Abstract After summarizing the classification methods of polynomial model, the linear transformation from a unit circle to any ellipse or circle is studied, thus the polynomial model based on linear transformation is derived. By comparing the polynomial model based on linear transformation with the traditional scalar polynomial model on the number of items, the model parameters, calculation properties and the collection of objects that can be represented by model, as well as giving an analytical example about the plane circle fitting,it is found that the new model has a more compact form, its parameters have perceptual geometric meaning and good operational properties, it is more suitable for the expression of the higher-dimensional and higher-degree polynomial object. Particularly it is more convenient to obtain the necessary parameters in industrial surveying field. On the whole, the polynomial model based on linear transformation has more advantages.
