Abstract
The μ-basis of a rational curve/surface is a new algebraic tool which plays an important role in connecting the rational parametric form and the implicit form of a rational curve/surface. However, most results for μ-bases are presented for proper rational parametrizations. In this paper we consider the μ-basis for an improper rational planar curve. Based on the known properties and new results, we design two new proper reparametrization algorithms using μ-basis. The inversion, degree of the induced rational map and implicitization formulas are also derived.
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