The author describes a new method to improve the algebraic surface fitting process by better approximating the Euclidean distance from a point to the surface. In the past they have used a simple first order approximation of the Euclidean distance from a point to an implicit curve or surface which yielded good results in the case of unconstrained algebraic curves or surfaces, and reasonable results in the case of bounded algebraic curves and surfaces. However, experiments with the exact Euclidean distance have shown the limitations of this simple approximation. Here, a more complex, and better, approximation to the Euclidean distance is introduced from a point to an alegbraic curve or surface. It is shown that this new approximate distance produces results of the same quality as those based on the exact Euclidean distance, and much better than those obtained using other available methods.
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