The moving line ideal basis of planar rational curves. (English) Zbl 0908.68174
Summary: This paper shows that the ideal of any degree n planar rational curve can be generated by two polynomials that are each linear in \(x,y\) and degree \(n_{1}\) and \(n_{2}\) \((\geq n_{1})\) in \(t\), \(n_{1}+n_{2}= n.\) The value of \(n_{1}\) is fixed for a given rational curve, and serves to split all degree n curves into \(\lfloor n/2\rfloor+ 1\) equivalence classes. These classes bear on the determinantal form of the implicit equation of the rational curve.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
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