B-spline curve fitting with different parameterization methods

Kheng, Jia Shen (2020) B-spline curve fitting with different parameterization methods. Final Year Project, UTAR.

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Abstract

B-spline curve is important in the geometric modelling field and Computer Aided Design (CAD) in the visualization and curve modelling. B-spline is considered as one of the approximation curves as it is flexible and could provide a better behaviour and local control. The shape of the curve is influenced by the control points. Parameterization of the curve or surface is important in computer graphics as it can improve the overall quality of the visualization. Various parameterization methods such as uniform, centripetal, chord length and exponential had been used for the B-spline data fitting. However, there is an issue in many fields which is to construct an optimal curve with the given data points. Therefore, a comparison is made between the parameterization methods in this research in order to determine the optimal method for the B-spline curve fitting. This research is only focused on B-spline curve and four parameterization methods. In addition, uniformly spaced and averaging knot vector generations are used in generating the knot vector. After generating control points, distance between the generated and original data points is used to identify the error of the algorithm. Later, genetic algorithm and differential evolution optimization are used to optimise the error of the curve. Based on the result produced, each of the parameterization generated varied curve shape due to the different properties of the datasets.

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