Analytic approach to intersection of all piecewise parametric rational cubic curves |
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| Affiliation: | 1. Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA;2. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia;3. Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana, Slovenia;4. Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Glagoljaška 8, Koper, Slovenia;5. Andrej Marušič Institute, University of Primorska, Muzejski trg 2, Koper, Slovenia |
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| Abstract: | Elimination theory is applied to develop an analytic approach to the intersection of any two piecewise parametric rational cubic curves. By splitting the general intersection problem into several simple cases, this algorithm reduces the intersection problem to the problem of finding the roots of a single polynomial in one variable of minimal degree. This technique is fast, automatic, efficient and robust. |
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