an error function and an energy function, is then developed for the optimisation of unknown parameters. The feasibility of the proposed method is demonstrated.