  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.
