通过比较基于线性变换的多项式模型和传统纯量多项式模型的项数、模型参数、模型运算性质以及模型所能表示对象的集合,并进行算例分析发现,基于线性变换的多项式模型形式更加简洁,模型参数具有直观的几何意义和良好的运算性质,更适合表达多维高次对象,在工业测量领域的应用中更容易确定必要的拟合参数,整体上更具有优越性.%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.
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