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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.
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Lamure et al. (1995) studied this question.
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