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Geometric modeling by constraints yields systems of equations. They are classically solved by Newton-Raphson's iteration, from a starting guess interactively provided by the designer. However, this method may fail to converge, or may converge to an unwanted solution after a 'chaotic' behaviour. This paper claims that, in such cases, the homotopic method is much more satisfactory. Just use homogenized coordinates (X, Y, H) for this point, iez H= X,yH= Y, translate constraints g, (z, y) = O into G,(X, Y, H) = H 'ed9*l~,(X{H,YfH) = O, add a new constraint like, say: X2+Y + H = 1, and solve: all solutions of the homogenized system are finite; in the previous example, homogenized system is XY = H2, Y = O, X2+ Y2+H2 = 1, solution is X = +1, Y = H = O. See [AG93, Mor86].

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