This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to various geometric shapes with minimal fitting parameters. Furthermore, the proposed method does not require any constraints and can handle incomplete data. The method is validated on synthetic and real-world data sets and compared with the existing methods in the literature for polygon and ellipse fitting. The test results show that the method achieves high accuracy and outperforms the referenced methods in terms of root-mean-square error, especially for noise-free data. The proposed method is a powerful tool for shape fitting in computer vision and geometry processing applications.

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