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This study presents a generalised least squares based method for fittingpolygons and ellipses to data points. The method is based on a trigonometricfitness function that approximates a unit shape accurately, making itapplicable to various geometric shapes with minimal fitting parameters.Furthermore, the proposed method does not require any constraints and canhandle incomplete data. The method is validated on synthetic and real-worlddata sets and compared with the existing methods in the literature for polygonand ellipse fitting. The test results show that the method achieves highaccuracy and outperforms the referenced methods in terms of root-mean-squareerror, especially for noise-free data. The proposed method is a powerful toolfor shape fitting in computer vision and geometry processing applications.

Optimised Least Squares Approach for Accurate Polygon and Ellipse Fitting