Developing hybrid symbolic-numerical and approximate algorithms for manipulating geometrical objects used in computer-aided geometric design and other fields is of increasing interest. I recommend this paper to all researchers interested in such algorithms.

The authors consider the problem of parametrizing approximate algebraic surfaces, and propose two algorithms for approximate parametrization by lines. The first algorithm deals with quadrics. The second algorithm is used to process surfaces of degree d with “almost” a point of multiplicity d-1.

A very good introduction, four sections, and the references are dedicated to the subject. In the first section, the reader will find the symbolic algorithm to parametrize surfaces by lines. The approximate algorithm for quadrics is found in the second section, which also includes two theorems and an example. The third section describes the general algorithm. Two theorems and a special subsection with five detailed examples illustrate the second algorithm. The fourth section is dedicated to the analysis of the error. It is proved that the output generated by the proposed method is close to the input surface. The final results are presented in the last two theorems.

The references are good and help make the presentation clear. The many examples and the comprehensive theoretical analysis about the performances of the proposed algorithms are useful.